spatial decision support systems for large arc routing...

Spatial Decision Support Systems

for Large Arc Routing Problems

Peter Bernard Keenan BComm MMangtSc

Dissertation presented to the Department of Management Information

Systems, Faculty of Commerce, University College Dublin, in partial

fulfilment of the requirements of the degree of Doctor of Philosophy.

June 2001

Supervisor: Professor H. C. Harrison

This dissertation is dedicated to my parents, for their encouragement and

support from the earliest days of my education.

i

Acknowledgements

I would like to express my appreciation to my supervisor, Professor

Harold Harrison for his involvement from the inception to the completion

of this dissertation. I would also like to thank my colleagues in the MIS

Department, especially Dr Cathal Brugha, for their support and

encouragement. Recognition is also due to everyone in UCD and

University Software Systems who has worked with me on arc routing

applications over the years.

ii

Abstract

The transport sector is a vital component of business operations and is of

considerable economic importance in modern economies. Better decision

making in this sector can make a significant contribution to business

operations. Information technology can greatly facilitate decision making,

especially in the form of Decision Support Systems (DSS). Transport

problems generally, and routing problems in particular, represent an

important area of DSS application. Within the routing field, most work

has centred on node routing problems; with much less attention paid to

arc routing problems. This dissertation reviews developments in DSS for

routing problems generally, and discusses in detail the design issues for a

DSS for large arc routing problems. This class of problem is especially

relevant for arc routing applications on rural road networks in Ireland.

Geographic Information Systems (GIS) technology is identified as

providing the means to enhance routing DSS. An extensive review is

provided of the GIS field and its relationship to other information

systems. This is followed by a comprehensive overview of the relationship

between routing and GIS. This analysis suggests that the integration of

GIS with routing models can allow the development of a Spatial Decision

Support System (SDSS) to provide superior decision support for this class

of problem.

The specific issues of building a GIS based DSS for large arc time

capacitated routing problems are discussed. Existing arc routing lower

bound procedures are modified for the time-capacitated problem. Three

potential heuristic modelling approaches for this problem are identified;

one approach was rejected as unpromising. The other two heuristics are

extensively tested against the modified lower bounds for the problem and

are evaluated from the point of view of probable user acceptability. This

work indicated that these heuristics could form the basis of an effective

DSS for this class of problem.

iii

Contents

Acknowledgements............................................................................. i

List of Tables .................................................................................... ix

List of Figures .................................................................................. xi

Glossary .......................................................................................... xiv

CHAPTER 1 : INTRODUCTION ............................................................. 1

1.1 Introduction................................................................................. 1

1.1.1 Preface.................................................................................................................... 1

1.1.2 Information Technology........................................................................................ 1

1.1.3 Growth of Information Systems (IS) .................................................................... 3

1.2 Decision Support Systems .......................................................... 4

1.2.1 Decision Structure................................................................................................. 4

1.1.2 Definitions of DSS................................................................................................. 6

1.1.3 The DSS field ...................................................................................................... 11

1.1.4 Contributions of DSS to decision-making ......................................................... 13

1.3 DSS Technology......................................................................... 14

1.3.1 Building DSS ...................................................................................................... 14

1.3.2 DSS generator approach..................................................................................... 15

1.3.3 ROMC approach.................................................................................................. 17

1.3.4 Current DSS technology ..................................................................................... 17

1.4 The nature of this research in DSS.......................................... 19

1.4.1 The current state of DSS..................................................................................... 19

1.4.2 The structure of this dissertation ....................................................................... 19

CHAPTER 2 : DECISION SUPPORT FOR ROUTING PROBLEMS

..................................................................................................................... 21

2.1 Routing DSS .............................................................................. 21

2.1.1 The nature of routing problems.......................................................................... 21

2.1.2 Suitability of routing problems for DSS ............................................................ 22

2.1.3 Early routing Software ....................................................................................... 23

2.2 Traditional Vehicle Routing DSS............................................. 26

2.2.1 Requirement for user interaction........................................................................ 26

2.2.2 The use of graphics in routing systems .............................................................. 27

iv

1.3 Impact of DSS Developments on Routing DSS ....................... 30

1.1.1 DSS developments............................................................................................... 30

1.1.2 Artificial Intelligence .......................................................................................... 31

1.1.3 User Defined algorithms..................................................................................... 32

1.1.4 Visual Interactive techniques ............................................................................. 33

1.4 Arc Routing Systems................................................................. 34

1.4.1 Characteristics of Arc Routing DSS................................................................... 34

1.4.2 Specific arc routing applications........................................................................ 35

1.4.3 Comprehensive arc routing software packages.................................................. 36

1.5 The Future of Routing DSS ...................................................... 39

1.5.1 Trends in Routing DSS....................................................................................... 39

1.1.2 Geographic Information Systems ....................................................................... 39

CHAPTER 3 : GEOGRAPHIC INFORMATION SYSTEMS.............. 41

3.1 Geographic Information Systems (GIS)................................... 41

3.1.1 Development of GIS Technology......................................................................... 41

1.1.2 GIS Data.............................................................................................................. 42

1.2 GIS Software ............................................................................. 44

1.2.1 Current developments in GIS software .............................................................. 44

1.2.2 Components of GIS.............................................................................................. 45

1.3 GIS and DSS.............................................................................. 47

1.3.1 Relationship between GIS and DSS research.................................................... 47

1.3.2 Is a GIS a DSS?................................................................................................... 49

1.4 Spatial Decision Support Systems ........................................... 52

1.4.1 SDSS decision makers ........................................................................................ 52

1.4.2 GIS as a DSS Generator ..................................................................................... 55

1.4.3 Extending GIS to a broader community ............................................................ 57

1.5 Current Spatial Decision Support Systems Technology ......... 60

1.5.1 Suitability of GIS Software for building DSS................................................... 60

1.5.2 Commercial GIS software................................................................................... 64

1.5.3 Future directions ................................................................................................. 66

CHAPTER 4 : MODELLING ROUTING PROBLEMS IN GIS ......... 67

4.1 Introduction .............................................................................. 67

4.1.1 GIS and routing .................................................................................................. 67

4.1.2 Spatial Decision Support Systems for routing .................................................. 68

v

4.2 Information Requirements for Routing ................................... 69

4.2.1 Categories of routing data .................................................................................. 69

4.2.2 Interdependence of routing parameters ............................................................. 73

4.2.3 Spatial interactions in routing problems........................................................... 78

4.3 The Role of GIS in Supporting Routing Problems................... 83

4.3.1 Routing problems supported by traditional DSS.............................................. 83

4.3.2 Routing problems requiring GIS support .......................................................... 85

4.3.3 Spatially complex routing problems .................................................................. 86

4.4 Implementing routing SDSS .................................................... 88

4.4.1 Data requirements for routing system implementation .................................... 88

4.4.2 Using GIS data in routing DSS ......................................................................... 89

4.5 The future of GIS and routing.................................................. 92

4.5.1 Types of Routing Software.................................................................................. 92

4.5.2 The use of GIS for routing .................................................................................. 93

CHAPTER 5 : ARC ROUTING PROBLEMS ....................................... 96

5.1 Routing Problems...................................................................... 96

5.1.1 Background ......................................................................................................... 96

5.1.2 Types of routing problem .................................................................................... 96

5.1.3 Problem complexity ............................................................................................. 98

5.2 Arc Routing Problems ............................................................. 100

5.2.1 The Chinese Postman Problem......................................................................... 100

5.2.2 The Rural Postman Problem ............................................................................ 102

5.2.3 Other Uncapacitated Arc Problems.................................................................. 103

5.3 The Capacitated Arc Routing Problem (CARP)..................... 104

5.3.1 Definition of CARP............................................................................................ 104

5.3.2 Representing Arc Routing problems as a TSP................................................. 105

5.4 Linear programming formulations of CARP ......................... 106

5.4.1 Golden and Wong formulation ......................................................................... 106

5.4.2 Belenguer and Benavent formulation .............................................................. 108

5.5 Lower bounds for the CARP ................................................... 109

5.5.1 Early graph theory bounds ............................................................................... 109

5.5.2 Node Duplication Lower Bound ....................................................................... 110

5.5.3 Bound LB1......................................................................................................... 114

5.5.4 Bounds exploiting cuts away from the depot ................................................... 117

5.5.5 Cutting Plane Bound ........................................................................................ 125

vi

CHAPTER 6 : SOLUTIONS FOR THE CARP................................... 126

6.1 Heuristic Solutions for the Capacitated Arc Routing Problem

........................................................................................................ 126

6.1.1 Single Pass heuristics ....................................................................................... 126

6.1.2 Route-first cluster-second heuristics ................................................................ 128

6.1.3 Cluster-first route-second heuristics ................................................................ 129

6.1.4 New approaches to CARP ................................................................................. 130

6.1.5 Real world network representation issues ....................................................... 131

6.2 Branching approaches to CARP............................................. 133

6.2.1 Branching techniques ....................................................................................... 133

6.2.2 The Tour Construction Algorithm.................................................................... 134

6.2.3 Practical feasibility of branch and bound algorithm...................................... 140

CHAPTER 7 : CARP ON IRISH RURAL NETWORKS ................... 142

7.1 Postal delivery of rural networks ........................................... 142

7.1.1 Irish Rural Road Networks .............................................................................. 142

7.1.2 Rural Postal Delivery........................................................................................ 146

7.2 CARP on large sparse networks............................................. 147

7.2.1 The Large Sparse Capacitated Arc Routing Problem (LSCARP)................... 147

7.2.2 Time Capacitated Arc Routing Problems ........................................................ 149

7.3 Modified bounds for LSCARP................................................. 150

7.3.1 Lower bounds for the LSCARP......................................................................... 150

7.3.2 Depot based lower Bounds for TCARP ............................................................ 150

7.3.3 Bounds for TCARP based on the entire graph................................................. 152

7.3.4 Modification to LB2 cutset strategy.................................................................. 154

7.4 Computational Results for TLB2 ........................................... 155

7.4.1 Example of new cutset strategy......................................................................... 155

7.4.2 Simple Computational Example for TCARP................................................... 157

7.5 Comparison of lower bound and optimal results................... 161

7.5.1 Time based branch and bound procedure........................................................ 161

7.5.2 Computational experiments.............................................................................. 164

7.5.3 Implications of computational results ............................................................. 166

CHAPTER 8 : SOLUTION PROCEDURES FOR TCARP............... 167

8.1 Introduction............................................................................. 167

8.1.1 Solutions for TCARP......................................................................................... 167

vii

8.1.2 Algorithm requirements for the LSCARP ........................................................ 167

8.2 Heuristic approaches .............................................................. 168

8.2.1 CARP solution techniques................................................................................. 168

8.2.2 Route-First Cluster-Second approach .............................................................. 169

8.2.3 Cluster-First Route-Second Approaches .......................................................... 169

8.3 Route first, cluster second algorithm..................................... 170

8.3.1 Tour construction .............................................................................................. 170

8.3.2 Computational example for the RFCS algorithm............................................ 171

8.3.3 Evaluation of the RFCS algorithm .................................................................. 173

8.4 Tree based Approach to clustering for the LSCARP............ 173

8.4.1 Clustering on rural road networks................................................................... 173

8.4.2 The shortest path tree clustering algorithm..................................................... 174

8.4.3 Computational example of tree clustering algorithm...................................... 175

8.4.4 Evaluation of shortest path tree clustering approach ..................................... 177

8.5 Insertion heuristic for clustering for the LSCARP................ 178

8.5.1 Justification for using insertion procedure...................................................... 178

8.5.2 Operation of the algorithm ............................................................................... 179

8.5.3 Computational example .................................................................................... 180

8.5.4 Evaluation of Insertion heuristic ..................................................................... 182

8.6 Refinements to heuristic algorithms...................................... 182

8.6.1 Network simplification ..................................................................................... 182

8.6.2 Route refinement ............................................................................................... 184

CHAPTER 9 : DECISION SUPPORT FOR THE LSCARP ON IRISH

ROAD NETWORKS. .............................................................................. 185

9.1 Specific DSS Characteristics .................................................. 185

9.1.1 Network characteristics .................................................................................... 185

9.1.2 Management Requirements .............................................................................. 185

9.1.3 Address structure .............................................................................................. 185

9.2 ROMC approach...................................................................... 188

9.2.1 Principles of the ROMC approach.................................................................... 188

9.2.2 Representations ................................................................................................. 188

9.2.3 Operations ......................................................................................................... 190

9.2.4 Memory Aids...................................................................................................... 191

9.2.5 Controls.............................................................................................................. 191

9.3 TransCAD GIS ........................................................................ 192

viii

9.3.1 TransCAD Software characteristics................................................................. 192

9.3.2 GDK ................................................................................................................... 193

9.3.3 User Interface Features..................................................................................... 194

9.4 Initial Computational Experiments with routing algorithms

........................................................................................................ 195

9.4.1 Early testing of RFCS and Tree based approaches ......................................... 195

9.4.2 Assessment of initial testing ............................................................................. 195

9.5 Final Computational Experiments with routing algorithms 196

9.5.1 Data sets used.................................................................................................... 196

9.5.2 Case One ............................................................................................................ 197

9.5.3 Case One solutions ............................................................................................ 199

9.5.4 Case Two............................................................................................................ 200

9.5.5 Case Three ......................................................................................................... 202

9.6 Conclusion ............................................................................... 205

9.6.1 Decision Support for Routing ........................................................................... 205

9.6.2 Modelling issues ................................................................................................ 205

9.6.3 Further Research on Modelling Techniques .................................................... 206

9.6.4 Developments in SDSS ..................................................................................... 208

References...................................................................................... 209

APPENDIX A ...........................................................................................A1

A.1.1 Case One Solution 1 ...........................................................................................A1

A.1.2 : Case One Solution 2 .........................................................................................A2







A.1.9 Case One Solution 9 ...........................................................................................A9

A.1.10 : Case One Solution ........................................................................................A10

APPENDIX B ..........................................................................................A11

B.1.1 : Case Two Solution..........................................................................................A11

APPENDIX C ..........................................................................................A12

C.1.1 : Case Three Solution A12

ix

List of Tables

Table 1-1 : Decision Structure (McCosh and Scott Morton, 1978,Page 8) 6

Table 1-2 : Alter’s Taxonomy of DSS (Alter, 1980) 9

Table 1-3 : DSS design guidelines (Barbosa and Hirko, 1980) 10

Table 2-1: Features of GeoRoute (Georoute) 38

Table 3-1 : Data operations in GIS 45

Table 3-2 : Computerised Support for Decision-making (adapted from

Turban, (1995 Page 19) 53

Table 3-3 : DSS Generator Features 56

Table 3-4 : Contextual Information in SDSS (Keenan, 1998b) 59

Table 3-5 : Software integration techniques for building SDSS (Keenan,

1998c) 63

Table 4-1 : Main Characteristics of Routing Systems (Keenan, 1998a) 69

Table 4-2 : Constraints in Vehicle Routing Problems (adapted from Bodin

and Golden) (1981) 70

Table 4-3 : GPS applications in routing 74

Table 4-4 : Types of Location Data 79

Table 4-5 : Types of Path Data 80

Table 4-6 : Example of an agricultural routing SDSS 91

Table 4-7 : Support Requirements of Routing Problems 93

Table 5-1 : Classification in Vehicle Routing and Scheduling (Bodin and

Golden, 1981). 97

Table 5-2 : Summary of LB2 Algorithm 123

Table 6-1 : Heuristic performance (adapted from Assad and Golden(1995))

128

Table 6-2 : Turn Penalties (Bodin and Kursh, 1979) 132

Table 6-3 : Outline Code of the Tour Construction Algorithm: 140

Table 7-1 : The sets at each iteration using the original LB2 procedure156

Table 7-2 : The sets at each iteration using the modified cutset selection

157

Table 7-3 : TLB2 example 158

Table 7-4 : Summary of Time based bound 160

x

Table 7-5 : Computational results for 35 arc network 164

Table 8-1 : Pseudo code for RFCS approach 171

Table 8-2 : Infeasible route for RFCS procedure 171

Table 8-3 : Routes generated by RFCS algorithm 173

Table 8-4 : Pseudo code of tree clustering algorithm 175

Table 8-5 : Routes from Tree Clustering approach 176

Table 8-6 : Pseudo code for insertion algorithm 179

Table 8-7 : Insertion heuristic route 182

Table 9-1 : Examples of GIS operations to facilitate use of townland

structure 187

Table 9-2 : Summary of ROMC features 191

Table 9-3 : Initial computational results 195

Table 9-4 : Region data 197

Table 9-5 : Case One - total time summary 199

Table 9-6 : Case Two - total time summary 202

Table 9-7 : Case Three - total time summary 204

xi

List of Figures

Figure 1-1 : Components of a DSS (Sprague, 1980) 7

Figure 1-2 : DSS Technology Levels (Sprague 1980) 15

Figure 2-1 : Use of barriers to prevent routes crossing geographic features

24

Figure 2-2: Graphic display of ROVER software 29

Figure 2-3 : GeoRoute interface 37

Figure 3-1 : Use of spatial techniques to identify neighbouring regions 46

Figure 3-2 : Example of GIS use to identify street segments close to a

route (Keenan, 1998c) 47

Figure 3-3 : Building a SDSS by integrating models with GIS 57

Figure 4-1 : Area served from bus stop will include neighbouring streets.

76

Figure 4-2 : The total service area is mapped on to a limited number of

locations. 77

Figure 4-3 : Network constrained route avoiding passing within a certain

distance of a point location. 81

Figure 4-4 : Patrol area around irregular boundary of sensitive

installation 82

Figure 5-1 : The Königsberg bridge problem (Euler, 1736) 100

Figure 5-2 : Graph with four odd points (C,D,E,F) and addition of

redundant arcs to make all nodes even (Kwan, 1962) 101

Figure 5-3 : Introducing new nodes for each original arc (Pearn, Assad

and Golden, 1987) 105

Figure 5-4 : Illegal and legal subtours (Golden and Wong(1981)) 108

Figure 5-5 : The Original Graph 111

Figure 5-6 : The Transformed Graph 112

Figure 5-7 : Initial NDLB MCPM on the 9-arc example 113

Figure 5-8 : Optimal Matching of Hs 116

Figure 5-9 : The Cutset from LB1 118

Figure 5-10 : The second cut 120

xii

Figure 6-1 : Block Design for snow ploughing (Gendreau, Laporte et al.,

1997) 132

Figure 6-2 : Network enhancement by addition of penalties at junctions

(Roy and Rousseau, 1989) 133

Figure 6-3 : Postman paths on the 9-arc example 136

Figure 6-4 : Branch and Bound Sub-Problems 138

Figure 6-5 : Fathomed Sub-Problems and Optimal Solution, Sub-Problem

G 138

Figure 7-1 : Network with arc-node ratio of 2 143

Figure 7-2 : Network with high arc/node ratio 143

Figure 7-3 : Extract from Irish Rural road network 144

Figure 7-4 : Extract from Dublin City main road network 145

Figure 7-5 : Extract from New York City road network 146

Figure 7-6 : Multiple nodes in U′ at each iteration 154

Figure 7-7 : Original LB2 cutsets 155

Figure 7-8 : Selecting Nodes one at a time, in increasing order of

connectivity 156

Figure 7-9 : 35 arc network 163

Figure 7-10 : Maximum TLB2 cut for vehicle capacity of 35 165

Figure 8-1 : Simplified network for heuristic examples 172

Figure 8-2 : Treelike structure of rural road network 174

Figure 8-3 : Routes derived from clusters 177

Figure 8-4 : Seed Arcs for Insertion heuristic 180

Figure 8-5 : Routes 1&2 using insertion heuristic 181

Figure 8-6 : Multiple arcs in a single road section 183

Figure 8-7 : Complex Cul-de-sac road section 183

Figure 9-1 : Overlay of townland boundaries and road network 187

Figure 9-2 : Removal of irrelevant detail in interface and algorithmic

representations 188

Figure 9-3 : Representation of arc attributes in different colours and line

weights 189

Figure 9-4 : Only sections of road visited more than once are shown 190

xiii

Figure 9-5 : TransCAD interface with TransCAD arc routing data 193

Figure 9-6 : Case One - road network with population density 198

Figure 9-7 : Case One - reduced network 198

Figure 9-8 : Case Two - road network and reduced network 201

Figure 9-9 : Case Three - road network and reduced network 203

xiv

Glossary

Arc Routing Problem An OR/MS problem concerned with visiting a

sequence of arcs (edges) in a graph.

Cluster-First Route-Second Approach (CFRS) Routing problem

where the the allocation of arcs or nodes to vehicles is established prior to

the routing sequence.

Decision Support System (DSS) A computer-based system consisting

of an interface, a database and a problem processing system whose

purpose is to support decision-making activities.

DSS Generator - Computer software that provides tools and capabilities

that help a developer quickly and easily build a specific DSS.

Capacitated Arc Routing Problem An OR/MS problem concerned with

a vehicle of limited capacity visiting a sequence of arcs (edges) in a graph.

Chinese Postman Problem (CPP) An arc routing problem where the

objective is to visit each arc at least once.

Geographic Information System (GIS) A computer-based system for

the storage and processing of spatial information.

Global Positioning System (GPS) A satellite based system for

establishing the location of a point on the Earth's surface.

Large Sparse Capacitated Arc Routing Problem (LSCARP) The arc

routing problem on large sparse networks that is the specific problem

discussed in this dissertation.

Minimum Cost Perfect Matching (MCPM) The minimum set of non

adjacent edges which joins all of the nodes in a graph.

ROMC (Representation, Operations, Memory Aids, Control)

Design Approach A systematic user-oriented approach for developing

large-scale DSS.

xv

Route-First Cluster-Second Approach (RFCS) Routing problem

where the routing sequence is established prior to the allocation of arcs or

nodes to vehicles.

Rural Postman Problem (RPP) is an extension of the CPP where only

a subset of arcs (edges) from the network must be traversed.

Spatial Decision Support System (SDSS) Decision Support System

for processing spatial information based on GIS technology.

Time Capacitated Arc Routing Problem (TCARP) Arc routing

problem where the vehicles routes are limited to a maximum time.

TransCAD The GIS software designed for working with transportation

problems that is used for the prototype systems discussed in this

disseratation.

Spatial Decision Support Systems for Large Arc Routing Problems

1

Chapter 1 : Introduction

1.1 Introduction

1.1.1 Preface

The arrival of digital computer technology has led to rapid and continuing

change in many aspects of human activity, especially that of business. As

with other technological innovations, the use of Information Technology

(IT) has allowed business to perform its operations more effectively.

However, the greatest contribution of the introduction of IT has been in

the improved planning of business operations. To allow this improvement

to take place, a variety of techniques have been developed to better

exploit the capacity of IT. In some cases, these computer-based

approaches have been quite different from the manual methods

previously employed. As research continues into how best to approach

problem solving using IT, new and distinctive computer based techniques

have been introduced. This research led to investigation into the

reconciliation of the problem representations used by the human decision-

makers with those used by the digital computer. This dissertation reports

one such piece of research. It looks at how computer technology and

computerised techniques can be synthesised with human problem solving

abilities to provide a superior approach to the management of a specific

problem, namely that of Decision Support Systems for large arc routing

problems.

1.1.2 Information Technology

Digital computer technology was introduced in the 1940s, its

development having been greatly accelerated by the needs of the Second

World War. Early computers were extremely limited in power by modern

standards, but they did enormously increase the rate at which


2

mathematical computation could take place, hence the name computer.

These machines were used initially for quantitative applications where

fast computation was essential, for instance code-breaking or ballistic

calculations. Early civilian applications were also essentially numerical

in nature and included payroll processing and census enumeration. The

introduction of these machines, capable of fast computation, led to the

development of techniques that exploited this ability. In particular

computer technology enabled the emergence of the field known as

Operational Research in the United Kingdom and Operations Research or

Management Science (OR/MS) in the United States. The field made a

great contribution by developing solution techniques that exploited the

rapidly growing power of computers. This allowed solutions to be derived

in a reasonable time, in circumstances where manual computation was

infeasible.

As computer technology developed, computational performance increased

exponentially. This was accompanied by enormous increases in the

storage capacity of computers. These developments meant that computers

became convenient ways to store and retrieve large amounts of data. The

potential usefulness of IT was greatly increased when this enhanced

storage capacity was allied to the rapidly accelerating computational

power of the machines. The full exploitation of these developments in

computer hardware required the design of appropriate computer

languages and new computer science techniques.

As time progressed, the peripheral devices associated with computers also

underwent rapid development. New input and output devices allowed

greater ease of use, for example, terminals, printers, plotters, keyboards,

etc. These developments became possible because the rapid increase in

computer speed allowed more resources be devoted to managing

input/output and achieved greater user-friendliness. This trend

culminated with the introduction of the personal computer (PC), which

offered colour screens and new input devices such as the mouse.


3

Computer technology has become very widely used and familiar to

business managers and, with the use of appropriate software, and now

plays an important role in management.

1.1.3 Growth of Information Systems (IS)

The rapid advancement in IT hardware capabilities provided the

potential for new IT applications, however this potential could be

released only by the use of appropriate software. Early mainstream

business applications of computer technology, such as payroll processing,

were known as Transaction Processing Systems (TPS). These applications

were characterised by the automation of repetitive clerical tasks and

exploited the computational abilities of the computer. These early

applications allowed cost savings in the clerical departments in which

they were implemented, but had no direct implications for management

planning in other areas. As computer power increased, it became

apparent that some information useful to management could be produced.

For example, summary reports of sales or purchasing could be derived

from the computerisation of these functions. This led to the introduction

of Management Information Systems (MIS) which provided routine

reports in standard formats for management use. However, not all

functional areas utilised the type of routine procedures embodied in these

systems. MIS reports could only be altered by programmers and were

therefore of little use for ad-hoc or unexpected decisions where

information needs could not be predicted far in advance.

In parallel with these developments, the growing computational power of

IT was also being exploited for mathematical modelling applications.

These techniques address problems such as the optimal allocation of

resources in production planning (linear programming), and inventory

management (economic order quantity). These modelling applications

were capable of addressing management problems, but could only be used

easily by specialists. Early computer technology required punched card

data input and had very limited facilities for presenting output, making it


4

extremely difficult for managers to operate these modelling applications

themselves. The limitations of the technology not only made computer

use inconvenient, but also imposed restricted computer-orientated

problem representations on the process. These problem representations

differed greatly from that familiar to mainstream managers. The impact

of IT on business has been hindered by this division between managers

with an understanding of the business problems and the technically

literate specialists who could best employ computer technology.

With the increase in IT capabilities, researchers began to propose a more

comprehensive use of the technology to support management needs. By

the early 1970s, obvious progress had been made in the application of

technology and in the use of problem solving techniques. A variety of in-

formation systems were proposed to meet the diverse needs of users

(Mentzas, 1994). One of the most important types of system introduced

was the Decision Support System (DSS), which focussed on better man-

agement performance rather than on the replacement of clerical labour.

1.2 Decision Support Systems

1.2.1 Decision Structure

Much of the early work on the concept of a DSS took place at the

Massachusetts Institute of Technology (Gorry and Scott-Morton, 1971;

Little, 1971). Gorry and Scott-Morton built on a management framework

introduced by Simon (1977), that identified decision structure as critical

to the process of decision-making. Gorry and Scott-Morton saw the

identification of the degree of decision structure as the starting point for

the design of an appropriate information system. At one end of a

spectrum were structured decisions. These were repetitive and routine

and so were sometimes called programmed decisions. For structured

decisions, a definite procedure exists to solve the problem and that can be

applied routinely to any new decision. By contrast, unstructured or

unprogrammed decisions were novel and had no clear-cut procedure to


5

solve them. Instead, a general adaptive strategy was used to solve such

problems. While many structured activities exist at the operational level

in an organisation, they may also be found at the tactical and strategic

level of decision-making. Unstructured decisions may also be found at all

levels of the organisation, although on balance long term strategic

decisions are more likely to be unstructured than those at lower levels of

the organisation

Much of the early contribution by the use of IT was made in structured

operational problems. However, many important problems are semi-

structured and this class of problem requires a system that provides for

easy interaction between man and machine. Examples include DSS

applications that aim to assist (support) the solving of problems using

both human and computer techniques.

Discussion of structure is complicated by the fact that many problems are

structured in principle, but are addressed in practice using management

judgement. A major reason for manual intervention in modelling occurs

where the problem is so complex as to be computationally infeasible.

Many problems are inherently structured, but are so complex that with-

out IT only simplified problem representations could be used. The advent

of new modelling techniques, coupled with the rapidly increasing power of

computers, meant that structure can be directly modelled for an

increasing range of problems. One example is linear programming, which

can be used for decision-making in fields that previously required great

management experience. Likewise, inventory models can model the struc-

ture inherent in reordering decisions, which previously required

management expertise (McCosh and Scott Morton, 1978,Page 10)

In addition to introducing three levels of decision structure (Table 1-1),

Simon proposed a structure for problem solving with three main phases.

! Intelligence : searching the environment

! Design : the development of possible courses of action

! Choice : selecting a particular course of action


6

In a given problem, some or all of these phases may be structured.

Problems may have one relatively structured phase with the other phases

much less structured. For instance, the environmental conditions may be

known, but there may not be any clarity in the courses of action available

to solve the problem. The choice phase may be totally structured, for

example if monetary value is used, but the previous stages may be more

ambiguous. It is desirable that a DSS support all phases of decision-

making.

1.2.2 Definitions of DSS

DSS became feasible in the 1970s following developments in computer

technology. As input/output devices improved, machines were introduced

which used a keyboard for input and which employed graphical terminals

capable of displaying computer output. This meant that a manager could

Table 1-1 : Decision Structure

(McCosh and Scott Morton, 1978,Page 8)

Operationalcontrol

Managementcontrol

StrategicPlanning

Structured Order entry

Accounts

receivable

Inventory control

Variance analysis

Short-term

forecasting

Tanker fleet structure

Factory location

Warehouse location

Unstructured Short term cash

management

Job-shop

scheduling

Advertising

selection

Budget

preparation

Sales planning

Production

planning

Price setting

New product planning

Mergers and

acquisitions


7

interact directly with the computer. The development of improved

computer storage and retrieval technology meant that managers could be

given access through such a terminal to large amounts of data. Increased

user control meant that managers could extract only that subset of data

of interest at any given point in time. When DSS were first proposed,

computer performance had advanced to the point where sophisticated

models could be solved in real time. The early definitions of DSS reflected

these aspects of technology in that they tended to define DSS as flexible

systems combining database and model components aimed at less

structured decisions (Sprague, 1980; Sprague and Carlson, 1982). These

modelling and database components are under the control of the user

through an interface or dialogue system (Figure 1-1).

Database Model base

DBMS MBMS

DGMS

The DSS

Task Environment

User

Figure 1-1 : Components of a DSS (Sprague, 1980)


8

The dialogue component of this system itself consists of three

components.

! The Database Management System (DBMS) allows easy

access to the data and the ability to alter and reorganise the

contents of the database.

! The Modelbase Management System (MBMS) allows the

user access to the models and provides the ability to intervene

in the modelling process.

! The Dialogue Generation Management System allows the

user control the presentation of information and the interaction

with the system.

Other authors have proposed broadly similar generic descriptions of DSS,

for example Bonczek, Holsapple and Whinston (1981). They identified a

DSS as comprising three parts, a definition that is broadly similar to that

of Sprague above.

! The Language System is the means by which the user

interacts with the DSS and is analogous to the user interface.

! The Knowledge System provides system access to domain

relevant information other than that in the mind of the user.

This is generally a DBMS but these authors use a deliberately

broad definition to include other knowledge representations

such as the rule base in an expert system.

! The Problem-processing System can interpret the knowledge

used in the knowledge system. This would include traditional

models but also techniques such as inference in an expert

system.


9

The modelling (problem-processing) component of DSS was able to exploit

the many techniques developed in the OR/MS and financial fields.

However, the nature of the definition of DSS allows varying degrees of

combination of database and modelling techniques. There is a lack of

agreement on what constitutes a DSS; some systems regarded as DSS by

one author might be excluded by another. Alter (1980) produced an

influential taxonomy of DSS that proposed seven subdivisions ranging

from data driven systems to model driven systems (Table 1-2). While

most DSS definitions would include categories at the centre of Alter’s

classification, many would exclude those at its extremes. For example,

File Drawer systems do not contain any models and therefore would be

excluded by Sprague’s definition. Similarly Suggestion systems could be

said to support decisions rather than make them and so could be excluded

from a definition of DSS.

The argument of what constitutes a DSS is an ongoing one. Keen (1986)

noted that there was a tendency for any system that contributes to

decision-making to be called a DSS. Stabell (1986) identified four schools

Table 1-2 : Alter’s Taxonomy of DSS (Alter, 1980)

System type Example

File Drawer Query Systems (MIS)

Airline Reservation

Data Analysis Database Management Systems

Analysis Information Systems Spreadsheets

Accounting Models Monetary Simulations

Representational Models Simulation

Optimisation Models Linear Programming

Suggestion Models AI Expert Systems


10

of DSS thought; these include the influences of modelling and decision

analysis. Silver (1991) proposed a classification of DSS that emphasised

the degree of guidance provided. Against this background of disagreement

on the definition of DSS we see many “decision support systems” that are

essentially OR/MS models with minimal database or interface features.

Other systems are little more than DBMS with some retrieval facilities

and little modelling capability. A recent comprehensive review of DSS

applications identified a large number of articles with the descriptor

“decision support systems” (Eom, Lee, Kim and Somarajan, 1998).

However, less than one-fifth of these articles were actually included in

the survey, as most systems did not meet their definition of a DSS.

In looking at the potential for incorporating OR/MS techniques in a DSS,

Barbosa and Hirko (1980) put forward a succinct set of guidelines for the

design of OR/MS based DSS (Table 1-3). Many systems described as being

DSS by their authors do not meet the requirements of these guidelines.

Table 1-3 : DSS design guidelines (Barbosa and Hirko, 1980)

DSSfeature

Design Guideline

Interface No unnecessary distractions, user should not have to laboriously enter control

parameters

Control parameters should be expressed in terms with which the user is

familiar

Control System should support a spectrum of control, e.g. manual and fully automated

operation

User should be able to provide information as required

Flexibility Algorithmic and manual operations should be interchangeable

Feedback User should be aware of the state of the process at all times

User feedback on usability should be used to improve the system


11

1.2.3 The DSS field

In the twenty-five years since the concept of DSS was first introduced, the

importance of DSS research has been widely recognised. For example, one

survey showed that more than one-third of IS researchers were working

in the DSS area (Teng and Galletta, 1990). The same survey found that

DSS was the topic that the most researchers felt was deserving of greater

research attention, with almost a quarter of researchers surveyed holding

this view. Another recent survey (Lee, Gosain and Im, 1999) suggested

that DSS was frequently discussed in academic journals, but was less

often the subject of attention in practitioner publications.

Several surveys have attempted to identify the nature of the DSS field.

Reviews of the field tend to indicate the use of DSS at operational levels,

while seeing the need for further development in applications directed at

higher levels of management. In one of the few contributions by an Irish

based author, Er (1988) notes the widespread use of DSS for short term

decisions and the less frequent use of DSS for longer term decision-

making at higher levels in the organisation. In a bibliographic survey of

DSS applications over a sixteen-year period (Eom and Lee, 1990), OR/MS

applications were to the fore, primarily in the operations management

and routing areas. Later work by the same authors (Eom, Lee, Somarajan

and Kim, 1997; Eom, Lee et al., 1998) found that OR/MS models were

still dominant, although other fields such as artificial intelligence were

making an impact. It is notable that mainstream OR/MS publications

represented four of the top five journals identified as being important for

DSS applications (Interfaces, European Journal of Operational Research,

Operations Research, and Computers and Operations Research).

Other work has reflected this distribution of DSS output between OR/MS

and IS journals (Abraham and Wankel, 1995). However, it is probable

that many applications in these publications, although described as DSS,

were discarded by this survey because they were not comprehensive

systems. Nevertheless, the close relationship between OR/MS and DSS is


12

clear. In the past some in the OR/MS community have seen DSS as

merely a subset of OR/MS, for instance see the paper by Naylor (1982)

and the counter argument by Watson and Hill (1983). Other authors have

identified related classes of system, such as the decision insight systems

reviewed by Golden, Hevner and Power (1986). Many of these systems

would be regarded as DSS by other authors.

DSS therefore exploits the vast range of modelling approaches found in

OR/MS. However, in a DSS, the model is only one part of a system and

other disciplines are of relevance. One study (Eom, Lee and Kim, 1993)

identified psychology, artificial intelligence, OR/MS, computer science,

organisational sciences and functional management theory as being the

reference disciplines for DSS. This work looked at author cocitation as a

means of classifying DSS research. The authors found that distinct

groups of researchers existed, notable fields being those of group DSS,

multi-criteria decision-making, routing, database management and other

OR/MS applications. They also noted that other themes in DSS research,

such as model management, had little influence on the DSS applications

reviewed.

In the context of this dissertation, it is notable that transportation

applications are a recognised area of application of DSS. Many survey

and review articles of DSS mention the importance of and give examples

of this type of application. DSS textbooks frequently use transportation

applications as examples, for instance Sauder and Westerman (1993).

Sprague (1980) discusses the use of the Geodata Analysis and Display

System (GADS) which was used to build routing DSS. GADS employed

map display as an important component of decision support and can be

regarded as a form of Spatial DSS, this class of DSS is discussed further

in Section 3.4. In his review, Er (1988) notes the importance of

transportation applications. Analyses of the literature (Eom and Lee,

1990; Eom, Lee et al., 1993) have identified routing as the most

important area of DSS application in business. The authors of these


13

reviews suggest that the relative importance of routing DSS reflects the

nature of routing problems. They suggest that these are less suitable for

the expert systems approach used in other business applications and

indicate the importance of skilled user intervention for problem solving in

the routing field.

1.2.4 Contributions of DSS to decision-making

A DSS may contribute in various ways to improving decision-making

(Forgionne, 1999). DSS use may improve the process of making a

decision. This might occur where by reducing the time taken to make the

decision. The increasing speed of modern computers makes this an

obvious advantage. DSS use may improve the outcomes of the decision

process by leading to better decisions being made. This may result from

more information being brought to bear on the problem, with a

consequent improvement in the intelligence phase of the decision. The

language system (interface) used in the DSS may facilitate easier

assimilation of the information presented, for example if graphics are

used. This dissertation focuses on mapping information as a form of

graphic representation of particular importance arc routing problems.

The information storage and retrieval components of the DSS may

contribute to this improvement. DSS use may lead to consideration of

more courses of action, leading to improvements in the choice phase of the

decision. This might result from the reduced time needed to model each

alternative. Modern computer technology allows extensive what-if

analysis take place in a relatively short time. DSS may lead to an

improved assessment of the value of those courses of action examined,

this might arise through the computer modelling of more complex system

models rather than alternative overly simplified manual techniques.

DSS use can also lead to long term benefits. DSS is recognised as

providing user learning benefits, although not all systems fully exploit

this potential gain (Santana, 1995). DSS use can also assist organisations


14

by allowing the capture of additional information relating to the decision-

making process. If a common DSS is used by different decision-makers, it

can help spread common practice throughout the organisation and assist

in the spread of knowledge. However, this type of benefit may be difficult

to realise where individual decision-makers have greatly different

approaches to decision-making.

1.3 DSS Technology

1.3.1 Building DSS

The emergence of DSS as a concept was greatly influenced by changes in

technology. In the 1970s, computer technology had advanced to the point

where it was usable by non-IT professionals and where costs had declined

to the point where greater use of the technology had become cost effective.

This trend was enhanced by the introduction of PCs at the end of the

decade; this technology was given respectability with the introduction of

the IBM PC in 1981. There has been rapid progress in technology since

then, to the point where modern microcomputers are some five hundred

times as powerful as the original IBM PC. Modern machines are provided

with two hundred times as much electronic memory and perhaps one

thousand times as much disk storage space. Yet, the real price of modern

machines is about one quarter of the original IBM PC. Against this

background the cost of the technology has become less of a limitation and

the growth of DSS is now determined by the ability of designers to

propose systems of genuine benefit to managers.

When the concept of DSS was first introduced, it had distinctive

characteristics differentiating it from earlier types of information system.

These earlier systems, such as MIS, were built by teams of IT

professionals, in departments removed from the mainstream

management in the organisation. Large MIS projects used a formal

process, such as the Systems Development Lifecycle (SDLC). These

systems were developed from complex specifications and were not easily


15

changed after completion. DSS, on the other hand, required a much closer

association with the decision-maker. Consequently, there was a greater

need for user input into the system design. The definition of DSS also

required that the user had good control over the operation of the system,

which raised the possibility of the user being able to alter the system.

Indeed, with the greater ease of use brought about by improvements in

IT, in some cases the user could develop the DSS his or herself.

1.3.2 DSS generator approach

An early comprehensive framework for the development of DSS was

provided by Sprague (1980; Sprague and Carlson, 1982). In Sprague's

framework, a DSS may be built from individual software components

called tools that were then combined to form a DSS. These could include

programming languages, programming libraries and small specialised

applications. At a higher level in Sprague's framework are DSS

generators, from which a specific DSS can be quickly built. Generators

might be built from lower level tools (Figure 1-2). Sprague envisioned

DSSGenerator

Specific Applications

DSS Tools

DSSGenerator

Figure 1-2 : DSS Technology Levels (Sprague 1980)


16

that different specific DSS applications would require different

combinations of the generator and tools. Sprague used GADS (Grace,

1977), as an example of a DSS generator.

In building DSS, specific generators were designed for certain classes of

problem. In other situations general-purpose software such as

spreadsheets or DBMS packages have been regarded as generators. In

modern DBMS and spreadsheet software, the use of macro and

programming languages facilitates the creation of specific applications.

Different generators had varying strengths and weaknesses in terms of

their provision of the essential components of a DSS: an interface, a

database, and models. In the case of a spreadsheet, modelling is the basic

function of the software; various interface features such as graphs are

provided, but the database organisation is simplistic. DBMS software,

such as Access or Paradox, has good database support, provision for

interface design using forms, report and charts, but almost no modelling

support. In this case, the modelling support has to be added to the specific

DSS built from such a system. In Sprague’s framework, the DSS builder

could make use of tools, which provide some, lower level, data processing.

In software design these might include operations such as sorting or

searching, which although important algorithms in their own right, are

not of direct interest to the decision maker. The design focus is on the

outcomes, the decision, and not on the technological and modelling inputs

to the system.

Sprague’s framework has been widely accepted by DSS researchers and is

frequently used as a basis for discussion of DSS in textbooks (Mallach,

1994; Sauter, 1997; Marakas, 1998; Turban and Aronson, 1998).

Nevertheless not all authors find this framework useful, for example

Holsapple and Whinston (1996) regard the distinction between tools and

a DSS generator as unclear. However, we believe that this framework is

useful for the purposes of this dissertation and so will form the basis of

the discussion on building arc routing DSS in Chapter 9.


17

1.3.3 ROMC approach

Sprague and Carlson (1982) proposed a framework for identifying the

features needed in a DSS. This is the Representations, Operations,

Memory Aids and Controls (ROMC) approach.

! Representations allow the decision-maker to better visualise

the problem and facilitate understanding of the solution

process.

! Operations are needed to reach a solution, these operations

can be identified at a logical level, in addition to the low level

mathematical and DP techniques employed.

! Memory Aids improve the productivity of the user, without

necessarily providing any conceptual assistance.

! Controls are the levers used by the user to achieve a solution,

the concept of user control of the solution process is inherent in

DSS.

Frameworks such the ROMC approach provide an initial emphasis on the

problem, rather than the techniques used to address that problem. We

believe that this approach is a useful one as it should provide a more

balanced system than many OR/MS systems that start with the model as

the basis for system design. In Chapter 9 we discuss this approach in

relation to our specific problem introduced in Section 7.1

1.3.4 Current DSS technology

The technological environment has changed greatly since Sprague’s

original proposal of this framework (Power and Kaparthi, 1998). Recent

developments include the widespread use of graphical user interfaces, the

growth of network connectivity, the Internet, and the development of

common standards for software. However most of these changes enhance


18

the relevance of Sprague’s framework as they facilitate system

integration and ease of alteration. New programming tools allow the easy

development of industry standard interfaces that are widely acceptable to

users. The developments include advances in database software and the

use of common standards that allow a wider range of programs

interchange data. There has been considerable development in the area of

client-server systems, where distributed systems, such as DSS, can make

use of centralised databases. Where databases are used, Structured

Query Language (SQL) has become a standard means of sending

database commands. Open database connectivity (ODBC) is an attempt

to provide a standard method of communication between programs and

databases. As most database software and programming tools support

ODBC, it becomes possible to make use of a wide range of data from a

variety of alternative software sources. This approach provides an

effective means of exchanging data between a DSS and other programs.

For example, a DSS might be built by combining separate modelling

programs with access to a database. Given the growth in client-server

systems, these data exchange technologies will have an important role to

play in the development of DSS.

In an assessment of the contribution of these new software developments,

it is important to note the need for a DSS to be a comprehensive system.

A variety of software tools may contribute to decision-making, but may

not constitute a system. A DSS is a system and not a collection of distinct

components. Consequently, the various system features must be closely

integrated. For a comprehensive system to exist, data exchange alone

may not be sufficient. If a DSS generator is to interact with other

software, it will need to interact directly with other program components.

As a DSS generator is part of a larger system, its interaction features will

reflect the trends in software design generally. Therefore, any

developments that facilitate software integration greatly assist in the

building of DSS.


19

1.4 The nature of this research in DSS

1.4.1 The current state of DSS

Since its introduction, DSS have been an important part of the IS field,

which remains an important one to researchers (Keen, 1998). There is

substantial, but by no means universal, agreement among DSS

researchers as to the definition of DSS. For the purposes of this

dissertation, a widely accepted definition of DSS is used. This defines a

DSS as complete system containing a database, models and a user

interface which allows the user effectively control the system. In a

broader world, where actual applications are being developed, the term

DSS might be used for many systems that do not fully meet this

definition. One important theme of this work is that decision support can

only be maximised by such a comprehensive system. Our objective is to

achieve a balanced examination of the role of the different components of

DSS in the context of a particular problem, that of arc routing DSS.

1.4.2 The structure of this dissertation

This dissertation focuses on a well-established area of DSS application,

that of routing. This area of DSS is discussed in the following chapter. It

goes on to argue for a general enhancement of routing DSS by the

incorporation of technology drawn from Geographic Information Systems

(GIS); the GIS field is reviewed in Chapter 3. Within the general field of

routing DSS, this research concentrates on arc routing problems, a sub

field that has not been extensively researched. The arc routing field is

introduced in Chapter 5 and Chapter 6 reviews the solution procedures

used for these problems.

As decision support is ultimately related to a specific problem, this work

expressly examines arc routing for large sparse networks. Irish rural road

networks are of this type and postal delivery in rural areas represents a

typical problem in this class. Very little work has previously taken place

on this specific sub-problem, which is introduced in Chapter 7. This


20

chapter develops modified lower bounds for time base arc routing

problems. New heuristics for this specific problem are proposed in

Chapter 8. This provides an examination of the algorithmic requirements

of arc routing for large sparse networks. Chapter 4 proposes a new

framework for the integration of routing techniques and GIS. The final

chapter completes the work by examining the implications of these

general principles on the design of a DSS for routing for large sparse

networks.


21

Chapter 2 : Decision support for routing

problems

2.1 Routing DSS

2.1.1 The nature of routing problems

The problem of how to collect from or deliver to multiple locations, the so-

called Routing Problem, is one of most important areas of investigation in

OR/MS. Routing problems require a set of locations to be visited in

sequence within some overall objective such as the minimisation of time

or distance. A wide range of constraints may exist which affect this

problem and which make the identification of appropriate routes more

difficult. Work in this area has been taking place for over forty years

since the original formulation of the problem (Dantzig and Ramser,

1959), and a variety of routing problems have been identified. Much

useful work in OR/MS took place in the 1970's, as the computers of the

day became powerful enough to solve an increasing range of problems

(Assad and Golden, 1982). A bibliographic review (Laporte and Osman,

1995) identified five hundred articles representing relatively important

contributions to routing related problems.

Considerable work has taken place in developing solution procedures for

routing problems (see Chapter 5). As computer technology has advanced,

it has become possible to obtain automated solutions to solve ever more

complex problems. As with other OR/MS applications, computerised

routing techniques have increasingly been integrated with other forms of

computer technology, especially databases and graphic interfaces. These

developments have led to modern routing DSS discussed in subsequent

sections.


22

2.1.2 Suitability of routing problems for DSS

Routing problems are in many ways a typical DSS application. Routing is

of considerable economic value, justifying efforts to support decision-

making in this field. The nature of routing problems is well understood,

so the intelligence phase of the problem is well structured. Many of the

decision variables associated with routing are quantitative in nature and

therefore suitable for modelling by OR/MS techniques. Variables of

interest include; distances travelled, time of journey, volumes carried in

relation to vehicle capacity. Modelling techniques, such as those outlined

in Chapter 5 and Chapter 6, are capable of greatly assisting decision-

making. If the model includes all the variables of interest, then the

solution phase of the problem might be regarded as a structured one.

However, the DSS approach becomes appropriate when other factors are

also relevant. Customer service issues may not be easily incorporated in a

mathematical model, but may be vital to the decision-maker. Some

degree of user intervention is necessary to allow these non-quantitative

factors be considered. While the numerical factors may be assessed using

modelling techniques, the current state of algorithms and technology does

not allow for completely optimal solutions to most practical problems. In

this context, user intervention can contribute to the achievement of

quantitative goals as well as those not included in the modelling process.

The criteria for assessing routing decisions, the choice phase, are largely

straightforward. However, it is difficult to synthesise the various criteria

by which the solution may be measured. How can customer preference be

sacrificed for a shorter route? Are balanced routes strictly required or is

there some scope for small variations in each driver’s workload? These

trade-offs are difficult to incorporate in the models and are usually made

by the user using their judgement and experience.

Consequently, routing problems offer a good example of semi-structured

decision-making, where a DSS may make a superior contribution to a

purely mechanistic algorithmic approach. Such a DSS will contain models


23

drawn from those identified in later Chapters. The database component

must provide the data to be used by these models but must also provide

the user with the means to direct the solution process towards non-

quantitative goals. The interface must represent both the input data and

the solution outcomes, in a way that allows the decision-maker interact

with the system.

2.1.3 Early routing Software

Typical early routing software was based on the use of location co-

ordinates and straight-line distance was used as a surrogate for actual

travel distance. This simplified the problem and reduced the data

requirements within the limitations of the computers of the period. This

abstraction of the problem assumed that selection of an appropriate path

was a trivial exercise. In practice, of course, the actual route is

constrained by the need to use suitable roads. Generally, the co-ordinate

distance was multiplied by a standard factor, between 1.1 and 1.25, to

allow for the fact that the actual road distance was slightly longer. Some

of these issues are discussed in Stocx and Tilanus (1991). Where there

were major natural features, such as lakes, rivers, mountains or bays, the

road distance might be much longer. This was taken into account by the

use of barriers, which meant that the straight-line distance was

calculated around the edge of the barrier. In the Irish context, these

barrier files would be critical in the long sea inlets found around the

coast. For example, barrier files might be used at Carlingford Lough or

the Shannon Estuary. Barrier files are an example of how the

representation of additional information in the system can make the

derived routes more realistic (Figure 2-1).

While the straight-line distance approach is unsatisfactory in some cases,

it is adequate for many classes of problem. In particular, problems where

widely dispersed points are to be visited can be approached using this

type of technique. Consequently, many successful early applications


24

concerned supplies delivery to a variety of towns on a regional scale,

where the detail of street networks was not very important.

The true distance approach, using distances calculated from the road

network, reduced these problems. This requires that the road network be

digitised in some way and that the distances between points be

accurately calculated. The use of the true distance approach has become

an almost universal feature of routing DSS design. However, this

approach requires increased data and a consequent increase in the

sophistication of the software used for the organisation of that data. In

practice, routing problems are frequently constrained by time rather than

by distance travelled. Estimates of the time taken for a route may be

derived by using different speeds on different sections of the road

network. The incorporation of this type of additional path data increased

the usefulness of the problem formulation at the cost of making the

software to solve it more complex.

A good example of early routing software was VSPX (Vehicle Scheduling

Program Extended), introduced in 1971. This software employed the

Clarke-Wright savings algorithm (Clarke and Wright, 1964) and ran in

Figure 2-1 : Use of barriers to prevent routes crossing geographic

features


25

batch mode on IBM mainframe computers. This software was extremely

inflexible and it could not be regarded as a DSS. However, it did allow the

modelling of substantial routing problems and the generation of solutions

to these problems which were relatively efficient in terms of distance

travelled. Early reviews of the field found few users of computerised

techniques, although the potential of these techniques was recognised

(Mole, 1979; Sussams, 1984). A Dutch study examined the suitability of

routing software for milk collection and placed particular emphasis in the

need for flexible, user friendly and interactive and cheap software (Bocxe

and Tilanus, 1985). The study identified limitations with all of the

packages studied, but found that almost all of the packages offered some

improvement over VSPX. This is hardly surprising given the relatively

user unfriendly and inflexible nature of VSPX, and it indicates the

direction in which routing software was developing.

Fisher (1995) suggests that there are no successful examples of this early

generation of routing software. While the inflexibility of the technology

made successful application difficult, this assertion is not entirely

justified. Successful early applications in the Irish context include a

Franz Edelman prize winning application (Harrison, 1979) and a later

paper describing a distribution optimisation project (Harrison and Wills,

1983). What is clear is that this type of early software could only be easily

used by specialists. This meant that it could only be employed at a

remove from the relevant managers in the organisation. This reduced the

effectiveness of routing projects, as managerial concerns might not be

fully communicated to the OR/MS specialists involved in the solution

process. Even if the specialists did have a good understanding of the

problem, the operation of the software did not closely reflect traditional

practice. Consequently, managers had difficulty understanding, and

therefore accepting, the output produced.


26

2.2 Traditional Vehicle Routing DSS

2.2.1 Requirement for user interaction

For a system to be considered a DSS, and not just a modelling package, it

must be possible for the user to interact with the software (Gorry and

Scott-Morton, 1971). Therefore, the software must reflect the users’ view

of the problem to some extent. When considering routing problems using

non-computerised methods, much reliance is placed on the spatial layout

of the problem. Routes will usually be devised using paper maps,

typically moving from one point to another, which appear to be visually

close. Such manually designed routes will generally form compact blocks

when completed. These compact blocks will generally seem reasonable to

all those involved, including the customers and the vehicle drivers.

Mathematical techniques will obviously tend to produce routes that link

neighbouring points, for example those produced by a travelling salesman

algorithm. However, the routing heuristics commonly used will

sometimes produce routes that look quite bizarre in shape. For a small

number of problems that are tightly constrained, by factors other than

the location of the points to be visited, unusually shaped routes may in

fact be optimal. However, for most problems, skilled manual alteration of

the shape of a route in a DSS can improve the routes generated by the

heuristics that are commonly used. These alterations will improve the

spatial organisation of the route. These changes will also tend to improve

the acceptability of the route to customers and staff. User intervention is

often the only way of ensuring that the routes meet “soft” constraints that

are not part of the mathematical formulation. Experienced schedulers

have considerable knowledge of local conditions and of the relative

importance of the various constraints. Human intervention in the routing

process can substantially improve the quality of the routes produced. For

these reasons there has been increasing recognition that the available

algorithmic techniques can most effectively be used as part of a DSS.


27

2.2.2 The use of graphics in routing systems

With the greater availability of graphics terminals and PCs, there was

increasing use of graphics to represent routes on screen. By the early

1980's there was increasing recognition of the need to combine OR/MS

algorithms with appropriate graphics (Barbosa and Hirko, 1980). The

latter paper also makes use of the routing related GADS example (Grace,

1977). In a mid-decade review of the vehicle routing field, Bott and Ballou

(1986) argued for the use of graphically based interactive techniques

combined with appropriate algorithms. However, a review of PC based

routing software (Golden, Bodin and Goodwin, 1986), published in the

same year, found that only one-third of the packages reviewed had

extensive graphic facilities. The role of visual interfaces is widely

recognised as a critical issue in the continuing development of OR/MS

generally (Jones, 1994b; Jones, 1999) and routing in particular (Bodin

and Levy, 1994).

One constraining factor on the development of routing software in the

1980's was the need for on-line access to increasing amounts of

information. For instance, in a survey of UK companies, Sussams (1984)

identified a need for order processing systems to be computerised in order

to facilitate computer based routing.

Consequently, routing systems increasingly attempted to incorporate

more of the information that a scheduler might require while evaluating

a route. This trend reflected recognition of the need to include a variety of

information sources relevant to a routing decision. Most traditional

routing problems use information that is particular to the problem.

Examples of such information might be the specific demand volumes of a

firm's customers or the size of an organisation's vehicles. This

information will probably already be available in the Management

Information System (MIS) of the organisation. Effective decision support,

for problems making use of this type of information, requires a suitable

link to the MIS database and an interface that is customised to the


28

specific problem. A good example of such a routing system was that used

in the Air Products Corporation in Canada (Bell, Dalberto et al., 1983). In

order to organise the larger amounts of information incorporated in

routing systems, database management systems were increasingly

required. An influential review of the field (Bodin, Golden, Assad and

Ball, 1983) noted the over-emphasis placed on algorithmic issues and

indicated that the future lay in a flexible user interface and in better

database support. By the mid-1980's, routing systems combined

algorithms with the increasing use of graphic interfaces and links to

databases. These systems could increasingly be seen as a form of DSS, as

they contain the recognised components of a DSS, i.e. the interface, solver

and database modules. The vendors of these systems increasingly began

to emphasise the flexibility and ease of user interaction of their products.

A good example of the new class of microcomputer based routing software

introduced in the mid-1980’s was the PC version of the ROVER software,

with which the author has had some experience. This was a development

of earlier mainframe software (Fisher, Greenfield, Jaikumar and Lester,

1982). This package could be regarded as a DSS, as it comprised a

database, an interactive interface, and a modelling component, based on

the Fisher-Jaikumar algorithm (Fisher and Jaikumar, 1981). This

software allowed the user select a set of points to be routed from the

database. When solved the user could modify the solution in a number of

ways. While the system could make use of a true distance matrix, in

addition to the co-ordinate approach, no road network detail was

displayed on screen. Consequently, only limited information was

displayed to the user. The system benefited from the use of the most

powerful microcomputers available and required a twin monitor

configuration. Report information was displayed on a text monitor while

the graphical display showed the spatial layout of the routes (Figure 2-2).

Where geographic features affecting the route structure exist, the lack of

information displayed on screen could make decision-making more

difficult. For example, in Figure 2-2 there is obviously some sort of


29

restriction North of the depot, perhaps a sea inlet. However, from the

information displayed on the interface it is not quite clear what this

might be. The limited visual details provided in this type of interface

meant that the user would probably also need a paper map for additional

information.

How well does this type of system meet the requirements of a DSS as

described in Chapter 1? The ROVER system is a candidate for

consideration as a DSS, as it comprised a database, an interactive

interface and a modelling component, based on the Fisher-Jaikumar

algorithm. This could be characterised as an optimisation model in Alter’s

framework. The model optimises the total distance travelled, subject to

restrictions on vehicle capacity and time window restrictions at the

customer locations. Limitations can be placed on the route structure by

time windows or by specifying the first or last customers to be visited.

When a solution has been derived users can alter the route sequence

manually. By using the interface, a user can perform operations such as

selecting a block of locations to be moved to another route. This type of

Figure 2-2: Graphic display of ROVER software


30

system represented a dramatic improvement over previous technology,

yet this class of system falls short of the full flexibility demanded by a

DSS. The system does not support a full spectrum of control, as the model

used is a largely a black box. The information provided to the user was

incomplete, owing to the limited nature of the information displayed on

screen. There are few options for the integration of this system with other

types of software.

The arrival of software innovations such as the graphical user interface

(GUI) has had an important effect on DSS design. Firstly, the

incorporation of graphical features in the software provides design

guidelines for systems, making it easier for users to learn to operate the

software. This advantage has existed for Apple Macintosh software for

many years and is now evident in Windows systems. A second important

advantage of modern graphical operating systems is that they allow easy

interchange of information between applications. These features can be

used to pass information to and from routing systems and consequently

can increase system integration. Modern routing DSS has taken

advantage of developments such as graphical user interfaces. Recent

examples include; the Fleetmanager DSS in New Zealand (Basnet,

Foulds and Igbaria, 1996), a system for routing vehicles delivering gas

cylinders in Hungary (Fölsz, Mészáros and Rapcsák, 1995) and an

example dealing with the delivery of dairy products in Spain (Adenso-

Diaz, González and García, 1998).

2.3 Impact of DSS Developments on Routing DSS

2.3.1 DSS developments

In the period since routing systems were first introduced, a variety of

innovations have occurred. New algorithms have been devised and new

forms of computer technology have become common. These developments

meant that computer graphics became relatively inexpensive and that

standard business PCs costing a little over one thousand pounds became


31

sufficiently powerful to do useful work. Eom et al (1997) note that OR/MS

techniques remain important for DSS, but that these techniques

increasingly are being embedded in systems. These systems incorporate

graphics, visual interactive techniques and a variety of artificial

intelligence techniques including expert systems and neural networks.

Authors reviewing the routing field have noted the potential of these

developments. Both academic and commercial routing software has been

introduced which meets more closely the definition of a DSS. A number of

systems sought to enrich the system dialogue with the user by

incorporating some sort of artificial intelligence. This trend was enhanced

by the exploitation of the improving graphics facilities to provide for

richer user interaction with the system. One theme was the use of

superior graphics and in the provision of enhanced database support to

provide for the display of additional information. Various proposals

related to the provision of a system providing a range of algorithmic

solution techniques, allowing the user select the appropriate technique.

2.3.2 Artificial Intelligence

The DSS field has been influenced by a variety of other technologies and

these have played an important role in routing DSS. One frequently

mentioned area of influence on DSS is that of expert systems and

artificial intelligence (AI). It has been argued that routing DSS can be

enhanced by including a knowledge base component, for instance in

Duchessi, Belardo et al. (1988). This is especially likely to be true for a

DSS designed to support more complex routing problems. In a review of

the vehicle routing field, Fisher (1995) notes that many solution

techniques are designed for specific and limited conditions and suggests

that artificial intelligence techniques may help to identify the appropriate

technique to use. This might arise in the context of model management,

where AI techniques could provide a means to identify the appropriate

models to use (Desrochers, Jones, Lenstra, Savelsbergh and Stoughie,

1999). AI techniques can also have a role in the scheduling phase of


32

routing decisions, for instance in the assignment of buses to fixed routes

(Chang, Yeh and Cheng, 1998).

One important prototype DSS is the prize winning Tolomeo system

(Angehrn and Lüthi 1990; Angehrn 1991). The design of this system

starts from the belief of the authors that the interface (or language

system) is the most critical element of DSS design. Tolomeo is described

as a DSS generator that can be applied to a wide range of specific

problems. The user can express their needs to the system by modelling by

example and Tolomeo uses artificial intelligence techniques to analyse

the problem representation. A wide range of algorithmic procedures are

provided in the system and the AI component helps the user identify the

appropriate algorithmic representation of a problem, including routing

type problems. In this system, the user can define the problem by using

visual interactive methods and the system then brings the appropriate

modelling techniques to bear on the problem.

2.3.3 User Defined algorithms

Bodin and Salamone (1988) describe a relatively early prototype system

that exploited PC graphics to provide a flexible interactive routing

system. This system, part of a project known as FULCRUM, allowed the

user construct his or her own algorithms for developing an initial solution

and for improving on it. This prototype raised some questions about how

best to represent problems graphically and indicated the need for better

user access to problem data, reflecting the database requirements of a

DSS.

ALTO (Potvin, Lapalme and Rousseau, 1989) and its successor Micro-

ALTO (Potvin, Lapalme and Rousseau, 1994) are good examples of a

more flexible ‘DSS’ approach to routing problems. The designers of Micro-

ALTO contrast the user control over the algorithms used in their system

with the ‘black box approach’ used in commercial routing software. Micro-

ALTO is designed to support node routing problems and provides a


33

number of general tools and operations to support solving this class of

problem. The system provides tools for the management and display of

transportation networks, including the ability to edit networks and add

or delete nodes and arcs. Micro-ALTO allows user control of the

specification of the problem; the location of the depot, the location of

customers, specification of customer characteristics and definition of the

vehicle fleet characteristics. This information is manipulated in a user

friendly graphical user interface (GUI) environment. Having defined the

network and the problem characteristics, the user can build a solution

procedure from a number of node routing heuristics. These can be easily

applied to the problem, allowing experimentation to identify the best

solution strategy.

2.3.4 Visual Interactive techniques

Visual interactive (VI) modelling is increasingly seen as a relevant

approach for many OR/MS problems (Hurrion, 1986). Bell (1985)

describes two types of VI models. Representational models use graphics to

display the operation of model, this might include the use of bar graphs or

pie charts present numeric results. Iconic graphic models represent a

system rather than a model, the maps used in routing would fall into this

category. Bell uses the example of routing problems to support the use of

VI techniques to facilitate data validation, improve as errors in the

network used can be readily identify from a map representation on

screen. This reflects the major contribution of VI models which is to

communicate with the user and therefore achieve greater user support for

the system. The area of visual modelling continues to be an important

one, see the comprehensive review by Jones (1994b) and the commentary

by Bell (1994) in the same edition of the ORSA Journal on Computing.

It has been argued that the user interface is the most important

component of a DSS and that the interface design may provide a

framework for the entire DSS (Jones, 1991). A similar philosophy

underlies the Tolomeo system described above. By designing the entire


34

DSS around the interface, the user's view of the problem can be more

accurately captured, thereby providing more effective decision support. In

the case of vehicle routing, the user's view of the problem is a spatial one

and the user can most effectively interact with a system that

accommodates this view. The trend within routing systems has been to

facilitate the spatial representation of routes as part of the interface, in

keeping with the user's perception of the problem.

Jones (1994a) discusses the concept of anchoring, which recognises that

people prefer the problem representation that they are first introduced to.

In Western societies, where a computer is not used, problem solvers

traditionally make use of paper maps for routing problems (this need not

be true in other cultures (Sahay and Walsham, 1996), (Walsham and

Sahay, 1999)). These maps provide a number of geographic reference

points other than just the location of the customers to be routed. In order

for a routing DSS to accommodate this anchored view of the problem, it

may be appropriate to display geographic information other than just the

customer locations. The most obvious need is for a display of the road

network, but other geographic information may also contribute to user

decision-making. Therefore, additional mapping information, such as

street layouts, has become a feature of routing DSS generally.

Progressive systems such as Tolomeo (Angehrn, 1991) or Micro-ALTO

(Potvin, Lapalme et al., 1994) display significant amounts of network and

other geographic information.

2.4 Arc Routing Systems

2.4.1 Characteristics of Arc Routing DSS

As has been the case with algorithmic development, the majority of

routing systems are directed at point-based problems rather than arc

routing problems. However, a number of arc routing systems do exist.

The use of arc routing algorithms imposes requirements on a routing

system that are less important than in the case of a point-based system.


35

Comprehensive network information is an absolute requirement of an

arc-based system. This may require not only the existence of roads but

restrictions such as no right/left turns. Therefore, arc routing techniques

are incorporated in systems that typically display and store a great deal

more geographic information than is usual in point routing applications.

This reflects the fact that arc routing systems are by definition interested

in the detail of road networks.

However, many arc routing problems also differ in the nature of the data

being used. Many node routing applications are concerned with deliveries

to customers and are quite dynamic in nature, as the delivery volumes for

each customer may change daily. This data is specific to the routing

application. Arc routing problems are often concerned with visiting every

house on a road, for postal delivery or refuse collection, and the data is

therefore relatively static. Data of this sort is frequently derived from

demographic information for the region of service. Where demographic

data is associated with geographic entities then these may become

relevant to an arc routing system.

2.4.2 Specific arc routing applications

Eglese and Murdock (1991) built a DSS to support the routing of road

sweepers travelling in rural areas of Lancashire in the north west of

England. This system was built using Turbo Pascal and incorporated an

onscreen map display. Visual interactive techniques were seen as an

important component of the system. Information on the progress of the

solution was provided by colour changes on the road segments visited.

The system provides for user interaction with the solution procedure by

using a manual override facility. The overall system was seen to be

useful, and brought about a significant improvement in the efficiency of

the routes for street sweepers in this region. Another project in the same

region concerned the routing of winter gritters (Li, 1992; Eglese, 1994; Li

and Eglese, 1996). Unlike the previous case, this problem requires only

one pass per road segment.


36

An application designed to support the routing of refuse vehicles in

Portugal (Coutinho-Rodrigues, Rodrigues and Climaco, 1993), provided

graphics and heuristic solution techniques on an IBM PC/AT. This class

of microcomputer is some fifty times less powerful than those available at

the end of 1998. This system used the Pascal programming language and

provided user-friendly graphics and data handling. While this system did

not employ a fully-fledged database, it did provide useful support for staff

involved in planning routes for refuse collection in five Portuguese cities.

An unusual routing application is the arc routing system for delivery of

cattle feed in Arizona (Tracey and Dror, 1997). In this case, animal feed

must be delivered to troughs situated in cattle pens along ranch roads

(the arcs). As this type of problem had not been approached using

computer-based techniques previously, it was felt that the display of

information and managerial interaction were important requirements, in

addition to the performance of the solution techniques used. The

requirements for such a system were to have a graphic display, to have a

development environment, which allowed programming of the

application, and to have data query and storage facilities. These

requirements were met by using a GIS as the basis of the system, in this

case PC Arc/Info (ESRI). The developers programmed a number of

routines to customise the system and provide information in a format

suitable for the specific application. This synthesis of arc routing

techniques and a system that could display information of interest to

management provided a successful DSS.

2.4.3 Comprehensive arc routing software packages

The GeoRoute package (Lapalme, Rosseau et al., 1992; Georoute, 1998)

represents the culmination of work undertaken at the Centre de

recherche sur les transports de l’Université de Montréal (CRT). This is

one of the foremost centres of vehicle routing research in the world.

GeoRoute was designed for urban routing problems and featured an

interface with relevant street information being displayed (Figure 2-3).


37

Network editing features are provided to allow for the alteration of the

comprehensive street database. GeoRoute contains a general framework

within which a variety of node and arc routing algorithms could be used,

inspired by the ALTO software (Potvin, Lapalme et al., 1989) discussed

above, which was previously produced at Montréal. The arc routing

component of GeoRoute was also developed from earlier work (Roy and

Rousseau, 1989). This type of software is very much inspired by the DSS

viewpoint as it offers comprehensive database and model management

facilities (Table 2-1).

GeoRoute has been enhanced and developed for a variety of arc routing

applications. A variant of the program for postal routing is in use in

Canada and number of European countries. Another program variant is

in use for other arc routing applications such as waste collection,

Figure 2-3 : GeoRoute interface


38

recycling collection, street cleaning, salt spreading and snow removal.

The latter application is especially important in a Canadian context.

Routesmart (Bodin, Fagan and Levy, 1992; Bodin and Levy, 1994) is a

comprehensive street routing system with point and arc routing

components designed to accommodate the complexities of street routing

in urban areas (Bodin, Fagan and Levy, 1997). This software has

provision for one way streets, no right turns and other restrictions. This

software grew out of a number of street routing projects (Bodin and Levy,

1991; Wunderlich, Collette, Levy and Bodin, 1992). Routesmart provides

a set of algorithms that operate with the TransCAD or Arcview GIS

software. These GIS products provide good interface facilities for the

display of maps, which is tailored by the Routesmart routines. The use of

GIS technology to provide an accurate representation of the road network

is seen as a critical component of the software.

Table 2-1: Features of GeoRoute (Georoute)

Enter and display on the map service location attributes such as

quantity, service time, servicing time windows and servicing pattern

(linear, zigzag).

Quickly select and/or colour routes or serviced locations based on the

value of one or more attributes.

Specify the vehicle type, serviced locations, and deadhead travel

paths for a given route.

Choose where and when complementary route activities (ex.: lunch,

unloading/refill, etc.) must take place.

Freeze a subset of routes you do not want to be modified.

Consult up-to-date detailed and summary route statistics.


39

2.5 The Future of Routing DSS

2.5.1 Trends in Routing DSS

Over the years routing systems have reflected the trend for OR/MS based

DSS generally to be very much model-driven with limited interface and

database components. In earlier years, these systems constituted

modelling software with inflexible data entry and output, the limited

nature of these systems meant that only experts could easily use them. In

recent years, relatively elaborate systems have been built where the

model is just one component of a comprehensive system. Later systems

have employed more sophisticated database techniques, allowing better

integration with other sources of data. Routing DSS is now recognised by

practitioners as an important tool for logistics management (Andel,

1996).

New technologies will influence the development of routing systems.

Network and Internet technology will allow distributed systems that

separate the location of decision from the database and modelling

components. Other developments in user interface design and visual

interactive modelling allow greater ease of use by non-expert users, make

these systems accessible to managers.

These developments will not remove the need for algorithmic

development, but will leverage this development into more useful

systems. Richer data input and more complete interaction with the user

will provide more realistic problem representations, but will require that

the solution procedures used are flexible enough to accommodate these

trends.

2.5.2 Geographic Information Systems

In the arc routing systems described above there has been great emphasis

on the provision of a detailed geographic database and the display of this

information on screen. These features are similar to those provided by a


40

GIS. Advanced arc routing systems either emulate GIS features in a

customised program (GeoRoute) or exploit GIS technology to build a

routing system (Routesmart). GIS technology is therefore of considerable

relevance to the future of routing DSS. Subsequent chapters of this

dissertation will examine more closely the nature of GIS and its

relationship to routing problems.


41

Chapter 3 : Geographic Information Systems

3.1 Geographic Information Systems (GIS)

3.1.1 Development of GIS Technology

One area of computer application that has expanded enormously in

recent years is that of Geographical Information Systems (GIS). This

development has largely taken place within a community composed of

traditional users of geographic data, in fields including geography,

geology, planning and forestry. The needs and paradigms of people

working in these fields, rather than the IS or OR/MS communities, have

influenced the development of the technology. The growth of GIS has

been rapid, as numerous potential applications have been recognised. A

recent paper prepared on behalf of the European Commission (IMO,

1995) indicates that the international GIS software market is worth

about one thousand million US dollars (€1100 million) in 1996. The value

of the GIS sector is also determined by the large amounts of computerised

geographic data now available. Indeed the trend in GIS has been for the

data to cost more than the software.

As is the case with DSS there are numerous definitions of GIS; for a

review of these see Maguire (1991). Most call for a system for storing and

displaying spatially or geographically related data. The acronym GIS has

also been used as an abbreviation for Geographical Information Science.

For example, a prominent journal in the area has recently changed its

name from the International Journal of Geographical Information

Systems, to the International Journal of Geographical Information

Science. This trend appears to reflect a view that there exists a core set of

geographical information processing techniques, which form a separate

body of research, distinct from the downstream information system

implementations of those techniques. Given this trend it seems


42

appropriate to define a GIS as an information system primarily concerned

with the techniques associated with geographical information science.

The development of GIS has been driven by technological innovations

that facilitated the storage and manipulation of large quantities of data.

This trend has its origins in the 1960s, with the fragmented use of

computer technology for automated cartography and the introduction of

address matching software. The development of comprehensive GIS

software required improvements in graphics and database techniques. By

the 1980s, a number of different forms of commercial GIS software

became available, including widely used products such as ARC/INFO

from ESRI. Such software generally used UNIX workstation based

proprietary technology. At the end of the 1980s, GIS software become

available on standard microcomputers, reflecting the increase in PC

performance to levels previously associated with workstations. By the

1990s, many different kinds of commercial GIS software were available.

GIS technology had by this time achieved widespread use in its

traditional areas of application, such as forestry and natural resource

applications. This explosion in the use of computer technology can also be

seen in other areas, where a virtuous circle of declining hardware costs

leads to larger software sales and therefore reduced software costs.

3.1.2 GIS Data

In addition to developments in data handling technology, widespread use

of GIS also required the availability of suitable geographic data. This was

influenced by technical developments in data capture. Initially data

collection from maps was achieved by digitisation using a hand-held

device, an error prone and time consuming process. Later the scanning of

entire maps became feasible and this approach greatly speeded up data

collection. Nevertheless collecting accurate digital data from paper maps

remains a difficult process, as human intervention is usually needed to

identify the objects on the map. Other technical developments such as

Global Positioning Systems (GPS) have greatly facilitated the collection


43

of geographic data in general. This technology has particular application

in routing as these devices can be placed on vehicles, allowing their

physical location be continuously recorded. Advances in data storage

technology have facilitated the distribution of large amounts of data.

Despite the technical developments, geographic data collection for once

off projects remains an expensive and error-prone procedure. However, as

GIS use becomes more widespread, datasets can be shared by different

users, reducing the cost of the data per project. The increasing use of GIS

was both facilitated by, and responsible for, the increasing volume of

digital spatial data becoming available in developed countries. The wider

availability of appropriately formatted data has also reduced the cost of

data assembly for a given GIS project. The growth of GIS has been driven

by the importance of spatially related data. It is estimated that up to 80%

of data needed for the activities of business and government is spatially

related (Franklin, 1992). There is increasing interest in the role of GIS in

business, with an increasing output of papers and books on the subject

(Grimshaw and Clarke, 1996; Grimshaw, 2000).

The level of GIS development varies from country to country. In the USA,

the basic government mapping data is available free of charge and this

has greatly facilitated the growth of GIS. In European countries, mapping

data tends to be available from government agencies on a cost recovery

basis, with a consequent increase in GIS data cost and a slowdown in its

use by the public. Despite standardisation efforts by the European Union,

concerns remain about the differences in the data formats used in various

European countries (Harding and Wilkinson, 1996). In Ireland, data has

been historically quite expensive and of poor quality because of

inadequate updating of maps. The situation is now improving with the

Ordnance Survey aiming to provide comprehensive digital mapping data

(Anonymous, 2000b). Currently off-the-shelf road networks are available

at various levels of detail, although these are relatively expensive.

Several private sector vendors (Gamma, IRIS) are producing their own


44

digital maps from satellite photography and global positioning system

(GPS) surveys. Some of these vendors are attempting to collect additional

data on speeds per individual road segment. This type of data collection

will greatly facilitate GIS use in Ireland in the future (Anonymous,

2000a).

3.2 GIS Software

3.2.1 Current developments in GIS software

The rapid expansion in the use of computer technology seen in the GIS

field can also be seen in other areas, where the virtuous circle of declining

hardware costs leads to larger software sales and consequent reduced

software costs. Consequently some mapping software is becoming

available on a mass-market basis, for example the inclusion of simple

mapping facilities in spreadsheets first introduced in Lotus 1-2-3 Release

5. A similar mapping facility is now available in Microsoft Excel. This

mass-market use of mapping and GIS products creates a large demand

for spatial data, causing more to be made available. The decision-makers,

that use such basic mapping products, frequently go on to become

interested in more sophisticated software. Recent improvements in

mainstream PC technologies facilitate this increase in the use of spatial

data. These include inexpensive gigabyte sized hard disks, large high-

resolution colour monitors, graphics accelerators and rewritable CD-ROM

storage.

There now exists a spectrum of software from simple mapping packages

to complex systems for handling spatial data. Many of these systems

operate on widely available PC equipment that already is being used for

decision-making applications. The cost of spatial data for use with this

software is declining and there is greater interest by the vendors of such

software in new (non-traditional) applications. These new applications

include the extension of GIS techniques into fields more usually

associated with OR/MS, for example many GIS products now provide the


45

facility to find a shortest path in a road network. Transport applications

are increasingly seen as an important application by GIS vendors (Lang,

1999).

3.2.2 Components of GIS

A GIS makes use of geographical and attribute data (Chrisman, 1997).

Attribute data, addresses, populations, etc., are associated with

geographical data. Attribute data can be stored in a conventional

database or flat-file format. Geographical data may be represented as

points, lines or polygons. It is the handling of the geographical data, such

as the existence of rivers, roads or contour lines that requires the use of

the special techniques that characterise the use of GIS. The full

representation of a map requires relatively large volumes of information

and high-powered software and hardware to deal with this volume of

information.

A GIS, as distinct from a simple mapping program, will have a database

of geographic data, allowing linkages between different types of data and

Table 3-1 : Data operations in GIS

GIS Operation Data Operated on Example

Adjacency Point/line

Polygon/polygon

Nearest point to a line

Neighbouring regions

Enclosure Point/Polygon

Line/Polygon

Point in region

Line in region

Buffering Point

Line

Area near point

Area within 500 m of a road

Overlay Polygon/Polygon Area within 2 different types of

region


46

the ability to query this spatial data. A comprehensive GIS package will

provide a variety of data handling routines (Table 3-1). For example a

GIS database query would allow a group of spatial entities to be

identified, for example all regions close to a region of interest (Figure

3-1). It would allow identification of all roads within a certain distance of

a river by using buffering techniques. In the routing context, this might

allow the identification of road segments close to a route (Figure 3-2).

Therefore, while traditional database approaches can support queries on

the attribute data, GIS is defined by its ability to cater for spatial

queries. Not all applications of mapping data require the full power of a

GIS. A comparison exists with non-spatial data where simple data

manipulation can take place in a spreadsheet program, without the use of

a fully-fledged DBMS.

Figure 3-1 : Use of spatial techniques to identify neighbouring

regions


47

3.3 GIS and DSS

3.3.1 Relationship between GIS and DSS research

Many areas of DSS application are concerned with geographic data, an

influential early example being the GADS system (Grace, 1977). A more

recent important prototype DSS, Tolomeo (1990), uses a geographical

context for the development of visual interactive techniques. However

mainstream GIS techniques have had limited impact on DSS research.

This situation is beginning to change. Some, but by no means all, recent

DSS textbooks include GIS as a component of management support

systems (Mallach, 1994, Page 428; Turban, 1995). While these texts

stress the usefulness of geographically related information, they do not

provide a complete picture of the relationship between GIS and other

management support systems.

Figure 3-2 : Example of GIS use to identify street segments close

to a route (Keenan, 1998c)


48

GIS related research is beginning to make an appearance at conferences

associated with DSS. Notable examples include GIS based sessions

organised at the Hawaii International Conference on System Sciences

(HICSS) (Grimshaw, 1996; Murphy, 1996) and the conference of the

Association of Information Systems (AIS) (Keenan, 1997). Some of the

authors presenting at these conferences have argued for better linkages

between GIS and DSS and optimisation (Rolland and Gupta, 1996). There

is increasing evidence of interest in GIS at OR/MS conferences, where

applications integrating GIS and Operations Research techniques are

discussed. Academic journals associated with the DSS field are beginning

to publish GIS related papers. Wilson (1994) explored the relationship

between DSS and GIS in a 1994 paper in an IS journal. Crossland (1995)

presented empirical evidence of the usefulness of a spatial approach to

decision-making, while another study extended cognitive fit theory to

map based presentations (Dennis and Carte, 1998).

Geographical techniques have been identified as being relevant to the

general field of computer graphics, on which much DSS research is based.

Researchers from the IS tradition have noted that computer technology is

especially appropriate for the display of mapping data (Ives, 1982).

Cartography has been seen as being an important source of principles for

the design of business graphics (DeSanctis, 1984). Recent work by

Smelcer (1997) indicated that map use was superior to the use of tables in

some situations. Another study (Swink and Speier, 1999) indicated that

the quality of decision-making using GIS could be influenced by the level

of detail included in the presentation of the data. A recent paper in the

prestigious MIS Quarterly discussed the benefits of SDSS for both

inexperienced and experienced decision makers (Mennecke, Crossland

and Killingsworth, 2000).

GIS techniques are beginning to have an impact on DSS applications.

Surveys of DSS applications, for instance (Eom, Lee et al., 1993), have

identified marketing and routing as important areas of DSS application.


49

These fields are also recognised as areas of GIS application (Maguire,

1991). Many areas of GIS application would be familiar to the OR/MS

field. One traditional example of the use of modelling is in selecting a

facility location (Harrison and Wills, 1983) and this can be related to GIS

techniques (Ding, Baveja and Batta, 1994). There might be a number of

criteria for such a decision; some of these would be spatial in nature. For

instance, a school might need to be located near to the districts from

which potential pupils would travel. A refuse disposal facility, on the

other hand, might need to be located away from populated areas. GIS

based spatial operations could be used to provide an index of suitability

for sites for such a facility.

These applications often employ demographic data that is widely

available in a suitable format for use in GIS software. Many OR/MS

applications feature a specific problem formulation set in a geographic or

demographic context common to many users. This common set of data is

likely to be available, at reasonable cost, for the GIS. A number of

specialised GIS products exist to exploit this data for a particular class of

applications, an example is the marketing oriented GIS products from

Tactician Corp (Tactician).

3.3.2 Is a GIS a DSS?

Within the GIS field there is increasing interest in the use of GIS

software to provide decision support. This is reflected in a recent GIS

conference entitled “DSS 2000” and in the increasing appearance of

papers referring to Spatial Decision Support Systems (SDSS) at GIS

conferences. While an increasing number of GIS based applications are

described as DSS, these descriptions suffer from a lack of agreement on

what exactly a DSS actually constitutes. This reflects the varying

definitions of DSS in the DSS research community, but also arises from

the separation of GIS research from mainstream IS. As Maguire (1991)

points out, some authors have argued that a GIS is a DSS. In some cases,

GIS applications are described as being DSS without reference to the


50

DSS literature. Many GIS based systems are described as being DSS on

the basis that the GIS assisted in the collection or organisation of data

used by the decision-maker. This may be a reflection of the trend

identified by Keen (1986) for the use of any computer system, by people

who make decisions, to be defined as a DSS.

However, other authors justify GIS being regarded as DSS in terms of the

definition of DSS. According to this line of argument GIS meets the

requirement of being a DSS, as GIS contains an interface, a database and

spatial modelling components. Mennecke (1997) sees SDSS as an easy to

use subset of GIS, which incorporate facilities for manipulating and

analysing spatial data. These differences of definition reflect the differing

needs of decision-makers that use spatial information. For many of the

current SDSS applications, the main information requirement of the

decision-makers is for relatively structured spatial information. This

group may indeed find that standard GIS software provides for their

decision-making needs.

Many widely accepted definitions of DSS, introduced in Chapter 1,

identify the need for a combination of database, interface and model

components directed at a specific problem. In terms of these definitions, a

GIS would not be regarded as a DSS as it lacks support for the use of

problem specific models. However, the view of GIS as a DSS is has some

support in the existing definitions of DSS. Alter (1980) proposed an

influential framework for DSS that includes data driven DSS that do not

have a substantial model component. As the database component, rather

than models, is central to standard GIS software, it could be regarded as

an Analysis Information System in Alter's framework. Common to all

definitions of DSS is a sense that these systems must support a particular

type of decision. This characteristic distinguishes DSS from general

purpose MIS. While GIS applications may contain the information

relevant to a decision, they are usually general-purpose systems, not

focused on a particular decision.


51

The view that SDSS is a subset of GIS reflects the need for decision-

makers to focus on their specific problem, and their lack of interest in GIS

features outside this domain. This view suggests that the techniques

needed for SDSS are already within the GIS domain and that a subset of

these techniques can be applied to a particular problem. For some

problems within the traditional area of application of GIS this approach

is sufficient. However, the range of problem areas where SDSS can be

used greatly exceeds the traditional areas of GIS application. It is widely

accepted (Franklin, 1992) that more than 80% of business data has a

spatial component. Therefore, SDSS can potentially be used to assist

decision-makers in problem areas where models drawn from other

disciplines have long been found useful. For these areas at least, a

standard GIS cannot be said to be a DSS as such a system lacks the

support that the use of customised models can provide. For this wider

range of second-order uses of spatial data, additional processing or use of

non-spatial models is required to support fully the decision-maker. The

view of GIS as a DSS would seem to propose that all existing techniques

from OR/MS, accounting, marketing etc., be included in standard GIS

software, a subset of which could then be used to build a SDSS. This all-

inclusive view may reflect a limited perspective on the range of modelling

and solution techniques that can be applied to spatial data.

This dissertation is based on the premise that SDSS can most usefully be

regarded as an extension of GIS, rather than just a subset of it. This view

is contrary to some authors, for instance Mennecke (1997). From this

viewpoint, a SDSS will employ a subset of GIS techniques in combination

with problem specific models not found in GIS. This will extend the

present use of GIS as a DSS, to a situation where a GIS will be used to

build a DSS. This will allow the range of decisions supported to be

extended from those incorporated in the standard GIS software, to other

specialist fields where some customisation of the software is needed. One

such field is routing and specifically the arc routing applications that are

the subject of this dissertation. It is therefore relevant to examine SDSS


52

in general and to specifically focus on the role of these systems in the

routing domain.

3.4 Spatial Decision Support Systems

3.4.1 SDSS decision makers

SDSS is an important subset of DSS, incorporating GIS techniques with

other modelling approaches, whose potential for rapid growth has been

facilitated by technical developments. The availability of appropriate

inexpensive technology for manipulating spatial data enables SDSS

applications to be created. The benefits of using GIS based systems for

decision-making are increasingly recognised. In a review of GIS, Muller

(1993) identified SDSS as a growth area in the application of GIS

technology. However, the value of SDSS is not determined by its

innovative use of technology. Rather the contribution of these

applications will be determined by how well they support the need for a

spatial component in decision-making.

An important group of SDSS users are those based in the traditional

areas of application of GIS. In these fields GIS was initially used as a

means of speeding up the processing of spatial data and for the

completion of activities that contribute directly to productivity. In this

context, the automated production of maps has a role similar to that of

data processing in business. Decision-making applications will develop

and SDSS become widespread in much the same way that data

processing applications evolved into DSS in traditional business

applications. An example is the DSS for the assessment of geological risk

by Mejia-Navarro (1995). This class of applications is distinguished by a

direct interest of the authors in the spatial operations provided by the

SDSS and by their considerable background knowledge of the spatial

techniques used. For this category of user, the spatial data and the

spatial processing techniques are of direct interest rather than simply

providing the context in which other variables are being manipulated.


53

The greater complexity of spatial information processing and its greater

demands on IT has lead to the ten to fifteen year time lag in the

development of SDSS (Densham, 1991). With the decline in IT costs,

inexpensive microcomputers can now cope with the demands imposed by

the manipulation of spatial data. The rapid increase in the 1980s in the

use of database managers, led by Dbase II, is being emulated by the

current growth in the use of spatial database tools at present. In the

context of decision support, the increasingly widespread use of PC based

GIS software is reminiscent of the move towards PC based DSS in the

1980s (Table 3-2).

The second group of decision-makers for whom SDSS can make an

important contribution is in fields such as routing and location analysis.

Although the spatial component of such decisions is clear, in the past DSS

design has been driven predominantly by the OR/MS models used. Such

model driven systems often had very limited database or interface

components and the DSS provided little contextual information to the

Table 3-2 : Computerised Support for Decision-making

(adapted from Turban, (1995 Page 19)

Phase Description Traditional Tools Spatial Tools

Early compute, “crunch numbers”,

summarise, organise

early computer

programs, OR/MS

models

computerised

cartography

Intermediate find, organise and display decision

relevant information

database management

systems, MIS

workstation GIS

Current perform decision relevant compu-

tations on decision relevant infor-

mation; organise and display

results. Query based and user

friendly approach. “What if” analysis

financial models,

spreadsheets, trend

exploration, OR/MS

models, decision

support systems.

spatial decision

support systems


54

user. In future these models will be incorporated into GIS based SDSS,

providing superior interface and database components to work with the

models. The role of the superior GIS data handling facilities will be to

provide a richer context for the use of the specific models and for display

on the user interface.

For the general class of routing problems, the variables of direct interest

might include distance travelled, the number of vehicles used, and the

loads on each vehicle. Early routing DSS were restricted to the use of

data related to directly relevant variables. However, the use of GIS

technology allows the inclusion of other indirectly important information.

For example the inclusion of elevation data would allow more realistic

travel times be used in quantitative modelling of routes. The display of

distinctive natural features such as rivers or mountains on the interface

can make it much easier for the user to understand the representation of

the routes generated. This synthesis of OR/MS and GIS techniques will

provide more effective decision-making.

This dissertation will argue that the use of GIS techniques can extend the

range of decision support to another group of potential SDSS users, those

whose main concern is with vehicle routing problems. GIS will allow

consideration of path constraints that have not been modelled

comprehensively in the past. This group of potential SDSS users has

limited experience of using manual spatial techniques. Such users are not

usually directly interested in the spatial processing techniques provided

by the SDSS but only in the interaction of these techniques with the

OR/MS models. However, the secondary use of spatial data by the models

and the display of spatial information on the interface can greatly enrich

the decision-making process. These could benefit from the geographic

context being fully reflected in the problem representations used.

The third group of decision-makers who will find SDSS important are

those where the importance of both spatial data and modelling is

somewhat neglected at present. In disciplines such as marketing,


55

additional possibilities for analysis are provided by the availability of

increasing amounts of spatially correlated information, for example

demographic data (Mennecke, 1997). The relevance of GIS to this type of

work is becoming widely recognised (Fung and Remsen, 1997).

Furthermore, the geographic convenience of product supply relative to

customers' locations is an important tool of market driven competition.

The availability of user friendly SDSS to manipulate this type of data will

lead to more use of formal modelling techniques in this field where rather

informal techniques have been used in the past.

3.4.2 GIS as a DSS Generator

Because of the variety of decision-making situations where spatial

information is of importance, clearly SDSS will be an increasingly

important subset of DSS in the future. It is useful to examine the

relationship of GIS software to such systems. Much of the research in the

GIS domain is poorly linked to the traditional DSS literature, even

though the concepts are similar, for instance Djokic (1996) presents a

framework for SDSS similar to that proposed by Sprague for DSS.

Densham (1991) discusses the development of SDSS in the context of the

framework proposed by Sprague (1980) (Table 3-3 below). In building

DSS, specific generators have been designed for certain classes of

problem. In other situations general-purpose software such as

spreadsheets or DBMS packages have been regarded as generators. In

modern DBMS and spreadsheet software, the use of macro languages

facilitates the creation of specific applications. Various generators have

strengths and weaknesses in terms of their provision of the essential

components of a DSS: an interface, a database, and models. In the case of

a spreadsheet, modelling is the basic function of the software; various

interface features such as graphs are provided, but the database

organisation is simplistic. DBMS software, such as Access or Paradox,

has good database support, provision for interface design using forms,

report and charts, but almost no modelling support. In this case, the


56

modelling support has to be added to the specific DSS built from such a

system (Figure 3-3).

In Sprague’s framework, the SDSS builder may make use of tools that

provide some lower level data processing. In software design these might

include operations such as sorting or searching that are important

algorithms in their own right but which are not of direct interest to the

decision maker. The decision regarding the appropriate mix of DSS tools

and the use of a generator is an important component of the process of

building a DSS. However there is a very real sense in which the types of

DSS design considered for a given class of problem are a function of the

available DSS generators for that class of problem. In practice, a small

DSS project could be built, using an off-the-shelf spreadsheet or DBMS

Table 3-3 : DSS Generator Features

DSSComponent

Spreadsheets DatabaseManagers

GIS

Interface tables, forms,

charts

tables, forms,

reports

multi-layer maps, plots

Database independent cell

entries

linked database

tables

linked spatial and non-

spatial databases

Database

Tools

rudimentary sort

and selection

comprehensive

queries

spatial query

Models built in

mathematical

functions,

statistical and

OR/MS tools

basic mathematical

functions

basic summarisation and

network analysis models

Model

Building Tools

recorded or

programmed

macros

macro and database

query languages

macro languages,

programming interfaces

to other programming

languages


57

package, in less time than it would take to evaluate fully the range of

alternative methods of constructing the DSS. Therefore, the DSS

solutions actually constructed are strongly influenced by the perceived

availability of suitable generators. Consequently, the effective application

of DSS technology can benefit from additional generator software

becoming available. Awareness of the potential of the use of GIS based

systems as DSS generators will lead to problems, currently being solved

in other ways, being approached by using a SDSS.

3.4.3 Extending GIS to a broader community

The user diversity of potential users of GIS techniques can largely be

catered by a clear focus on the specific problem, rather than on the

SDSS

Spatial Data Non - Spatial Data

Data Access Tools

Models

Interface

GIS ExternalComponents

Figure 3-3 : Building a SDSS by integrating models with GIS


58

technology used. For ease of system building a DSS generator may be

used, such as a GIS, that has multiple functions. However, for any one

problem or one user many of these facilities may not be needed. Existing

design frameworks such as the ROMC approach (Sprague and Carlson,

1982) introduced in Section 1.3.3, should be used to identify the system

features of interest to the specific user. The general-purpose features of

the generator can then be customised by the system builder to provide the

representations, operations, memory aids and controls appropriate to the

problem. These may differ substantially from user to user. It is an

important characteristic of successful information systems that they

provide information in a format appropriate to the user. Different users of

a given type of information may be accustomed to quite different

presentation formats for the information. This diversity of user

requirement places important demands on the design of the components

of the SDSS, not only the interface but also the database and modelling

components (Grimshaw, Mott and Roberts, 1997).

Another issue that arises when techniques spread to a different class of

application is that distinctive nomenclature may be used in different

disciplines. This poses a problem in the context of SDSS where the

language used by geographers, which underlies the documentation and

interface paradigms for GIS software, may be quite different than that

used by potential users of SDSS. A successful system must provide

system builders with the flexibility to accommodate user preferences. The

DSS components can be configured to provide direct user access to

information of interest, while other features of the DSS provide

contextual information to enrich the decision-making process. Contextual

information can be found in the database, processed by spatial models

and displayed in an appropriate representation on the interface (Table

3-4).

If GIS software is to be seen as a DSS generator, rather than as an end in

itself, then different strategies for interface design might present


59

themselves. The aim of the system builder must be to cater for the

problem representation of the user, the logical view of the problem, rather

than provide a system too closely related to the physical geographic data.

Different users might have different system representations and

operations. This might operate in a similar way to the concept of sub-

schemas in the context of database management that provide a

distinctive presentation of a database to each user. Not all the data in the

system need be made directly available to every user. Limited access to

information may be provided if required, but the full range of GIS

operations need not be made available. Simplified information

representations, that might be appropriate for users who only indirectly

employ that information, might be inadequate for other users directly

interested in that data. Unlike earlier systems, modern DSS can utilise

richer and more complex information representations, for example GIS

based SDSS is an excellent example of this trend. This implies multiple

features at a level of detail that goes beyond that needed by any one user.

For a given user, some of these representations are directly important,

while others provide only background information (Table 3-4).

A user-based design will not impose unfamiliar control concepts on the

user. For example, a typical operation in GIS might involve selecting a

procedure from several levels of submenu. The spatial data to be used for

Table 3-4 : Contextual Information in SDSS (Keenan, 1998b)

Directly Relevant Contextual Information

Solver customised business models e.g.

marketing, routing, location

General spatial processing tools e.g.

buffering

Database data on planning units, e.g. routes,

administrative regions

Elevation data, base geographic

entities, points, arcs, polygons

Interface decision outcomes, e.g. routes, areas

of influence

Geographic features, e.g. lakes

rivers, mountains


60

this operation might be then identified by drawing a box on the screen

with the mouse. This approach presents problems for the SDSS user who

is not familiar with many of the operations provided by the GIS. A more

user-centric approach might allow the user draw the box on screen with

the mouse and then a menu would appear offering only that subset of

operations appropriate to that set of data.

Artificial intelligence (AI) techniques might be used to facilitate this

interface simplification. Such an approach might draw on systems such

as Tolomeo (Angehrn and Lüthi, 1990) and ALTO (Potvin, Lapalme et al.,

1994) discussed above (Section 2.3.2). Tolomeo allows the users describe

the problem visually and the interface includes a map that facilitates the

representation of visual features other than those that can be directly

manipulated by the user. These features provide a geographic context

within which the user specifies the problem in terms of the cities to be

visited, etc. This type of intelligent DSS interface could usefully be

incorporated in a fully-fledged SDSS to increase its acceptance to a

broader user community. One such community would be those using

OR/MS in general and routing in particular.

3.5 Current Spatial Decision Support Systems Technology

3.5.1 Suitability of GIS Software for building DSS

There is evidence that GIS software is becoming increasingly suitable for

use as SDSS generator. As GIS designers gain a greater awareness of

decision-making possibilities, their systems will be designed to facilitate

interaction with models. GIS software provides a sophisticated interface

for spatial information. Even limited functionality GIS software will

provide the ability to zoom and to display or highlight different features.

GIS provides database support that is designed to allow for the effective

storage of spatial data. Furthermore, GIS software provides a link

between the interface and database to allow the user easily query spatial

data. However, a GIS is not a complete DSS for the full range of potential


61

uses of spatial data in decision-making because of the almost complete

absence of problem specific models or support for the organisation of such

models.

The ability to integrate GIS software and models is being facilitated by

modern software techniques that allow a variety of forms of interaction

between the GIS software and the modelling software. The simplest form

of software interaction is the exchange of data. In its most basic form,

this might be achieved by a program preparing a file for subsequent use

by other software. This requires a common file format for use by both

pieces of software. Current trends favour the use of integrated databases

that can be accessed by all types of software. This has led to the use of

common standards, such as SQL and ODBC, which allow a wider range of

programs interchange data. Where databases are used, SQL has become

a standard means of sending database commands. These developments

provide an effective means of exchanging data between GIS and other

programs. For example, separate modelling programs might access a GIS

database. Given the growth in client-server systems, these data exchange

technologies will have an important role to play in the integration of GIS

into DSS.

For a comprehensive system to exist, data exchange alone may not be

sufficient. If a DSS generator is to interact with other software, it will

need to interact directly with other program components. As a DSS

generator is part of a larger system, its interaction features will reflect

the trends in software design generally. The trend in software

engineering has been to make use of self contained modules that interact

in clearly defined and controlled ways. This tendency has led to the

development of structured programming techniques and the use of

modular procedures and functions within programs. In well-designed

software each of these modules should perform a single task and have

well-defined inputs and outputs. Provision exists for these modules to be

included in program libraries that can be used by other programs. In this


62

context, GIS software can provide an application-programming interface

(API) which allows external programs interact with the GIS software.

GIS software frequently provides some type of API, and this approach has

proved useful for building SDSS. However, this approach requires the

SDSS builder to have a good knowledge of the operation and technical

parameters of the GIS software. The API approach is suitable where ad-

hoc models are being used, but is less suitable where different software

packages need to be integrated. For example, it would be difficult to build

an integrated system using GIS software with an API for the C

programming language and a modelling package with a FORTRAN API.

Using the API approach to add decision support functionality to GIS is

likely to meet the requirement for a comprehensive system, but might not

meet the requirement that a system should be quickly and easily built.

A more recent concept in software engineering is object orientation. This

approach makes use of modules (objects) which bring together both data

and the program elements that operate on that data. The advantages of

the object-oriented approach include information hiding. This means that

the system builder does not need to be familiar with the detailed

operation of the procedures or data structures used, as implicitly the

procedures are designed to work with the data with which they are

connected. This means that the object code can be used without detailed

knowledge of its internal operation. The object-oriented approach

facilitates faster application development while reducing the possibility of

errors being introduced by alteration of the programs. This approach uses

rather larger building blocks than the traditional API approach. The

object-oriented approach may prove somewhat less flexible in meeting the

needs of decision-maker and is less efficient from the point of view of

machine performance. However, for most problems it offers a quick

means of building systems.

Modern programming languages generally include object-oriented

features and GIS software may have an API that can interact with such a


63

language. The object-oriented concept has been extended to the use of

stand-alone components; these are independent of any particular

programming language. These can pass instructions and data to each

other in accordance with widely used standards. These components may

exist within a single computer or within a network. An example of this

type of technology is the Object Linking and Embedding (OLE)

introduced by Microsoft. Each component has its own data and some

documented operations on that data, commands can be sent to that

component from other programs to perform those operations. If the

industry standards are used a wide range of programs can potentially

make use of these components. Therefore a program can be written in one

of several programming languages and still make use of existing modules.

This provides a degree of flexibility not found with the API approach.

Software applications, for example spreadsheets can make some use of

these standards, allowing communication between these applications and

GIS software. The main advantage of this approach is the flexibility it

allows in the integration of different types of software (Table 3-5).

Present software development trends suggest an object-oriented future, in

which small specialised applications, or applets, will be available for use

Table 3-5 : Software integration techniques for building SDSS

(Keenan, 1998c)

SDSS buildingtechnique

modellingintegration

ease ofsystemintegration

programefficiency

separate programs, data

interchange

low high low

Application programming

interface (API)

high low high

object components e.g. OLE/OCX high high low


64

as part of a larger package. In the PC environment, the development of

such small applications will be facilitated by the use of visual

development tools. On the PC platform, the dominant standard for

applets is based on Microsoft's OCX standard. An extension of these

trends is the availability of a version of Microsoft's applet technology,

known as ActiveX, developed for use over the Internet.

At present, GIS software is often found on UNIX workstations. However,

in the future, as SDSS spreads to a broader user community, systems are

increasingly likely to be based on widely used industry standards, for

example Microsoft Windows NT. The use of OLE/OCX allows system

builders quickly build systems that concentrate on the detailed modelling

of the specific problem rather than the detail of the lower level processing

of information. Increasing connectivity will mean that these systems will

not stand alone but can connect to more powerful spatial database and

processing facilities by employing client server technology and even by

using the Internet.

3.5.2 Commercial GIS software

Within commonly accepted definitions, GIS software can be combined

with OR/MS models to build a SDSS. Technical developments are moving

in a direction that facilitates this integration. In this context, PC based

GIS products with limited functionality may prove more manageable for

applications design than full workstation based GIS systems. While these

desktop systems lack the power of a full GIS, they may be able to make

effective use of data that has been pre-processed by a full feature GIS. In

order to form the basis of SDSS, however, such systems must offer spatial

database handling with appropriate access tools. It is not sufficient

simply to employ a mapping tool that may provide simple maps, but lacks

spatial query features. The use of this type of technology offers two

possibilities. GIS software may be used for the main interface and

database facilities, using applets for additional modelling or interface

requirements. Therefore marketing or logistics models might be


65

incorporated in an OCX to be used by PC based GIS software.

Alternatively, the main application might be developed in another

programming language and OCX type applets used to provide some

element of GIS functionality. A number of GIS related tools of this sort

exist, for example Sylvan maps (Sylvan) or MapObjects from ESRI

(ESRI), the market leaders in GIS software. However, these tools have to

be assessed to establish the extent to which they provide true GIS

operations, or whether they are simply mapping tools.

The developments in GIS software since 1990 may allow the use of off-

the-shelf software as the basis for a SDSS. An example of this type of

software is the ArcView package from ESRI. As its name suggests, this

software is primarily designed as to allow the user to view and query

spatial data. ArcView has its own macro language: Avenue, which can

interact with SQL database servers, and use platform specific links with

other software. An optional network analysis package is available for

ArcView allowing its use for a variety of applications that need this

functionality, for example transportation modelling. Another widely used

desktop mapping product is MapInfo (Mapinfo). The MapInfo package

provides the Mapbasic language, which is likely to be developed to

become increasingly similar to other programming tools, such as

Microsoft Visual Basic.

TransCAD (Transcad, 1996) is a PC-based GIS designed specifically for

managing transportation data and to facilitate the use of transportation

models. As such, it is an excellent example of a potential DSS generator

as it provides a number of features that specifically support

transportation modelling. These include provision for a road network

layer, with the ability to store relevant network characteristics such as

turn penalties. The concept of a route layer is supported, allowing

multiple routes to use each road. TransCAD allows extensive tailoring of

the interface around the standard GIS components using the GDK

supplied (Geographic Information System Developers Kit). Applications


66

developed using this toolbox can communicate with external software

using the widely used DDE, OLE and ODBC standards. SDSS

applications can be built using a combination of these features, for

instance a customised interface together with the use of macros.

3.5.3 Future directions

Given the advances in IT, modern DSS can incorporate a more extensive

range of directly and indirectly relevant information. The designers of

these systems must aim to provide maximum user control over those

aspects of the decision where the user has specific expertise, while

providing the user with maximum support for areas where the user is

less expert. This may require that DSS generator software, such as GIS,

be designed to be flexible so that different types of user can make use of

the intelligence in the system for less critical parts of the decision.

This dissertation suggests, therefore, that much DSS development in the

future will use relatively complex combinations of DSS generators and

tools. A substantial variation in the types of problem and user will exist

within the general group of systems built from such generators. Spatial

systems are a good example of a class of sophisticated DSS. Such systems

have largely been used in the past for problems where the manipulation

of spatial data was the key or only information component of the decision

to be taken. This type of decision required a system that provided users

with full control over the spatial operations in the system. In the future,

SDSS use will be extended to applications where the spatial information

is only an interim stage or a subset of the information required for the

decision. Such information provides the geographic context within which

specific decisions are taken. Users dealing with this broader set of

applications need to be given control over the important variables in the

decision while other processing is performed without the need for

extensive user interaction. With the development of such systems, new

classes of decision and new types of user can be effectively supported.


67

Chapter 4 : Modelling routing problems in GIS

4.1 Introduction 1

4.1.1 GIS and routing

In Chapter 2 we discussed the development of routing DSS and saw a

number of relatively sophisticated routing systems which incorporate

geographic data and network algorithms, without using conventional GIS

software, for example GeoRoute (Georoute, 1998). Other routing systems

use GIS technology as a platform for building a routing DSS. The use of

mapping data enriches the problem representation found in these

systems. However, many routing systems that use GIS do so only to

provide map display and take little advantage of the spatial data

processing capabilities of modern GIS software. This chapter examines

the way that GIS functionality can be used to support a broader class of

routing problems.

GIS developed in a very different environment from routing DSS. Coming

from a different user base, GIS software frequently did not have any

routing capability. For example, a GIS might be capable of displaying a

road network on screen, but may not have had a road network data

structure that could be easily integrated with OR/MS algorithms. While

GIS has a recognised role in transport applications (Thill, 2000), many of

these applications do not involve network processing in the form required

for vehicle routing.

Because many potential GIS applications require the use of networks,

later products did incorporate network functionality. For example,

Arc/Info and Arcview incorporate a number of network tools. In earlier

versions of these products, the network functionality was not fully

1 A substantial part of this chapter was published in Keenan (1998a)


68

integrated with the other GIS features. However, in the current version

(Release 8) networks are a fundamental part of the product. In addition,

an increasing variety third party add-ons are becoming available.

Network utilities in most types of GIS software will provide routines for

the calculation of shortest paths. As shortest paths are the basis of

routing calculations, this functionality is of potential use. Shortest path

calculation can be enhanced by a rich representation of the road network,

with full provision for one ways streets etc. Newer software frequently

has a more comprehensive set of routing procedures. A good example of

this trend is the TransCAD GIS software (Transcad, 1996), which offers a

variety of routing tools. However, these routing tools must inevitably be

general-purpose in nature, while effective decision support requires

specific customised techniques for the problems being supported. In

Section 3.4.2 above, we discussed the use of GIS as a DSS generator for a

routing, with the inclusion of appropriate customised algorithms. GIS

products are increasingly available on inexpensive microcomputers.

These products offer significant GIS functionality at much lower cost

than traditional workstation based software. While some of these PC-

based GIS systems are less powerful than their workstation based

equivalents, the subset of functionality offered is often quite suitable for

routing applications.

4.1.2 Spatial Decision Support Systems for routing

Any examination of the role of SDSS in routing starts from the enhanced

potential for spatial data handling inherent in such systems. Traditional

routing DSS incorporates a relatively restricted range of data structures.

On the other hand, GIS allows the use of point, line and polygon

structures. The ability to store and manipulate these structures is

complemented by sophisticated editing tools allowing easy alteration of

spatial data. GIS provides various tools to allow adjacent points and arcs

be identified or to identify the areas of polygon overlay (Chapter 3).

Appropriate spatial algorithms are provided to support these facilities.


69

However, in the context of routing problems these only provide interim

data that must be utilised by the routing models. Additional routing

functionality must be added to the basic GIS to build a routing SDSS. We

can therefore distinguish between routing DSS, GIS and SDSS that

incorporate GIS and appropriate routing techniques (Table 4-1).

4.2 Information Requirements for Routing

4.2.1 Categories of routing data

In modelling routing problems, three categories of data can be identified.

Routing problems will contain data associated with locations, for instance

data relating to the depots in the problem and the customers to be

Table 4-1 : Main Characteristics of Routing Systems

(Keenan, 1998a)

Vehicle RoutingDSS

GIS SDSS

Data location co-ordinates,

true-distance matrix,

multiple vehicle

parameters

points, arcs and

polygons, complex

network data

points, arcs and polygons,

complex network data and

multiple vehicle parameters

Models customised multi-

vehicle multi-depot

routing models

general purpose

one vehicle shortest

path type models

customised multi-vehicle

multi-depot routing models

Interface

Representation

representation of

points and routes

representation of

multiple layers of

spatial data

customised subset of

available spatial data

Interface

Operations

ability to edit

parameters and alter

route sequence

map editing

facilities

ability to edit maps, routing

parameters and alter route

sequence


70

serviced. The second category of data in a routing problem relates to the

vehicles that must visit these locations. Vehicle parameters include speed

and capacity. Finally, the problem will contain a set of paths between

locations. From the paths the distances travelled and the travel time can

be derived. The vehicle routing problem can then be defined as a set of

visits by vehicles to locations along a set of paths between these locations.

Constraints in the problem will exist for locations, paths and vehicles.

Many of these constraints are independent of each other. For example, a

change in the stop time at a location may not directly affect the paths

that can be used. Other constraints are interdependent; they are affected

by the interaction between two types of data. For instance, a particular

type of vehicle may not be able to visit a certain location or use a certain

path.

Traditional views of the routing problem have tended to emphasise the

vehicle and location constraints without paying much attention to path

constraints. This chapter recommends a broader definition of vehicle

Table 4-2 : Constraints in Vehicle Routing Problems (adapted

from Bodin and Golden) (1981)

location constraints time to service a location

number of depots

nature of demands - deterministic or stochastic

location of demands - on points or arcs or polygons

operations - pickups or drop-offs

vehicle constraints number of depots

size of fleet

vehicle capacity constraints

maximum vehicle route times

path constraints underlying network - directed or undirected

time to travel a given network segment

vehicle type limitations on network segments


71

routing problems to accommodate problems where the path taken is an

important component of the problem. In such a broader context,

information factors can be usefully categorised into location, vehicle and

path data. The main constraints of interest in routing problems are

classified in Table 4-2 (also see Table 5-1).

The traditional optimisation techniques used in routing, for example

travelling salesman algorithms, consider a number of points on an XY

plane. As discussed above in Section 2.1.3, early routing software

frequently used location co-ordinates and straight-line distance was used

as a surrogate for actual travel distance. This abstraction of the problem

assumed that selection of an appropriate path was a trivial exercise. In

practice, the actual route is constrained by the need to use suitable roads.

The abstraction used does not require data on the paths used, although

the use of straight-line distance is unsatisfactory in many cases. Using

distances calculated from the road network, the true-distance approach,

reduced these problems; this approach has become an increasingly

important feature of routing DSS design, especially for arc routing

problems (see Chapter 5). Nevertheless, this approach entails greater

data requirements and a consequent increase in the sophistication of the

software used for the organisation of that data. The incorporation of

additional path data increased the usefulness of the problem formulation,

but at the cost of making the software to solve it more complex.

The traditional true-distance approach calculates travel distances in

advance of the actual routing process. This approach reduces a complex

road network into a relatively straightforward matrix of distances

between locations. However simple distance is not the only issue arising

in many types of real world problem. In practice routing problems are

frequently constrained by time rather than by distance travelled. It is

therefore important to associate appropriate speeds with different

sections of the road network. The speeds attached to the road network

may be derived from the road classification, or from measures such as the


72

number of traffic lanes. Sophisticated routing models may adjust these

associated speeds to take traffic congestion or the existence of steep

gradients. The traditional representation of distance or travel times as a

simple matrix can accommodate only a few of these extra constraints. For

complex problems, a simple matrix approach may be inadequate as it

operates on the basis that the data does not change during the routing

process. This assumption may represent an unreasonable simplification

of the real world situation.

An alternative is to maintain a comprehensive model of the road network

available for real-time calculation of travel times. In urban applications

additional concerns include one way streets, no right or left turns, and

vehicle size restrictions. In rural areas large vehicles may not be able to

negotiate all the roads in the network due to steep gradients or limited

road width. As greater detail is required, more complex decision support

software becomes increasingly justified. GIS software provides the means

to store and manipulate detailed network representation. However, the

GIS software may not have been designed to be easily used with routing

models (Ralston and Zhu, 1991). Successful SDSS implementation

requires both the availability of appropriate data and software that can

provide the relevant network representions. Detailed road network data

is not easily collected by an individual user and the necessary data may

not be available, for instance the detailed layout of grade separated

junctions (Bodin and Levy, 1994). These issues become especially

important in arc routing problems where a variety of traffic restrictions

must be modelled (Eiselt, Gendreau and Laporte, 1995b). Despite these

problems, the value of GIS is recognised as a means of representing real

world road networks and displaying them on screen. However, this

dissertation suggests that there has not yet been full recognition for the

potential of GIS for modelling new and more sophisticated types of

routing problem.


73

4.2.2 Interdependence of routing parameters

The data requirements for vehicle routing are greatly increased if the

parameters are interdependent or dependent on some other variable such

as time. For example, if traffic congestion is modelled the appropriate

speed may depend on the time of day. Other time related restrictions

might exist such as restrictions on the use of vehicles in pedestrianised

areas, where deliveries might be required to take place early in the

morning. An important class of problem where complex data interactions

exist are dynamic routing problems. In these problems additional data is

generated, in an unpredictable way, during the routing process (Psaraftis,

1995). An example of such a problem, where the location data can change,

is courier parcel collection and delivery where a request to collect a

package from a new location may arise at any time. Similarly real time

information may be obtained on the paths available for routing if

information is received on traffic congestion or road closures due to

accidents, etc. Bertsimas and Simchi-Levi (1996) discuss the modelling

issues for a number of dynamic routing problems. One example is routing

in situations where orders are received in real time.

In a review of dynamic routing, Psaraftis (1995) notes the growth of GIS

systems and GIS related technology. GPS is seen as an important

development in data collection for routing (Imielinski and Navas, 1999).

GPS allows the collection of point and time data, either as single data

points or as a stream of data. A GPS installed in a moving vehicle can

collect continuous data on the vehicle location and the time that it

reached those locations. This is valuable both for data collection in

advance of route optimisation and for validation of the routes produced

(Table 4-3).

The increasing availability of digital geographic data has prompted the

development of a variety of systems for vehicle guidance, and GPS plays

an important role in these. This class of problem, where real time

information is used, requires a routing system that can work in real- time


74

with all the detail involved, as pre-processing of data cannot readily be

used.

Complex interactions between vehicle parameters and paths may mean

that fully loaded vehicles cannot use all the segments of a network, due to

steep gradients or because of weight limits on bridges, etc. Therefore, a

situation may arise where a vehicle can use a certain route on its return

journey when empty, but not on its fully laden outward journey. In this

situation, the road network cannot be pre-processed easily into a simple

distance matrix; instead the interactions between vehicles and paths

have to be incorporated in the vehicle routing model. This requires the

use of to appropriate routing algorithms and a sophisticated road network

representation. The use of these more sophisticated models places

increasing demands on a DSS designed to incorporate them. These

requirements arise largely from the need to provide additional geographic

Table 4-3 : GPS applications in routing

Data Type Typicalapplication

Point Data Customer Location

Streaming Data Identification of road segment

length

Pre-Optimisation

(data collection)Time related data Identification of speed per road

segment

Point Data Data revision

New customer data

Streaming Data Route length validation

Post-Optimisation

(routevalidation) Time related data Time window validation


75

information in the database and interface, to support the use of this

geographic data in more realistic models.

The combined location-routing problem is a second form of real world

problem where the geographic parameters are interdependent. Location

problems are complex in themselves and are an existing area of

integration of modelling techniques and GIS (Ding, Baveja et al., 1994).

Many types of problem require both a location phase and a routing phase;

these can usefully be combined into a more complex model. In such

problems, the total demand or supply in the problem needs to be allocated

to a limited number of locations. Vehicle routes are then generated to

visit those locations. Location-routing problems are very relevant to arc

routing, for example in urban postal delivery (park and loop). This

problem arises where the postman must collect his post from a parked

van and service a series of arcs from that point (Bodin and Levy, 1991).

Traditionally these problems had a number of depots with the objective to

associate customers with depots and generate routes to visit those

customers. In addition to these, however, there are some situations where

the initial phase of the problem is an allocation of demand to delivery

locations. In many real world problems, the actual demand is distributed

over a larger area than the actual location where delivery/collection takes

place. For example in public transport routing, a bus stop on a main

street will service people travelling to a segment of that street and to

segments of neighbouring side-streets. Customers will walk from the area

serviced to the bus stop (Figure 4-1). The location of the bus stops is in

itself an important problem that affects the routes generated. The

location to be visited, the bus stop can be represented as a point.

However, the actual demand is distributed on another type of location, for

example an arc or a polygon.


76

In such a problem there may be a series of potential feasible locations

only one of which will be used in a given area, this may be modelled as a

generalised travelling salesman problem (Laporte, Asef-Vaziri and

Sriskandarajah, 1996). A complete solution of the location-routing

problem will require the allocation of the total travel demand in a town to

a limited number of service locations which are then routed (Figure 4-1).

An example of this type of application is school bus routing which has

long been of interest in the OR/MS field (Chapleau, Ferland and

Rousseau, 1985). School bus routing has also been seen as an application

of GIS techniques (Cortez, Meek and Koger, 1994; Braca, Bramel, Posner

and Simchi-Levi, 1997).

A related problem might arise with convenience shops that provide

customers in their local area with everyday purchases such as

newspapers or bread. These shop locations can be modelled as a point in a

routing delivery problem. However some routing problems might be

concerned with identifying an appropriate subset of shops to visit,

estimating their potential sales from population data. These types of

Figure 4-1 : Area served from bus stop will include

neighbouring streets.


77

problems can be approached on a two-phase basis, with the allocations

being processed first and the routing completed as a separate stage.

However, this may lead to unrealistic representations of the problem.

Comprehensive modelling of such a problem requires that a model be able

to evaluate trade-offs between the location and routing phases of the

problem. A decision support system for such modelling must be capable of

representing the interactions between these differing types of location

(Figure 4-2).

The scale of the geographic area of interest in a routing problem may also

differ greatly. Routes may service an area comprising several thousands

of square kilometres. In other cases the area to be covered by the route is

much smaller, for example an urban parcel delivery route. In problems

where only a small area is of interest, the detailed geography of the area

becomes a significant issue. In general, modelling urban applications will

require additional attention to geographic parameters. As greater detail

is required, more complex decision support software becomes increasingly

justified.

Figure 4-2 : The total service area is mapped on to a limited

number of locations.


78

For some classes of routing problem, for example public transport

scheduling, the data required for the problem may be available from

public sources. For instance, the census of population might provide a

means of estimating demand for a variety of routing problems. Much of

this information is associated with spatial units, such as administrative

districts, rather than directly with the network. This requires that

population associated with arcs or polygons is allocated to points, for

example such as rapid transit stations, which are then visited by routes.

For some problems, routing makes use of data on geographic objects other

than the road network. An example might occur in census enumeration,

where an enumerator wishes to complete visits in one census district

before moving on to the next one. In a postal delivery problem, the postal

addresses may be based on street or district names. In a postal problem,

the quantities of letters to be delivered may be derived from population

data based on these districts. This requires a system that can manipulate

polygon data effectively.

4.2.3 Spatial interactions in routing problems

In representing the vehicle routing problem in a DSS, three classes of

data have been identified, data relating to locations, data relating to

paths and data relating to vehicles. The first two of these data types,

locations and paths, are inherently spatial in nature. GIS has the

appropriate database tools to store and manipulate sophisticated

representations of the locations and paths found in complex routing

problems. Therefore, a DSS incorporating GIS techniques can facilitate

problem solving for more complex real world problems.

We would suggest that GIS based systems are needed where data

associated with locations and paths is complex. This is especially true

where elements of the data are interdependent rather than entirely

independent, for instance where the location or path constraints depend

on time or on the parameters of the vehicles in the problem.


79

The data requirements for the representation of routing problems are

therefore increased if pre-processing of paths into a simple distance

matrix is not possible. This situation occurs where there are multiple

path constraints or where the path constraints are not constant but are

dependent on time or on changing vehicle or location parameters. Some

well-known routing problems fall into this category, primarily the arc

routing problems that are the subject of this dissertation. For these

problems the network itself is the object of the routing process and a

detailed network representation is therefore required.

Table 4-4 : Types of Location Data

Data Types Type of Problem Example

Basic Types point traditional delivery

problems

delivery from warehouses to

shops

arc arc routing postal delivery

polygon generalised TSP post-box collection

Data Inter-

dependencies

predictable

variation by time

differing volumes at

different times

milk collection

dynamic

generation of

locations

real time data

generation

"dial-a-ride" problem

interaction with

vehicle

parameters

continuous demand,

intermittent vehicle

service

refuse collection - volumes

depend on time since last

collection

interaction with

path parameters

location - routing

problem

public transport routing with

siting of transit stops


80

Table 4-4 indicates some of the types of location data encountered. Those

routing problems with data interdependencies require additional

complexity in system designed to support. Traditional techniques have

neglected the importance of path constraints, where interdependencies

occur between paths and other aspects of the problem (Table 4-5) a more

complex problem results.

One example of a routing problem with potentially complex interactions

between paths and location parameters is hazardous goods routing, for

example the transport of toxic waste or nuclear materials. Routing for the

transport of hazardous goods may wish to avoid certain areas, such as

environmentally sensitive areas, roads with steep gradients, or areas

with bad weather conditions. Hazardous waste routing problems are

documented both in the GIS literature (Freckmann, 1993) and in the

OR/MS literature (Beroggi, 1994). Erkut (1996) notes the potential

contribution of DSS and the importance of GIS in this field.

Routes generated for hazardous goods might wish to avoid populated

areas, while at the same time remaining within a specified distance of

Table 4-5 : Types of Path Data

Data Types Type of Problem Example

Basic Types planar XY co-ordinate distance ship routing at sea

network constrained true-distance approach urban delivery over

street networks

Data Inter-

dependencies

variation by time different speeds in rush

hour congestion

urban courier delivery

interaction with

location parameters

paths avoid objects ship routing in relation

to islands

interaction with

vehicle parameters

vehicle load restrictions weight limits on bridges


81

emergency facilities (e.g. fire stations). In such situations vehicles may be

required to travel on network constrained paths and to maintain a

certain straight-line distance between the vehicle and point or polygon

locations. Such vehicles might also wish to remain within a certain road

distance of emergency facilities (Figure 4-3). This problem might be

further complicated by the existence of time constraints that limit the

times at which these hazardous products might be transported, for

example avoiding periods when roads are congested. Hazardous materials

routing may need to respond to adverse weather conditions, such as

snowstorms; DSS can help schedulers make these changes (Beroggi and

Wallace, 1994). A GIS based system could model the path of such a storm,

exploiting real time meteorological data.

An example of interaction between paths and locations is security

patrolling around a sensitive installation, such as an airport. This might

require patrols on roads near to the airport. The precise security risk of a

section of road would be influenced by factors such as its distance from

the installation, which might be the irregular boundary of a large airport.

Location to be avoided

Figure 4-3 : Network constrained route avoiding passing

within a certain distance of a point location.


82

Other factors such as elevation or sight lines to the installation could be

considered. The actual patrols might take place using road vehicles which

are constrained to use the road network, while the region to be patrolled

is derived from the polygon location of the airport (Figure 4-4). The

routines could provide a measure of the need to patrol each road section

and an appropriate arc routing algorithm could be used to design routes.

A system to support such a routing process would need to be capable of

working with multiple interactions between the data structures in the

problem.

Another important class of routing problems, where these techniques are

very relevant, are emergency evacuation applications. These applications

may be concerned with evacuation from an area close to a fixed location.

In many cases potential disaster situations can be simulated for

evacuation planning purposes, for example around a nuclear power plant

(Hobieka, Kim and Beckwith, 1994).

SensitiveInstallation

Figure 4-4 : Patrol area around irregular boundary of sensitive

installation


83

Other evacuation situations arise in dynamic conditions; for this type of

problem the design of the routes may be strongly influenced by

geographic features. If a flood or earthquake has taken place, many of the

potential routes may pass through areas rendered unsafe by the disaster.

The extent of the danger may be calculated by the GIS by reference to

geographic data and the suitability of particular road segments can be

derived from this (de Silva, Gatrell, Pidd and Eglese, 1993; de Silva and

Eglese, 2000). For example, routes may be required to allow emergency

services visit buildings in the path of a forest fire. The sequencing of such

routes would be largely determined by the need to visit those in most

danger. This situation could be modelled on a GIS based system, using

data on elevation, type of vegetation, etc. Therefore, effective decision

support for this type of problem might benefit from a combination of GIS

and routing techniques. Such a system would allow interactions between

population data, elevation data and location data be modelled. Recent

work in this area (Patel and Horowitz, 1994) utilised GIS software to

derive an approximate measure of risk at different points in a road

network. This network was then used with OR/MS algorithms to evaluate

the minimum risk path through the network. Although this paper does

not address all of the geographic features of the problem, it indicates the

potential usefulness of a combination of GIS and routing techniques.

However, we are not aware of any existing examples of a comprehensive

combination of GIS and OR/MS techniques in a SDSS for this type of

problem.

4.3 The Role of GIS in Supporting Routing Problems

4.3.1 Routing problems supported by traditional DSS

The contribution that GIS techniques can make to a routing DSS will be

small for problems that have no great spatial content. This is especially

true if they are largely concerned with internal data and therefore have

few geographic parameters. Such problems might include many of the

delivery problems addressed in the vehicle routing literature. In such


84

problems, the schedules may be tightly constrained by non-geographic

elements such as time windows. Some type of GIS software might be used

to provide an attractive on-screen mapping facility, but the database and

spatial query capabilities of the GIS will have little role to play.

One example of such a problem is that of fuel delivery. A variety of

problems are documented in the literature where a multi-compartment

tanker is used to service customer orders of different sizes. The vehicle

may be required to carry a number of different types of fuel such as

different octane grades, unleaded or leaded, heating fuel, or diesel. In

some countries differences exist between fuels for tax reasons, for

example in Ireland diesel for agricultural use is taxed less than that for

road vehicles. A fuel tanker can typically service only a small number of

orders per trip, as few as three or four deliveries per trip. The vehicles

used for fuel delivery will typically have a number of compartments;

orders will have to be allocated to these compartments without mixing

different types of fuel. As different fuel types cannot be mixed, and as

there are only a small number of points to be delivered, the efficient

packing of the vehicle is the most important consideration. For this type

of problem a graphic interface is hardly needed, the quality of solution

being largely determined by the algorithm used. This group of problems

has long been of concern to researchers in OR/MS (Önal, Jaramillo and

Mazzocco, 1996).

For problems that have few geographic parameters, a graphic interface is

clearly useful if there are a large number of delivery/collection points.

However such an interface need not include a great deal of geographic

information and need not be as complex as a GIS. Problems that fall into

this category include the large number of routing problems that are

concerned with delivery of parcels, supplies, etc. to a set of specific

customers.

The spatial complexity of such problems is largely determined by the

number of customers to be delivered, as geographic features other than


85

the location of customers are not relevant. The complex nature of these

problems means that routing models can be of assistance. However, the

large number of routing possibilities increases the difficulty of the

problems, for example large travelling salesmen problems. Therefore,

suitable algorithms and a facility to modify the routes using a graphic

interface are required. However, the visual component of the interface

and the database component need not include a large number of

geographic features. Commonly used interactive vehicle scheduling

software is well suited to solving this group of problems.

4.3.2 Routing problems requiring GIS support

Routing for standard delivery problems in geographically compact

regions, such as urban areas, requires additional attention to geographic

features. In this case, one-way streets, no left or right turns, traffic

congestion, etc., will have an important part to play. These additional

requirements indicate that a more sophisticated support system is

appropriate. Such a system requires the ability to store and display the

level of detail appropriate to the problem. Therefore, while many routing

problems are straightforward on a regional scale, at a detailed urban

scale more information is needed and therefore GIS based techniques will

be more useful.

For some types of routing problems, additional geographic parameters are

introduced by the fact that the relevant data for the problem is largely

external. Relevant external data will usually include population data,

including socio-economic data for that population. For instance, a

marketing research project may require researchers to visit a number of

locations. The route generated will largely be determined by non-spatial

considerations such as structuring the age or socio-economic groups in the

sample. For such problems a traditional GIS may be useful, but

sophisticated routing techniques are probably not needed. Problems of

this type are frequently addressed by people with GIS expertise, with

little explicit use of operations research techniques. There is an


86

increasing trend for network analysis tools, for example shortest path

algorithms, to be included in GIS software. These tools allow useful

analysis but are not complete routing algorithms.

For problems that are spatially complex and have a number of geographic

entities involved, this dissertation suggests that the use of a SDSS is

appropriate. Such a SDSS would combine appropriate algorithms with

that subset of GIS data that is pertinent to the problem. Population data

is relevant to most problems for which a SDSS is appropriate. However,

other information found in a GIS may be relevant, including the existence

of geographic features such as mountains, lakes and rivers. Complex

interactions between these features and the road network may have to be

modelled for some types of routing problem. The potential contribution of

GIS software is great because of the facilities for database interactions

between different geographic features found in this software. This

dissertation suggests that a SDSS with both GIS techniques and

sophisticated vehicle routing models is needed for this type of problem.

4.3.3 Spatially complex routing problems

SDSS based systems will provide an important contribution in any

situation where routing, and the road networks used for routing, needs to

be related to other geographic features. Tourist routing may aim to

design routes with the maximum scenic value or with a desired mixture

of sights (van der Knapp, 1993). These routes would require interaction of

a routing algorithm with data on elevation, type of vegetation, location of

rivers and lakes, etc.

An example of routing applications with potentially complex interactions

between spatial parameters might exist in the military field. Military

applications typically make use of off-road vehicles. While such vehicles

are in principle capable of straight-line travel over all terrain, the actual

ground conditions greatly affect the speed at which such vehicles could

travel. Military applications might involve a desire for vehicles to travel


87

on high ground to gain a commanding position or to travel below the

horizon to facilitate concealment (Rasmussen, 1997). A GIS based system

with the ability to handle elevation data could provide the necessary

routing support environment for such an application.

Agriculture and forestry provide examples where GIS and routing

techniques might usefully be combined; Martell (1998) notes the

relevance of GIS to the use of OR/MS in forestry. Agricultural routing

problems provide an example where complex interaction may take place

between the routes and various geographic features. A variety of

agricultural and forestry routing applications might use off-road vehicles.

These vehicles might be capable of low speed travel across fields, and

higher speed travel on roads. The routes provided would have to optimise

the point at which the off-road vehicle rejoined the road. A GIS could

calculate the quantities of product to be transported by reference to

measures such as crop yield per hectare. A GIS based system could model

travel speeds for such vehicles taking into account gradients, various

types of ground conditions and the existence of obstacles. The ground

conditions or gradient might influence the type of crop planted, which

would determine the quantity of product to be removed from the fields.

The type of crop planted might alter ground conditions sufficiently to

significantly change the speeds of the vehicles, for example if the ground

was ploughed. Therefore routing for this type of problem would involve

many geographic parameters and complex interactions between them.

Such a problem could only be approached by an effective synthesis of

routing algorithms, and a DSS based on GIS techniques. As far as we are

aware, there are no examples of the use of GIS techniques and routing

algorithms to provide comprehensive decision support for a problem of

this complexity.


88

4.4 Implementing routing SDSS

4.4.1 Data requirements for routing system implementation

The starting point for a system builder considering the relevance of SDSS

techniques to routing DSS is to evaluate three factors. Firstly, the nature

of the input data used in the problem, to what degree is this spatial in

nature? Then consider the spatial content of the processing operations

required and the nature of the output data. Any problem may be

considered in terms of the location, vehicle and path constraints

identified above (Table 4-2). A problem dominated by vehicle and point

location constraints, e.g. loading restrictions, time windows, may not

need spatial techniques. However, the existence of arc or polygon-based

locations, or complex path constraints, indicates a need for GIS

techniques. The routing algorithms used will be largely determined by

the nature of the locations and the vehicle constraints in the problem.

The designer of a SDSS for vehicle routing faces problems reconciling the

different traditional approaches to data between that found in GIS and

that found in the routing software. In a routing SDSS, sections of the

road network will have a traditional role as components of a graph; this

representation will be used for algorithmic purposes. For spatial

processing purposes, the road network must also be seen in relation to

other spatial features. For example, administrative boundaries and

contours might exist independently of the road network. However, the

GIS environment represents the use of road networks from a very

different point of view than does traditional OR/MS software. Therefore,

one obstacle to the development of a SDSS is that GIS software does not

always characterise road networks in a way that facilitates their use by

routing algorithms (Ralston and Zhu, 1991).

As GIS use increases, comprehensive integrated databases of road

networks will become available, for instance the databases for many

countries provided by Navtech (1999). In Ireland road network data is

available from both public sector and private sector sources (Gamma;


89

IRIS). These can be used in a variety of routing and vehicle navigation

applications (Cova and Goodchild, 1994). These databases will contain

data from different sources and will require some reorganisation to be

entirely suitable for routing programs. The interest in automated car

guidance systems has led to research into the more realistic modelling

road networks (Newcomb and Medan, 1993). Other researchers (Portier,

Berthet and Moreno, 1994) have examined the use of shortest path

algorithms on complex road network representation.

4.4.2 Using GIS data in routing DSS

Decision-making in a DSS is a combination of modelling and user

judgement, requiring the SDSS system builder to identify the role played

by spatial data for both the models and the users. Traditional routing

algorithms do not require much of the data stored in a GIS. Decision

support might be better enhanced by the provision of additional

geographic data for use directly by the user, rather than the introduction

of ever more complex mathematical techniques. The simplest and most

common integration of geographic data and routing is to provide

additional information to the decision-maker, without necessarily

incorporating that data in models used. For example, a map might be

displayed on screen, providing the decision-maker with information about

features that are not explicitly used by the models. This map could

display the routes generated against a background of natural features

such as rivers etc., which help orientate the decision-maker.

This type of system may be largely designed as a traditional routing DSS

with no direct interaction with the GIS database. A routing sequence is

produced as a succession of points in the GIS and these can be displayed

on screen. The only user interface feature required is likely to be the

querying of routes and the insertion and deletion of customer locations.

This functionality can be added by using the graphics features in modern

programming languages (Fölsz, Mészáros and Rapcsák, 1995). However,

it is likely to be more efficient to use existing software for the display of


90

maps (Tracey and Dror, 1997). For the situation where spatial features

are not used by the models a mapping toolbox, rather than a

comprehensive GIS, is likely to be the basis of such a DSS. Systems of

this level of complexity are likely to become standard in the future, as

they will take advantage of improved computer graphics and the

availability of additional mapping resources. However, such systems

would not constitute a fully-fledged SDSS.

The presence of complex path constraints requires that the models

require input data from the GIS database. This requires a degree of

integration sufficient to allow the GIS database provide the data for the

routing problem, in particular the distance data. Such integration would

be greatly facilitated by the use of GIS software with the software

features to support the use of route structures or distance matrices.

Appropriate GIS software would allow such issues as one way streets and

turn restrictions be modelled. In many cases spatial data is needed at the

input and output stage but no spatial processing is required. This could

be achieved by a three-phase operation. Initially data might be extracted

from the GIS to form a distance matrix. The routing algorithms could

then solve the problem without reference to the GIS, and the completed

routes could be displayed on a map on the screen.

If a static set of points is involved then the operational routing system

might not require a comprehensive GIS at all. Instead, a GIS could be

used to build the distance matrix, which could then be used by a system

not directly connected to the GIS. A mapping program, rather than a

comprehensive GIS, could then display the proposed routes. If the system

is built within a GIS, the modelling programs only require access to the

database, perhaps through technologies such as open database

connectivity (ODBC). In this case, the modelling routines could be run as

external programs from within the GIS, with both the GIS and the

models sharing the database.


91

Where there is a dynamic component to the path or location data, or there

are complex interactions with vehicle data a true SDSS is needed. This

would require that that the routing models make use of spatial

processing, requiring interaction with the spatial data handling features

of the GIS. This would mean that the routing algorithms would

dynamically seek complex data sets from the database, requiring the use

of GIS operations to build this data. This would require that the

modelling routines dynamically call spatial data handling routines within

the GIS. Therefore, the software techniques used must be capable of

accommodating this form of connection between the programs. Table 4-6

indicates the type of operations that must be implemented in a SDSS for

an agricultural routing problem requiring SDSS techniques.

SDSS applications entail a greater diversity of modelling approaches

than traditional vehicle routing applications. Therefore, SDSS routing

Table 4-6 : Example of an agricultural routing SDSS

Objective Actions Required SDSS technique

identify collection

points

identify convenient locations

on roads for collections

associate polygon volumes with arcs

on road network

build routing problem identify quantities to be

transported

calculate polygon areas in database

and derive volumes from these

build road network generate distance/ travel time

data for use by mathematical

procedures

standard GIS operation called

within macro

establish routing

parameters

enter speed, capacity etc. user intervention using form

interface

route vehicles apply routing algorithmf customised routing model calling

SDSS routines as appropriate

refine solution interactive user modification of

routes

Display routes in GIS interface,

user alterations lead to dynamic

recalculation of volumes


92

software will employ classic techniques, such as the travelling salesman

and linear programming approaches, in conjunction with techniques

drawn from other fields. These fields might include risk analysis, which is

especially relevant to hazardous materials transportation (List,

Mirchandani, Turnquist and Zografos, 1991). Modelling approaches

drawn from the GIS environment will need to be used in addition to the

traditional techniques used in the routing domain. While dealing with

broadly the same set of data these different approaches may have quite

different problem representations, presenting the system builder with

significant problems. The construction of a SDSS will require an effective

synthesis of these diverse techniques and the data needed to support

them.

4.5 The future of GIS and routing

4.5.1 Types of Routing Software

This chapter has looked at routing problems in terms of the geographic

complexity of the problem and has suggested that a richer set of routing

problems can be modelled by incorporating more geographic data in

routing problem formulation. This diverse range of routing problems will

require different software tools for decision support. Those problems that

have few geographic parameters can be supported using traditional

decision support system software for vehicle routing. These traditional

problems will typically involve only point and arc data, without the use of

polygon data, and will have few path constraints. Those problems that

have complex geographic interactions require a SDSS for maximum

decision support.

Table 4-7 outlines the main features of problems that can be supported

using the different types of software available. In general, traditional

interactive DSS applications will have greatest application where the

number of spatial interactions is high but few different types of

geographic data are involved. A GIS based system will be of greater use


93

for problems that have a larger number of geographic parameters.

Problems with many geographic parameters may be approached using

conventional GIS tools, if there are not a large number of spatial

interactions taking place. Where problems require the use of vehicle

routing models, then SDSS functionality is needed. The growth of GIS

based decision support for routing will be enhanced by the growing

interest in arc based routing problems that tend to involve more

geographic data.

4.5.2 The use of GIS for routing

GIS is increasingly being seen as a technology relevant to routing. Recent

surveys of routing software (Hall and Partyka, 1997; Partyka and Hall,

2000), in a practitioner orientated publication, included information on

the ability of the software to interact with GIS. Most of the routing

software packages had some ability to interact with GIS, the most

popular GIS tools being Arcview and MapInfo. However, it seems likely

that the degree of interaction between the routing software and the GIS

functionality is currently rather less than the maximum potential

identified above.

Table 4-7 : Support Requirements of Routing Problems

Problem Characteristics Problem Examples Software Required

Model

few geographic parameters,straightforward paths, smallnumber of locations pervehicle

problems mainlyconstrained by non-spatial factors e.g.loading constraints

numerical optimisationsoftware, little need forspatial interface

Intensive few geographic parameters,many potentialcombinations of vehicle andlocation.

delivery problemsover regional areas

interactive routing

Data

many geographicalparameters, complex paths,few combinations of vehicleand location

path finding problems,public transit routing

GIS

Intensive multiple interactionsbetween path, vehicle andlocation constraints

urban routingproblems, arc routing

SDSS


94

In the academic sphere, in recent years, a number of GIS based

applications have been described at OR/MS conferences and in OR/MS

journals. These applications typically emphasise the value of GIS as a

means of providing a visual map display on screen and as a means of

storing data. For example, in a health care worker routing application

(Begur, Miller and Weaver, 1997), the comprehensive restructuring of a

Proctor and Gamble’s logistics (Camm, Chorman et al., 1997) or the

technician routing application at Sears (Weigel and Cao, 1999). In

general, this class of applications does not appear to exploit the

opportunities for spatial processing and richer path modelling outlined in

this chapter.

This chapter has identified the role of GIS techniques in modelling a

richer set of routing problems. This dissertation has looked at a broad

spectrum of routing problems with respect to three types of constraint;

locations, paths and vehicles. This dissertation has suggested that the

first two of these are inherently spatial in nature, and that path

restrictions have been given less attention in traditional routing

applications. The arc routing problems that are discussed in this

dissertation must, by definition, consider paths. This section has

identified some of the interactions that can take place between these

different types of spatial parameters. The incorporation of routing

techniques into GIS would allow the building of a SDSS. This dissertation

has identified the class of problems where we believe that a SDSS may

contribute. Such a system would incorporate elements of a GIS with

appropriate OR/MS techniques.

Existing work in the GIS and OR/MS fields have concentrated on

different aspects of the routing problem. OR/MS researchers have

developed sophisticated algorithms to deal with various vehicle and

location constraints while paying less attention to path constraints. GIS

researchers have developed techniques to represent different types of

location and networks and to generate appropriate paths through these


95

networks. This dissertation suggests that a well-integrated combination

of GIS and OR/MS techniques would facilitate decision support for

problems with complex path restrictions and multiple vehicles. This

includes arc routing problems, including the large sparse network

problem, discussed in Chapter 7, that forms the primary focus of this

dissertation.


96

Chapter 5 : Arc Routing Problems

5.1 Routing Problems

5.1.1 Background

Routing problem definitions include reference to the types of vehicles

used, the types of products carried and the types of road networks on

which the vehicles must travel. In OR/MS the mathematical description

of road networks is drawn from graph theory and routing problems form a

subset of graph theory problems (Evans and Minieka, 1992, Ch. 8, 9 ). An

undirected graph (simply graph) G is an ordered pair (V; E) consisting a

non-empty set of V vertices (nodes) and E edges (arcs) linking them. Arcs

are of the form (i, j) from vertex i to vertex j. The number of arcs from a

vertex defines the degree of a node. We refer to a node as odd or even if its

degree is odd or even. A path exists between two nodes u and v if a

sequence of arcs exists, possibly through other nodes, which would allow

a vehicle pass from u to v.

5.1.2 Types of routing problem

Routing problems come in a number of forms, a widely used classification

is that of Bodin and Golden (1981) (Table 5-1). In its basic form, a routing

problem requires the visiting of a sequence of locations with minimum

distance travelled. Where the locations to be visited are points (nodes),

this is a Node Routing Problem, the best-known example of which is the

Travelling Salesman Problem (TSP). This class of problem has been

intensively researched.


97

Table 5-1 : Classification in Vehicle Routing and Scheduling

(Bodin and Golden, 1981).

A. time to service a particular node1. time specified and fixed in advance2. time windows3. time unspecified

B. number of domiciles 1. one domicile 2. more than one domicileC. size of vehicle fleet available 1. one vehicle 2. more than one vehicleD. type of fleet available 1. homogeneous case 2. heterogeneous caseE. nature of demand 1. deterministic 2. stochasticF. location of demands 1. at nodes (not necessarily all) 2. on arcs (not necessarily all) 3. mixedG. underlying network 1. undirected 2. directed 3. mixedH. vehicle capacity constraints 1. imposed - all the same 2. imposed - not all the same 3. not imposedI. maximum vehicle route-times 1. imposed - all the same 2. imposed - not all the same 3. not imposedJ. costs 1. variable or routing costs 2. fixed operating or vehicle acquisition costsK. operations 1. pickup only 2. drop offs only 3. mixedL. objective 1. minimise routing costs incurred 2. minimise sum of fixed and variable costs 3. minimise number of vehicles required


98

The problem of traversing all road segments (arcs or links) in a network

while minimising the total distance travelled is an Arc Routing Problem,

known as the Chinese Postman Problem (CPP). The General Routing

Problem (GRP) is a generalisation in which the TSP and CPP are special

cases (Lenstra and Rinnooy Kan, 1976). In the GRP, we require a

minimum cost cycle that visits a set of required nodes and traverses a set

of required arcs. Research continues in the GRP to identify a unifying

framework for routing problems (Letchford, 1999; Ghiani and Improta,

2000).

In practice, the vehicles used have a limited capacity in terms of the

volume carried or the maximum time of the journey, therefore most

routing problems are said to be capacitated. A capacitated node routing

problem is usually known as the Vehicle Routing Problem (VRP). This

type of problem has been very extensively researched, as can be seen in

Laporte and Osman’s survey review (1995). Where arcs rather than nodes

must be visited, we have the Capacitated Arc Routing Problem (CARP).

This is a much less thoroughly researched field than that of node based

problems. However, many practical problems can be best represented by

CARP rather than VRP formulations. Obvious examples include postal

delivery, refuse collection, and snow removal. Other examples include

meter reading, inspection of electrical cables, and distribution of animal

feed. In 1995, two surveys of the arc routing field appeared which provide

many examples of applications. One a review of postman problems

(Eiselt, Gendreau and Laporte, 1995a; Eiselt, Gendreau et al., 1995b), the

other (Assad and Golden, 1995) a comprehensive review of the arc routing

field. The latter provided a good overview of routing problems generally.

5.1.3 Problem complexity

Combinatorial optimisation problems come in two varieties; those which

can be solved in time bounded by a polynomial in the input length, and

those for which all known algorithms require time which, in the worst

case, is exponential in the input length. Most exponential time


99

algorithms are merely variations on exhaustive search, whereas

polynomial time algorithms generally exploit some deeper insight into the

structure of the problem. Exponential time algorithms are generally not

regarded as "good" because of the speed with which the computation

times rise as the size of the problem increases. A problem is then said to

be intractable if no polynomial time algorithm can be found for it.

In assessing the solution time of algorithms, those that can be solved in

worst-case polynomial time are known as P-Problems (e.g. an Euler tour).

If the input is of size n, the running time must be O(nk). Note that k can

depend on the problem class, but not the particular instance. The

problems in complexity class P are called tractable. The class of decision

problem that has solutions than can be verified in polynomial time on a

non-deterministic computer is known as NP. These problems form a

subset of the general class of combinatorial problems. It has been shown

that a large number of problems have this property of being the "hardest"

member of NP. These problems are known as NP complete. Garey and

Johnson (1979) list over 300 problems in this class. Routing problems are

generally NP complete (Lenstra and Rinnooy Kan, 1981). This implies

that the number of computations required to solve a problem grows

exponentially with a parameter of the problem, for example the number

of nodes or arcs in a network. This makes it unlikely that an algorithm

can be devised which is guaranteed to give the answer in a time that is

polynomial in the size of the problem.

While a general algorithm cannot be devised to solve the full range of NP

complete problems, special cases may be solved successfully. A variety of

stratagems has been used to devise algorithms that solve special cases of

these problems. These specialised approaches have facilitated the

solution of some particular large TSP problems to optimality. Capacitated

problems are much more difficult to solve than the classical TSP. For

many practical routing problems, only heuristic solutions can currently

be used. These provide good, but not optimal, solutions.


100

5.2 Arc Routing Problems

5.2.1 The Chinese Postman Problem

The problem of visiting a sequence of arcs has long been of practical

interest and was the subject of much early study. The famous

mathematician Leonhard Euler (1707-1783) first addressed the problem.

Euler was the most prolific mathematical writer ever, finding time (as

well as having thirteen children) to publish over eight hundred papers in

his lifetime. During his travels between Russia and Berlin, Euler visited

the Prussian city of Königsberg (since the Second World War the city is

called Kaliningrad and is part of Russia). The city was divided by the

river Pregel into four separate parts (Figure 5-1) linked by seven bridges.

Euler became interested in the local challenge of crossing each of the

bridges exactly once and returning to the place you started from. Euler

identified that it was only possible to cross a network of bridges if all the

landmasses have an even number of bridges or exactly two landmasses

have an odd number of bridges. As this was not the case in Königsberg,

Euler showed that it was not possible to cross each bridge exactly once.

A

B

C

D

Figure 5-1 : The Königsberg bridge problem (Euler, 1736)


101

The CPP is so called because of work by the Chinese mathematician

Kwan Mei-Ko, who worked for the postal service during the cultural

revolution. On his return to academia, Kwan wrote a paper on the

problem (Kwan, 1962). The CPP is simply stated as follows: “A postman

has to cover his assigned segments before returning to the post office. The

problem is to find the shortest walking distance for the postman”.

Formally this class of problem is defined on a graph G=(V,A) where V is

the vertex set and A is the arc set. Associated with the graph G is a non

negative cost matrix Cij, giving the weight of the arc from vertex i to

vertex j. If each node in the network has an even number of arcs (nodes

are of even degree), then a postman tour can be directly generated. If this

is not the case, and some of the nodes have an odd number of incident

arcs, then there must be at least one additional traversal of an arc

already visited. These redundant arc traversals serve to make each node

of even degree (Figure 5-2) in the enhanced graph G′. By definition, the

CPP visits all arcs at least once, the object of any solution procedure is to

minimise any additional traversals. Kwan proved that a necessary and

sufficient condition for the optimality of a Eulerian tour on G′, is that not

more than two edges link any vertex pair, and that the length of the

added edges on every cycle does not exceed half the length of the cycle.

A solution to the CPP may be found by adding additional traversals

between the nodes of odd degree. Edmonds (1965) recognised that the

A B

C D

E F

G H

A B

C D

E F

G H

Figure 5-2 : Graph with four odd points (C,D,E,F) and addition of

redundant arcs to make all nodes even (Kwan, 1962)


102

most efficient set of traversals, as defined by the distances in Cij , may be

identified by solving a Minimum Cost Perfect Matching (MCPM) problem.

Efficient MCPM algorithms exist which can solve the problem in

polynomial time, the best-known approach is the algorithm by Edmonds

and Johnson (1973). Further research has taken place into near optimal

techniques (Avis, 1983) and faster optimal implementations (Cook and

Rohe, 1999). Consequently, a CPP can be solved optimally by using a

matching algorithm to add the minimum set of extra traversals required

making each node of even degree. When this has been achieved, an Euler

tour can be formed on the expanded graph. That provides a tour that

visits each original arc or matching arc exactly once. On a given matched

network there may be many Euler tours, allowing alternative routes that

have a different sequence but all still be optimal.

5.2.2 The Rural Postman Problem

The Rural Postman Problem (RPP) is an extension of the CPP where only

a subset of arcs (edges) from the network are to be traversed (Eiselt,

Gendreau et al., 1995b). This problem is so called because it might arise

in rural areas where not every road is inhabited. The RPP was first

introduced by Orloff (1974) and has been the subject of limited research

since then. The RPP has been shown to be NP-complete if the required

edges are not connected, but instead form a set of disconnected

components. Some work has taken place on optimal approaches

(Corberán and Sanchis, 1994) but given the difficulty of the problem

practical solution techniques have been heuristic based. Many employ a

procedure to connect the network, for instance by using a minimum

spanning tree algorithm. When a connected network has been derived, a

CPP procedure is used to derive a postman (Euler) tour (Pearn and Wu,

1995). Another heuristic approach used a Monte Carlo simulation

approach to generate multiple solutions for the RPP (Fernandez de

Córdoba, Garcia Raffi and Sanchis, 1998), the best of the solutions is then

used. Specialised variations of the RPP exist, for example the RPP with


103

deadline classes (Letchford and Eglese, 1998) or with turn penalties at

intersections in the network (Benavent and Soler, 1999; Clossey, Laporte

and Soriano, 2001).

5.2.3 Other Uncapacitated Arc Problems

The basic CPP is defined on an undirected network, however a different

situation arises where some or all of the arcs in the network are directed

arcs. A variety of problems are discussed in (Assad and Golden, 1995;

Eiselt, Gendreau et al., 1995a; Dror, 2000). For the directed CPP a

solution can be found if a directed path exists between every pair of nodes

(Edmonds and Johnson, 1973), see Beltrami and Bodin (1974) for a

practical example. The Windy Postman Problem (WPP) arises where the

travel time in one direction on an arc is not the same as the other. An

analysis of this problem is given in Win (1988), other recent work

includes that by Pearn and Li (1994). The Mixed Chinese Postman

Problem is a NP-hard problem, unlike the undirected and directed cases

(Minieka, 1979; Pearn and Chou, 1999). Both heuristic and optimal

branch and cut procedures have been employed to achieve solutions for

this class of problem (Hong and Thompson, 1998). These problems are

comprehensively reviewed in Eiselt, Gendreau and Laporte (1995a). The

Maximum Benefit Postman Problem (Malandraki and Daskin, 1993) aims

to find a tour of maximum net benefit where a benefit is realised each

time an arc is traversed. In such a tour, not every arc will be traversed,

while some arcs may be traversed more than once. An example of this

class of problem is snow ploughing, where multiple passes on a street are

preferable to allowing large amounts of snow to accumulate and then

trying to clear it in one pass.


104

5.3 The Capacitated Arc Routing Problem (CARP)

5.3.1 Definition of CARP

While an optimal solution exists for the basic CPP, real world problems

require more than one vehicle to visit a given set of arcs. The Capacitated

Chinese Postman (CCPP) is an extension of the CPP to a situation where

a number of vehicles of limited capacity are used to service the arc

network. Each arc in the graph G=(V,A) has a non-negative weight qij and

each vehicle a capacity of W. The restriction on vehicle capacity may be

distance travelled, duration of route or quantity of goods carried.

Therefore the CPP can be regarded as a subset of the CCPP where W >

ΣiΣj qij. The CCPP is a subset of the broader set of CARP formulations.

The CCPP implies that all arcs in the network will be visited. Just as in

the CCP, additional traversals will be needed where nodes of odd degree

exist. However, in the capacitated problem a further set of additional

traversals exists where more than one vehicle travels along the same arc.

If these can be minimised or eliminated then a good solution for the

CCPP will exist. In practical problems some cases arise where more than

one vehicle must use the same arc. In this case, one vehicle will service

the arc while subsequent traversals by that vehicle or other vehicles

merely pass through the arc without servicing it.

The most general formulation of CARP includes the Capacitated Rural

Postman Problem (CRPP), which arises where not all arcs in the problem

are demand arcs. In formulating CARP as a linear program (LP), two

approaches may be used. A complete graph may be assumed or a sparse

graph formulation may be used, the latter approach possibly reducing the

size of the problem. While a number of different approaches have been

examined, the complexity of CARP means that optimal LP solutions are

extremely difficult to achieve.

The presence of capacity constraints in routing problems implies that the

problem solution has two components. Firstly the question of what


105

vehicle visits each arc or node; this is the allocation phase. The second

issue is the sequence within each route, the sequencing phase. These

phases can be attempted separately or together. In node routing problems

a variety of clustering procedures exist to solve the allocation phase, a

sequencing algorithm like the TSP may be then be used to derive the

complete route. A variety of approaches to finding a CARP solution exist,

and these are discussed below. One approach is to transform the problem

into a node based formulation, this is discussed in the next section.

Linear programming approaches are introduced in Section 5.4 and lower

bounding techniques are discussed in the remainder of this chapter. In

Chapter 6 a variety of heuristic approaches to CARP are discussed.

5.3.2 Representing Arc Routing problems as a TSP

Both node routing problems and arc routing problems can be seen as

subsets of the GRP introduced by Orloff (1974). Therefore, it is possible to

formulate arc routing problems as VRPs and vice-versa. The generalised

TSP is an extension of the TSP where the objective is to visit several

clusters of vertices. Laporte, Asef-Vaziri and Sriskandarajah (1996) show

that arc routing problems, including the CPP and RPP, can be modelled

as generalised TSPs. Jansen (1993) discusses the General Capacitated

Routing Problem, which includes both VRP and CARP.

Pearn, Assad and Golden (1987) examine the relationship between node

routing problems and CARP. They describe a transformation of an arc

routing problem where each arc is replaced by three nodes, called side

and middle nodes. These are spaced equally along the arc (Figure 5-3).

This transformation establishes the equivalence of arc and node routing

problems. However in practical terms the node transformation is not

sij sij mij

Figure 5-3 : Introducing new nodes for each original arc (Pearn,

Assad and Golden, 1987)


106

likely to be significantly easier to work with than the original CARP

formulation.

The classic CPP is defined on an undirected network, other variations of

arc routing problems are defined on directed networks. The modelling of

real world routing problems utilises a number of modifications of these

basic categories. One way streets can be characterised as directed arcs.

Problems that require both side of the road to be serviced can be

represented as two directed arcs in opposite directions. However, for

problems such as street sweeping a one way street may be serviced by a

vehicle travelling against the flow of traffic. Indeed such an arrangement

may be required if the kerb side sweeping equipment is only fitted on one

side of the vehicle. In this case, service arcs exist in both directions but

extra traversals can take place in one direction only. One example of this

situation occurs in the rural road-sweeping project discussed by Eglese

and Murdock (1991). In this case, where both sides of the road are to be

visited, an Euler tour can be easily formed as all nodes are of even

degree. However, a variety of service level issues may influence the tour

actually produced and significantly complicate the solution procedure.

5.4 Linear programming formulations of CARP

5.4.1 Golden and Wong formulation

A mathematical programming formulation for CARP on a complete graph

was introduced by Golden and Wong (1981)). This provided an integer

programming (IP) formulation of the problem. The objective function (5-1)

seeks to minimise total distance travelled. Constraints (5-2) ensure route

continuity. Constraints (5-3) state that each arc with positive demand is

serviced exactly once. For each arc (i,j) the constraints represented by

(5-4) ensure that it can be serviced by postman p only if he visits arc (i,j).

Constraint (5-5) refers to vehicle capacity and the constraints in (5-6)

prohibit the formation of illegal subtours. Integrality constraints are

given in (5-7).


107

IP Formulation of CARP (Golden and Wong (1981))

Minimise pij

K

pij

n

j

n

ixc∑∑∑

=== 111

(5-1)

Subject to0

11=− ∑∑

==

n

k

pik

n

k

pki xx for i = 1,….,n

p= 1,….,K

(5-2)

1)(1

=+∑=

pji

K

p

pij ll for (i,j) ∈ E

(5-3)

pij

pij lx ≥

for (i,j) ∈ E

p= 1,….,K

(5-4)

Wql ij

n

j

pij

n

i≤∑∑

== 11

for p = 1,….,K (5-5)

(5-6)

{ }{ }

∈

∈≤+

≥−

−≤−

∑∑

∑∑

∉∈

∈∈

1,0

1,0,;1

1

1~

,

~2~1~2~1

~2~~

~12

~~

pij

pij

pq

pq

pq

pq

pq

Qi

pij

Qi

pq

Qi

pij

Qi

lx

yyyy

yx

Qynx

},....,3,2{of~ofsubset

emptynoneveryand12,...,1~

,...,1for1

nQ

qKp

n −==

−

(5-7)

where n = the number of nodes in the network

K = the number of available postmen or vehicles

W = the postman capacity (W ≥ maximum of qij

j)(i, arc of demand the

j)(i, arc oflength the

=

=

ij

ij

qc

ppostman by serviced is j)(i, arcif 1 otherwise 0

ppostman by traversedis j)(i, arcif 1 otherwise 0

==

==

pij

pij

l

x

E = the set of all edges on the network


108

Linear programming (LP) formulations of arc routing problems, in

common with LP formations of travelling salesman and vehicle routing

problems, must ensure that illegal subtours are not formed. In the CARP

example a series of cycles could be formed which do not visit the depot

(Figure 5-4). In constraints (5-6) we aim to prevent illegal tours but allow

legal ones.

5.4.2 Belenguer and Benavent formulation

An alternative integer formulation of CARP is available from Belenguer

and Benavent (1998). This uses undirected edges and slightly different

notation than the Golden and Wong formulation. The objective function

minimises the sum of the serviced and deadhead arcs. Constraints (5-9)

(obligatory constraints) and the capacity constraints (5-10) ensure,

respectively, that each required edge will be serviced and that the

capacity of the vehicle is not exceeded. This formulation is difficult to use

directly for optimal solutions. However, it does make an important

contribution as it forms the basis of a lower bounding procedure in

Section 5.5.5 below.

Figure 5-4 : Illegal and legal subtours (Golden and Wong(1981))


109

5.5 Lower bounds for the CARP

5.5.1 Early graph theory bounds

A number of lower bounds for the CARP have been proposed. The starting

point for a lower bound of a capacitated problem is the basic CPP, which

represents a lower bound for a problem with more than one vehicle.

Superior bounds can result from the identification of areas of the network

where it is known that more than one vehicle will traverse the same arc.

This is especially likely to occur near the depot as all vehicles must enter

Belenguer and Benavent formulation

Let R be the set of required edges and let I ={1,…,K}

.itservicingwithoutedgetraversesvehicletimesofnumber

edgeservesvehicleif1otherwise0

Repy

Repx

ep

ep

∈= ∈=

Minimise epIp Ee

eepIp Re

e ycxc ∑∑∑∑∈ ∈∈ ∈

+ (5-8)

Subject to RexIp

ep ∈=∑∈

allfor1(5-9)

IpQxdRe

epe ∈≤∑∈

allfor(5-10)

{ }1and)(

1allfor2))(())((

∈∈

−⊆≥+

PSEfVSxSxSx

R

fppRp δδ(5-11)

{}1and

1allforeven))(())((

∈

−⊆+

PVSSySx pRp δδ (5-12)

{ } integerand0,1,0 ≥∈ epep yx (5-13)


110

and leave the depot. Therefore, if there are four vehicles in a problem and

only two arcs linking the depot, it is inevitable that there will be six

additional traversals of one or other of these arcs. Much of the work on

arc routing lower bounds has attempted to identify the distance

inevitably added by these traversals; when added to the CPP solution a

lower bound is derived. An early bound was identified by Christofides

(1973). This bound identified the number of vehicles required M = [ΣiΣj qij

/W] and added to the CPP solution 2M-1 times the length of the shortest

arc incident with the depot. Golden and Wong (1981) point out that the

Christofides bound was invalid in certain cases where the matching

required for the CPP already included additional traversals to the depot.

They proposed a new bound based on the addition of new artificial nodes

to replicate the depot and the inclusion of these and the original network

in the matching process. Further important contributions were made by

bounds developed by Assad, Pearn and Golden (1987) and Pearn (1988).

These bounds require the solution of a matching algorithm on a modified

graph H derived from G; this modified graph incorporates additional

traversals near the depot.

5.5.2 Node Duplication Lower Bound

The Node Duplication Lower Bound (NDLB), (Saruwatari, Hirabayashi

and Nishida, 1992) provides a lower bound for the CARP. This bound

involves the transformation of a given graph G = (V,E) into a graph Gt =

(Vt, Et) which is an augmented graph. This graph comprises the original

demand arcs and a number of artificial arcs. The significance of the

artificial arcs will be explained later in this chapter. This procedure is

more computationally intensive than LB1 but facilitates use of the

branch and bound algorithm.

A new set of nodes, representing copies of the nodes of the original graph,

V, must be created. For each node i ∈ V that is adjacent to a demand arc,

create the set called ‘Family of i’ where Family(i) contains Degree(i)

copies of node i from the original graph. Effectively for each node in V, it


111

makes a number of copies of the node as is equal to the degree of that

node. Now obtain the set VD is formed by the union of Family(i) for all i ∈

V. Therefore VD = Family(1) ∪ Family(2) ∪ ... ∪ Family(n), where n is

the number of nodes in the original graph.

Then create a set of nodes VS, representing copies of the depot. Letting ‘M’

denote the number of postmen who will service the network, the set VS is

comprised of (2 × M) nodes where each node represents a copy of the

depot node, in the original graph G. The set Vt is now obtained by forming

the union of the two sets VD and VS (i.e. Vt = VS ∪ VD )

One then has to assign each demand arc in G to some arc in Gt. For any

demand arc (i,j) in G, a node is selected in Vt from Family(i), denoted by

‘k’, and another node in Vt from Family(j), denoted by ‘l’. Arc (k,l) is now

set as the demand arc in Gt corresponding to the demand arc (i,j) in the

original graph G. The demand on this arc (k,l) is set equal to that of arc

(i,j) in G. This is repeated for all demand arcs so that no two demand arcs

in Gt have common nodes. This is made possible by the fact that the

number of nodes in Family(i) equals Degree(i) for any node i ∈ VD .

2 3

4 5

6 7

1,2 2,2

3,2

2,2 2,2

1,1

1,3

1,1 1,1

1

Arc Attributes : Cost (Distance) , Volume

Figure 5-5 : The Original Graph


112

The graph shown in Figure 5-5 above (nine arcs and seven nodes) is used

as an example (Benavent, Campos, Corberan and Mota, 1992). The

transformation of this basic graph into the graph needed for the NDLB is

shown in Figure 5-6. The depot node is adjacent to two demand arcs, and

thus Family(1) contains two copies of node 1. These as nodes are

renumbered as ‘1’ and ‘2’ in the transformed graph. This procedure is

applied to each node in the original graph, simultaneously incrementing

the corresponding node number in the transformed graph accordingly. If

four vehicles are required (M = 4), then there are eight (2M) copies of the

depot node, referred to as ‘depot nodes’, numbered in this case as nodes 19

through to 26 inclusive. The demand arcs are then inserted into Gt , with

arc (1,3) in Gt corresponding to arc (1,2) in G, arc (2,6) in Gt corresponding

to arc (1,3) in G, and similarly for the remaining demand arcs.

The next step is to form a complete graph with a complete cost matrix.

The cost on each demand arc is set to infinity (i.e. they are prohibited

from the MCPM solution). If two nodes are from separate families, the

1

2

3

4

5 7

6

8

9

10

11

12

13

14

15

16

17

18

3

3

1

1

2

2

2

2

2

Volume

Figure 5-6 : The Transformed Graph


113

cost on the arc between them is set equal to the shortest path between

their original nodes in the original graph G. If one node of an arc (i,j) is

from a family (i.e. i ∈ VD ) and the other node is a depot node (i.e. j ∈ VS),

the cost on the arc between them is set equal to the shortest path from

the node to the depot (node 1) in the original graph G. The cost on an arc

between two nodes from the same family is set to zero. The cost on an arc

between two depot nodes is set to infinity (i.e. these arcs are prohibited).

The lower bound is calculated from the summation of the costs on the

arcs in the optimal matching on the transformed network. This is a lower

bound on the sum of the traversal costs or times for the optimal vehicle

route required for this network. If we take our example in Figure 5-5

above, the initial MCPM of the cost matrix is shown in Figure 5-7. In this

1 2

3

4

5 7

6

8

9

10 11

12 13

14

15

16

17

18

19 20 21 22 23 24 25 26

1,3

1,3 1,1

1,1

2,3 2,3

3,2

1,2

Cost, Volume

1,2

1,2

0,0 0,0 2,2 2,2

2,2

2,2

0,0 0,0

1,2

0,0 0,0

0,0

1,1

Figure 5-7 : Initial NDLB MCPM on the 9-arc example


114

example, many of the matching arcs are between nodes in the same

family, these have zero cost. Also as there are several vehicles used, there

are additional traversals to the depot. There is also an additional

traversal between node 4 and node 5. This arises because these nodes are

of odd degree. This solution gives a value of 24 for NDLB, (additional

matching 10 + service cost 14).

5.5.3 Bound LB1

Benavent, Campos, Corberán and Mota (1992) provide a comprehensive

review of previous work and introduce new bounds, which they showed to

be superior to previous ones. It is useful to examine these bounds as they

form the basis of the new bounds presented in Chapter 7. The basic

Benavent et al bound is known as LB1. It follows a similar strategy to

earlier bounds, but relies on a more sophisticated analysis of the paths

leading to the depot. Additional nodes and paths are added to a modified

graph H derived from G and a matching algorithm is used to derive a

lower bound from this modified graph. LB1 provides at least as good a

performance as the NDLB discussed in the previous section, but is less

computationally intensive.

LB1 is calculated by reference to the modified graph GR where the

vertices are 1, 2, ..., |Vr|, numbered in non-decreasing order with respect

to their distances to the depot, so s12 ≤ s13 ≤ ... (where s1j is the shortest

path from the depot to node j) and construct a complete graph Ga = (Va ,

Ea) with Va = A ∪ B ∪ S′, where

A = {a1, ...., ar} is a set of copies of the depot.

B contains Degree(i) copies of vertex i, for i = 2, ... , r where r is the

minimum value of p such that degree(2) + ... + degree(k) >= J.

S′ contains a copy of each vertex in S (S contains the nodes of odd degree

in the original graph, G) excluding the depot and those odd vertices

whose copies are already included in set B.


115

Costs on the edges of Ea are defined as follows: cost infinity between

every pair of vertices in set A, and, for all other pairs, the cost of the

shortest path in G between the corresponding vertices of Ga. The costs of

the edges between copies of the same node will be zero except for the

copies of the depot.

The calculation of LB1 will be explained by the examples below which are

based on the nine-arc problem presented above in Figure 5-5. Suppose

there are four vehicles, each with a capacity of five units. On each

vehicle’s route, it must travel ‘out’ of the depot along an adjacent arc,

using either arc (1,2) or arc (1,3), at the beginning of its route. Similarly,

at the end of the route, each vehicle must travel ‘in’ to the depot along one

of these adjacent arcs. In total, there will be eight traversals of the arcs

adjacent to the depot, four on outgoing journeys and four on incoming

journeys. However, in the original graph there are only two arcs adjacent

to the depot. Consequently, there will be at least six additional traversals

shared between the arcs adjacent to the depot.

The procedure proposed by Benavent et al for the LB1 bound requires the

inclusion of six artificial vertices in Vt which represent copies of the

depot. Call this set A.

A = {11, 12, 13, 14, 15, 16}.

These six copies of the depot are included in Hs so that six traversals of

arcs adjacent to the depot will be included in the lower bound. For each of

these six traversals, a copy of a vertex incident to the depot needs to be

included in Hs . This requires enough copies of vertices 2 and 3 to pair off

with the copies of the depot.

Choose the vertex closest to the depot. In this example, the shortest arc is

(1,2), so a copy of node 2 is included in Vt. When a vehicle arrives at node

2, it must travel along (or have travelled from) another adjacent arc of

that vertex to continue its journey. However, node 2 only has three

adjacent arcs so it cannot match the six traversals needed for the depot.


116

Therefore, three copies of node 2 are included in Vt (This does not mean

that the construction of Hs eliminates the possibility of more traversals of

arc (1,2) as will be explained later). We proceed by looking at the next

closest vertex to the depot. In this example, this is node 3, which also has

three adjacent arcs. Between vertices 2 and 3, six artificial vertices are

included in Vt. This is enough to offset the traversals ‘to’ and ‘from’ the

depot.

Include three copies of node 2 in Vt and three copies of node 3. Call this

set B.

B = {21, 22, 23, 31, 32, 33}

Consequently, extra traversals are added due to the presence of nodes of

odd degree in G. Of the remaining vertices in the graph, nodes 4, 5, 6, and

7, two of them, nodes 4 and 5, are of odd degree. These vertices must be

matched with other vertices. Therefore, an artificial copy of each of these

vertices is created and added to Vt. Call this set S′. Note that vertices of

odd degree of which copies have been included in set B cannot be included

in set S′ (Figure 5-8).

S′ = {4*, 5*}.

Va = A ∪ B ∪ S′

In set A vehicles cannot travel directly from one copy of the depot to

another. Therefore, between all other pairs of arcs, the cost of the shortest

path ascertained from the original graph will be used. Costs between

Set A

Set B

Set S′

Node 2

4 5

Node 3

Figure 5-8 : Optimal Matching of Hs


117

copies of the same node will be zero. We then carry out a MCPM on Hs.

LB1 now estimates that arc (1,2) will be traversed (or repeated) at least

three times, as will arc (1,3). In addition, arc (4,5) will be traversed at

least once. This gives a bound of 24, (10+14) which means that for this

example LB1 gives the same bound as NDLB discussed above. It is worth

noting that the inclusion of three copies of nodes 2 or 3 in set B does not

mean that the matching of Hs cannot represent additional traversals of

arc (1,2) or arc (1,3). This possibility is not restricted by the MCPM.

5.5.4 Bounds exploiting cuts away from the depot

Win (1988) studied a number of issues related to arc routing problems

and devised an improved bound which he called ZAW2. This work

recognised that CARP lower bounds could be improved by examining

additional traversals away from the depot, at any point where a

constriction occurred in the graph. Win’s work was extended by

Benavent, Campos, Corberán and Mota (1992) who proposed a superior

bound LB2. This is based on the concepts introduced in LB1, but

improves the bound by also examining cuts in all parts of the graph, and

not just at the depot.

LB2 exploits the properties of cutsets. In looking at LB1 (Section 5.5.2)

we examined the number of times vehicles travelled along the arcs

adjacent to the depot. The set of arcs adjacent to the depot would make

up a valid cutset (as shown in Figure 5-9 below). If these arcs were

removed from the graph, the graph would be split into two components.

Component 1 = {1}

Component 2 = {2, 3, 4, 5, 6, 7}

When dealing with lower bounds, a cutset gives us a lot of information.

Call arcs (1,2) and (1,3) the ‘cutset’ and the arcs (2,4), (2,3), (3,5), (4,5),

(4,6), (5,7), (6,7) the ‘cut sub-graph’. The arcs in the cut sub-graph can be

referred to as arcs ‘beyond the cut’. This means those arcs on the opposite


118

side of the cut to the depot. We will use the following notation, drawn

from Benevant et al, in the following examples.

ps = number of vehicles to service the cut and the cut sub-graph.

qs = the number of arcs in the cut.

rs = 2ps - qs, the number of extra traversals required of those arcs in q.

cs = the length of the shortest arcs in the cut.

In the example in Figure 5-5 on page 111, assume that there are four

vehicles each with a capacity of five units. Then the number of vehicles

required (ps) to cross the cut is 4 and the number of arcs (qs) crossing the

cut is 2. Consequently, the number of extra arc traversals across the cut

is six. There will be four outgoing crossings, and four incoming crossings.

Of these eight crossings, only two can service arcs, therefore the six other

crossings must be traversals.

rs = (2 ×4) - 2 = 6.

The shortest arc in the cut is arc (1,2). This has a length of 1.

cs = 1.

2 3

4 5

6 7

1,2 2,2

3,2

2,2 2,2

1,1

1,3

1,1 1,1

1

Figure 5-9 : The Cutset from LB1


119

Benavent et al proposed a new bound, known as LB2, which further

improves on LB1 by considering successive edge cutsets. Consider again

the example above. In calculating LB2 (Figure 5-9) a set U is formed

which initially contains the depot, a second set V′ is formed from V – U.

Sets A, B are calculated in similar way to LB1.

S′ = S ∩ V′s (that is the set of odd degree vertices beyond the cut)

One difference is that we will no longer refer to the elements of set A as

copies of the depot, as we will also be dealing with cuts removed from the

depot. The calculation of LB2 introduces another set of nodes, called set

X. This is not relevant for the cut at the depot, but arises for all cuts away

from the depot.

A = is a set of rs artificial vertices

B contains d(i) copies of vertex ij, where ij ∈ V′s where j = 1,…, h

S″ contains a copy of each vertex in S′ (S contains the nodes of odd degree

beyond the cut) except for those whose copies are already included.

X is a set of max{0, |S′| - rs} artificial vertices

Va = A ∪ B ∪ S′ ∪ X

Costs on the arcs Et are calculated so that the cost on the edges between

set B and set S″ are the shortest paths between the corresponding

vertices in the original graph. Note that the cost on edges between copies

of the same vertex will be zero. For edges between u ∈ B ∪ S″ and v ∈ A

∪ X, the cost on the edge is the minimum distance from node i to any

node in U.

If we perform these calculations for the graph shown in Figure 5-9, then

U = {1}, V′ = {2, 3, 4, 5, 6, 7}

A = {a1, a2, a3, a4, a5, a6}.

B = {21, 22, 23, 31, 32, 33}.


120

S″ = {4*, 5*}.

X = {} (not relevant at depot)

The MCPM on Hs with a cut at the depot returns a value of 10 (the same

value as LB1). We have now found a lower bound using the information

from the Cut (1-2, 1-3) and the matching of the remaining nodes of odd

degree (nodes 4 and 5). Nevertheless, from the research by Win (1988)

(further developed by Benavent et al) it is clear that more information

can be gained by looking at successive edge cutsets. Moving away from

the depot, out into the graph, in search of ‘good cuts’ generates such

cutsets. A significant cut is likely to arise where the road network is

constricted, for example where there are bridges over a river.

The current lower bound is 10 + total service cost = (10 + 14) = 24. Since

the cost of servicing the graph is constant, henceforth we will use the

term ‘lower bound’ to refer to that time that is additional to the servicing

time. In this case the lower bound is ten. The shortest arc out of the depot

is arc (1,2), with a traversal time of 1 and six additional traversal of arcs

out of node 1 were required. A value L1 is stored to represent the

minimum traversal distance for crossing the cut, this calculation is

similar to that proposed by Zaw.

2 3

4 5

6 7

1,2 2,2

3,2

2,2 2,2

1,1

1,3

1,1 1,1

1

Figure 5-10 : The second cut


121

L1 = cs × rs

cs = 1

rs = 6

L1 = 6.

Suppose that the dotted line in Figure 5-10 shows a natural cut in the

graph (e.g. a river crossing) the cutset is (2-4, 3-5).

U = {1, 2, 3}.

Suppose that this was the river, the ‘North’ side of the graph has a

demand of 12 (including the bridges across the cut). With a vehicle

capacity of four, three such vehicles are required to cross the river to

service the arcs beyond and including the cut. Each of these three

vehicles will also have to return. In total, the river must be crossed six

times, three times on outgoing traversals and three on incoming

traversals. However, only two demand arcs cross the cut. As a result four

out of the six times that the cut is crossed, a bridge will be traversed

without servicing. We create four artificial vertices that can represent

nodes on the ‘South’ side of the graph.

A = {a1, a2, a3, a4}.

In order to provide for the four artificial edges that will create the

traversals across the cut, we need to match set A with copies of the nodes

on the ‘North’ side of the cut. Following a similar argument as was used

to create set B in LB1, 3 copies of node 4 will be created and 3 copies of

node 5 will created since both nodes have degree 3.

B = {41, 42, 43, 51, 52, 53}.

Also, within the North Side, there may be nodes of odd degree (not

already included in set B) which need to be matched with each other. In

this instance, for nodes 6 and 7, we can see that there are no such

additional nodes.

S″ = {}


122

Including set S″ in Vt represents the odd nodes not yet included in Vt. Odd

nodes between the depot and the cut are not included. Including only

some of the odd nodes from the original graph might possibly result in a

sub-optimal matching (i.e. a matching which is too high). This might

occur if a MCPM of odd nodes in the original graph involved matchings

across the cut. If in a MCPM on the original graph, a node of odd degree

beyond the cut would be matched with a node of odd degree on the depot

side of the cut, this cannot be catered for by a matching on Hs alone.

L1 = L1+ (cs × rs) = 6 + (4 × 2) = 14.

Therefore, we include artificial vertices in Vt which will prevent this

occurring. The number of artificial nodes created for set X is equal to the

number of nodes in set S″ less rs. If this number is negative, set X is

empty. The costs on At, the arcs in the complete graph Hs should be

calculated same as before.

X = max{0, |S″| - rs}

Va = A ∪ B ∪ S″ ∪ X

The MCPM on this graph returns a value of 8. At first sight, this bound is

inferior to the initial bound of 10. However, if we add the L1 value of 6

calculated earlier, the estimated traversals behind the cut, and add this

to the new bound of 8, we get a total of 14. This gives a better lower

bound than the 10 given earlier, so we save this as our new lower bound.

Create the next cutset.

U = {1, 2, 3, 4, 5}

Using the same principles as before:

A = {a1, a2, a3, a4} (as two vehicles needed to service arcs (4,6), (5,7), (6,7))

B = {61, 62, 71, 72}

S″ = {}

X = {}

Va = A ∪ B ∪ S″ ∪ X


123

Table 5-2 : Summary of LB2 Algorithm

Set U = { 1 }, L = L1 = L2 = 0;

WHILE U <> V DO

Let V' = V - U and G' be the graph induced by V'

Find the connected components of G'. Suppose G' has ‘k’

components G's = (V's , E's ) and

},:),({)(cutsetedge UjViEjieV ∈′∈∈==′δ

FOR s := 1 TO k DO

)(setandbelow)(seegraphweightedaconstruct then0orIf

Let}2,0{max

min0:)({

q

.

)(

)(e

ss

sss

ss

sss

eves

ess

VEes

HMPmHrS

VSqpr

ccqVeq

Wp

s

ss

=>≠′

′=′−=

=>′∈=

=

′∈

′′∈∑

φ

δ

δ

δ

ENDFOR s.

s

t

Ss

T

t

ss

crLL

LLCLL

mL

∑

∑

=

=

+=

++=

=

1

1

11

}1,2max{2

Set U' = the set of nodes {i ∈ V | i is adjacent to a vertex in

U }.

U := U ∪ U'.

ENDWHILE.

Set LB2 = L2.

ENDALG


124

Construction of Complete Weighted Graph HS for LB 2

Preliminary

Let Mdist(i) denote the minimum distance between vertex ‘i’ in V'i and any vertex of U .

Suppose that the vertices in V'i are renumbered i1 , i2 ,..... in such a way that Mdist(i1)

Mdist(i2) ........

Let h be the minimum integer such that Degree(i1) + ........+ Degree(ih) ri.

The Vertex Set

Graph HS is a complete weighted graph with vertices are drawn from 4 sets : Set A ∪ Set

B ∪ Set S″ ∪ Set X

Set A is a set of artificial vertices, where = ri

Set B contains Degree(ik) copies of vertex ik V'i for k = 1....h.

Set S″ contains a copy of each vertex in S'i except for those copies who are already in Set

B.

Set X is a set of artificial vertices, where = Max [ 0, (number of nodes in S'i ) - ri ]

The Arc-Cost Matrix

Let wij represent the cost on edge (i,j) in HS . The costs on the edges in HS are infinite

except for the following:

• if i, j ∈ {Set B ∪ Set S″} then wij = the shortest path between the corresponding

vertices in G ( Note that wij = 0 if i and j are copies of the same vertex).

• if i ∈ {Set B ∪ Set S″} and j ∈ {Set A ∪ Set X} then wij = Mdist(ki) where ki

denotes the corresponding vertex to i in G.

• if i, j ∈ Set D then wij = 0.

Again, form the complete graph Hs=(Vt, Et) and carry out a MCPM. The

MCPM on this graph returns a value of 2. Costs on the edges of Et are

calculated as before. Adding the estimated traversals behind the cut, 14,

to 2, we get a new lower bound of 16. Since this is higher than any bound

seen before we store this as our bound. Next, we look at the adjacent

nodes of the cutset. We see that all nodes in E are now members of U, and

so the lower bound algorithm stops. The current, i.e. best, value of LB2 is

16; adding this to the total service time for the graph, we get a lower

bound of 30. The optimal solution for this graph is 32. Therefore, a

solution of 30 appears to be a good lower bound for this problem.


125

We believe that LB2 provides the best graph theory based CARP bound

published to date. Although LB2 is computationally expensive, owing to

its use of MCPM techniques, it can be feasibly implemented for quite

large graphs. LB2 (Table 5-2) will form the basis of a modified bound for

the Time Capacitated Arc Routing Problem (TCARP) in Chapter 7.

5.5.5 Cutting Plane Bound

While most of the work on lower bounds for CARP has been based on

graph theory rather than linear programming approaches, it seems likely

that, in the future, the latter approach will lead to superior bounds.

Belenguer and Benevent (1997) discuss a cutting plane approach for

CARP that uses a linear programming relaxation to provide a lower

bound. This is partly based on the LP formulation by the same authors

discussed above (Belenguer and Benavent, 1998). The cutting plane

algorithm solves a relaxation of the linear program containing a subset of

valid inequalities for the CARP formulation. A solution is generated and

a set of valid inequalities violated by the optimal solution is identified.

This set of inequalities is added to the optimal solution. This process is

terminated when an upper bound is reached, in which case the optimal

solution has been found, or when no known inequalities are breached.

The latter case provides a lower bound for the solution.

Belenguer and Benevent conducted computational testing on problems

that had previously appeared in the literature, these were relatively

small problems with up to 50 nodes. These results indicated that the

cutting plane algorithm (CPA) produced a superior bound to LB2 and

problems with 50 nodes and 97 vertices were solved to optimality. Their

calculations showed that LB2 had an average gap of 4.21% from the

upper bound. The cutting plane algorithm had a much-reduced gap of

0.74%. The latter reached the optimal value in over half the test

problems; some three times the proportion of optimal solutions reached

using LB2.


126

Chapter 6 : Solutions for the CARP

6.1 Heuristic Solutions for the Capacitated Arc Routing Problem

6.1.1 Single Pass heuristics

One approach to CARP is to use an algorithm that considers vehicle

allocation and route sequence simultaneously. A variety of single pass

(parallel) heuristic algorithms have been proposed to derive feasible, but

not necessarily optimal, solutions for arc routing problems. These use

heuristic methods to build directly a postman tour. Christofides (1973)

introduced the first of these generic algorithms, which is known as the

Construct-Strike Algorithm. In this algorithm feasible cycles (with total

arc demand less than or equal to the vehicle capacity) are constructed

which, when removed, do not cause the remaining graph to become

disconnected. Then the arcs serviced in the cycles created in the first are

deleted from the current graph and this process is repeated until no more

cycles are found. Then a matching problem is solved for the nodes of odd

degree and two copies of the depot, the additional paths are added to the

graph and the initial step is repeated. This approach was developed by

Pearn (1989) who developed a Modified Construct-Strike Algorithm with

an improved arc selection procedure. Pearn indicated that the original

algorithm was O(mn3) and the revised algorithm O(mn4), indicating that

solutions can be found reasonably effectively. Later work (Coutinho-

Rodrigues, Rodrigues et al., 1993) tested the algorithms using a heuristic

matching of the odd degree nodes (odd nodes were matched with the

lowest cost path between them). They found that this approach achieved

similar results, but avoided the excessive computation time entailed in

the use of an optimal MCPM algorithm.


127

Golden and Wong introduced an algorithm inspired by the Clarke-Wright

heuristic for vehicle routing (Clarke and Wright, 1964). This begins with

each demand arc being serviced by a separate cycle and then attempts to

combine the cycles. This became known as the Augment-Merge Algorithm.

Pearn (1991) improved on this algorithm, making it suitable for operation

on relatively sparse graphs with large edge demands, relative to the

vehicle size. The Parallel Insertion Algorithm (Chapleau, Ferland,

Lapalme and Rousseau, 1984) was inspired by the insertion procedures

used for node routing problems. This requires assessment of two issues;

which arc to insert and where to insert it. For each arc we must

determine the existing route into which it should be inserted in order to

minimise the detour incurred. When this route has been identified, we

must determine which remaining arc should be inserted next.

The Path-Scanning Algorithm (Golden, DeArmon and Baker, 1983) forms

a cycle by adding an edge according to one of five edge selection criteria.

Each of the criteria is used to form a solution and the one with the lowest

cost is used. Pearn (1989) proposed that the edge selection criteria be

chosen randomly and found that this improved the solution. Coutinho-

Rodrigues, Rodrigues, and Climaco (1993) proposed the use of three

additional criteria.

Single pass heuristics are appropriate for many classes for problems,

where substantial volumes are to be collected or delivered. Coutinho-

Rodrigues et al (1993) review a number of heuristics in the context of a

refuse collection application in Portugal. A review of these algorithms is

given by Assad and Golden (1995), who compare the computational

performance of the various algorithms, this is reproduced in Table 6-1. It

can be seen from this table, that the data sets used were much smaller

than most practical real-world arc routing problems. Furthermore, the

networks used to test these algorithms were largely complete, which is

untypical of real road networks.


128

6.1.2 Route-first cluster-second heuristics

The Route-First Cluster-Second Approach (RFCS) is based on the creation

of a giant tour through all the arcs. This tour is then decomposed into a

set of sub-tours, each of which is feasible with regard to the capacity of

Table 6-1 : Heuristic performance (adapted from Assad and

Golden(1995))

GDB P89A P89B P91

Test Beds

Number of problems 23 20 15 30

Number of nodes (n) 7-27 11-17 11-17 13-27

Number of edges (m) 11-55 55-136 45-116 23-51

Density (%) 13-100 100 70-90 15-30

Algorithms (% over

Lower bound)

Construct-strike CS 17.91 2.29 3.85 71.95

Path-scanning PS 11.03 3.13 3.59 57.97

Augment-merge AM 9.16 56.78

Random path scan RPS 8.05 2.76 3.16 51.30

Augment-Insert I AI1S 12.39 44.17

Augment-Insert II AI2 13.95 44.97

GDB (Golden, DeArmon et al., 1983)

P89A (Pearn, 1989) dataset A

P89B (Pearn, 1989) dataset B

P91 (Pearn, 1991)


129

the vehicle. This approach can be used for VRP applications (Beasley,

1983). In the arc routing context, Beltrami and Bodin (1974) describe a

RFCS solution approach for a refuse collection problem. In this

application, a giant Euler tour is constructed, using a simplified matching

procedure, and this route is subsequently partitioned into feasible route

segments. A similar problem was faced by Stern and Dror (1979), who

describe a meter reading application in Israel. They initially solve a RPP

using a heuristic matching technique. The large Euler tour is

subsequently partitioned by removing edges from the tour until the time

based capacity constraint for each route is met. In this application, the

subdivision of the tour was made easier by the fact that the required

routes were open ended. This arose as the meter reader was not required

to return on foot to the depot, but could travel by public transport

instead. The RFCS approach can take advantage of the fact that the CPP

can be solved optimally. Therefore, if a good partition can be achieved,

good solutions can be derived by this technique. However, in practical

problems it is not always straightforward to subdivide the uncapacitated

solution.

6.1.3 Cluster-first route-second heuristics

An alternative approach to RFCS is to derive an initial cluster and then

sequence the points or arcs within that cluster, this is the Cluster-First

Route-Second Approach (CFRS). This approach has been successfully

used in node routing problems, a well-known example of an algorithm of

this type being the sweep algorithm of Gillett and Millar (1974). This

algorithm assumes a problem with a set of n customer locations (in terms

of rectangular co-ordinates with the depot at the origin) and demands,

and a set of vehicles and capacities. The customers are re-numbered in

terms of increasing polar co-ordinate angle. Then starting with the

customer with the smallest co-ordinate angle, the locations are

partitioned into groups. The first route consists of locations 1,2,...,J

(remembering that the depot is location 0), where J is the last location


130

that can be added without exceeding the vehicle capacity constraint. The

second route contains locations J+1, J+2,...,L, where L is the last location

that can be added to the second route without exceeding the vehicle

capacity constraint. The remaining routes are formed in the same

manner. The second stage of the algorithm involves evaluating the

impact of swapping customers between routes, in an effort to improve the

solution. A variety of stratagems are used to identify other possibilities,

including shifting the X and Y axes so that the first location becomes the

last, the second the first and so forth.

In the arc routing field, CFRS solutions are less common. One recent

example of the use of a CFRS approach in arc routing is in winter gritting

in Germany (Amberg, Domschke and Voß, 2000). Another example of

interest is the Arc-Partitioning Problem (Levy and Bodin, 1989; Bodin

and Levy, 1991) which arises in postal delivery in the US. This is a

location routing problem, where a series of walking tours are generated

from a parked vehicle. The algorithm must derive both the location where

the vehicle is parked and the sequence of arcs to be visited from that

location. The objective is to break a network into partitions where the

workload in each partition is approximately the same. Seed points are

used as the basis of the partitions, these can be input by the user or

generated automatically by the algorithm. This automatic procedure aims

to maximise the minimum distance between all pairs of seed points.

When seed points have been generated, partitions are derived and a

balancing routine is used to swap arcs between partitions to better

balance the solutions. The balancing step may lead to a revision of the

seed points.

6.1.4 New approaches to CARP

Considerable recent work has taken place in OR/MS on new general local

search heuristic techniques, for example genetic algorithms and

simulated annealing (Eglese, 1990). These could be used to improve an

arc routing solution; Eglese (1994) discusses the use of simulated


131

annealing for a winter gritting problem on rural road networks.

Greistorfer (1994) discusses the use of tabu search for arc routing. A

recent paper (Hertz, Laporte and Mittaz, 2000) conducts extensive testing

of the tabu search approach on the CARP datasets used by some of the

earlier researchers (Section 6.1.1). The tabu search approach was shown

to reach the optimal solution in eighteen of the twenty-three cases tested

and was shown to be superior to earlier heuristics. On larger randomly

generated examples, the tabu search approach was compared to the best

lower bound derived from three approaches; the CPA bound (Section

5.5.5) the LB2 bound (Section 5.5.4) and the NDLB bound (Section 5.5.2).

The tabu search approach obtained solutions within 5% of the best lower

bound, which was probably not optimal. These results suggest that this

area of research is likely to provide further useful approaches for arc

routing problems.

6.1.5 Real world network representation issues

Heuristic approaches may have an advantage over optimal techniques in

that they can be more easily modified to accommodate a variety of issues

that arise in practical problems. In arc routing, several potential

complications arise at junctions. Left or right turns may be prohibited or

be undesirable for slow moving vehicles, depending on which side of the

road that vehicles use. In the case of some applications, such as snow

clearance (Figure 6-1), a right turn (in a country where vehicles travel on

the right) may be preferable to travelling through an intersection

(Gendreau, Laporte and Yelle, 1997). Similar issues arise in street

sweeping applications, where it may be more desirable for the vehicle to

continue along the street or turn right rather than turn left or to make a

U turn. Bodin and Kursh (1979) describe the use of penalties to reduce

the number of undesirable pairings of arcs (Table 6-2). Similar issues

arise in the paper on refuse collection by McBride (1982).


132

Where both sides of the street are to be visited a number of issues arise at

junctions. In pedestrian applications, for instance urban mail delivery,

crossing the road may impose a significant delay. This type of constraint

can be modelled by the use of penalties. In an urban postal delivery

application Roy and Rousseau (1989) discuss the use of penalties at

junctions to reflect the additional time take to cross the street (Figure

6-2).

Table 6-2 : Turn Penalties (Bodin and Kursh, 1979)

Movements Points

U-turns 8

Deadhead to sweep 5

Sweep to deadhead 5

Left hand turn 4

Right hand turn 1

Straight ahead (no turn) 0

Figure 6-1 : Block Design for snow ploughing

(Gendreau, Laporte et al., 1997)


133

6.2 Branching approaches to CARP

6.2.1 Branching techniques

The heuristic procedures described above provide a method of reaching a

good solution to arc routing problems. Each heuristic is likely, but not

guaranteed, to reach a solution close to the optimal. Linear programming

approaches, discussed in Chapter 5, could be used to identify the optimal

solution to the problem. Unfortunately, optimal approaches are currently

impractical for many real world problems. In OR/MS, a synthesis of

optimal and heuristic approaches exists in the class of techniques known

as branching algorithms. These identify a lower bound for the problem

and an upper bound (i.e. a feasible, but non-optimal solution). The

algorithm then uses a systematic enumerative procedure to find a

feasible solution closer to the lower bound, which may be recalculated

using information generated from the procedure. When the lower and

upper bounds are equal, an optimal solution has been found.

Figure 6-2 : Network enhancement by addition of penalties at

junctions (Roy and Rousseau, 1989)


134

The discussion above and in Chapter 5 indicated that lower and upper

bounds for the CARP could be identified. However reaching an optimal

solution from this information remains extremely difficult. While lower

bounds can be calculated, these calculations do not provide feasible

solutions. A feasible solution may not exist at a lower bound, and it is

extremely difficult to establish whether such a solution exists or not.

Branching algorithms will perform better than total enumeration if some

possibilities can be discarded, when further calculation would lead to

answers above the upper bound (not optimal) or below the lower bound

(infeasible). Branching techniques will therefore perform better if the gap

between the upper and lower bounds is extremely small, allowing many

possibilities be discarded. Where this gap is large, it will be

computationally impractical to find the optimal solution.

A branching approach might be based on an LP based formulation of the

problem, for example the cutting-plane (CPA) lower bound (Belenguer

and Benavent, 1997) discussed in Section 5.5.5. These authors state that

they are working on a fully automated Branch and Cut procedure for

CARP. This will allow larger examples be solved to optimality, although

heuristic procedures will still be needed for many classes of practical

problem. Other branching procedures can be based on customised

approaches, such as the only known example of an optimal branch and

bound CARP procedure by Hirabayashi, Saruwatari, and Nishida (1992).

We will examine this algorithm in further detail in the following section

and will use it for some computational comparisons will lower bounds in

Section 7.5.

6.2.2 The Tour Construction Algorithm

The linear programming formulations discussed in Section 5.4 could

potentially form the basis of an optimal solution procedure for CARP.

Problems of a practical size are intractable with these formulations.

Therefore, in most real world problems other approaches must be used.

An optimal solution procedure for CARP was introduced by Hirabayashi,


135

Saruwatari, and Nishida (1992). This used a customised, graph theory

based, branch and bound procedure based on a lower bound by the same

authors, the Node Duplication Lower Bound (NDLB) (Saruwatari,

Hirabayashi et al., 1992) (see Section 5.5.2). The Tour Construction (T.C.)

algorithm, as devised by Hirabayashi et al (1992), is an algorithm based

upon the Branch and Bound method, where an original problem is split

into two sub-problems. Then each sub-problem is dealt with in turn and

split into two further sub-problems, and so on. We must determine how to

create two sub-problems from each sub-problem, and identify what

characteristic differentiates each of the two subsequent sub-problems.

In this algorithm, the left sub-problem is characterised by an arc that is

prohibited from the optimal solution. The right sub-problem and all child

sub-problems will definitely contain that arc in the solution. The T.C.

algorithm uses a MCPM function, which is passed a matrix of the costs on

the arcs in the specific graph. The MCPM function returns the optimal

matching and a value for the lower bound. However, the algorithm may

require the creation of a very large number of sub-problems before a

feasible solution is found. This requires multiple use of the MCPM

algorithm. This is both processor and memory intensive, making it

difficult to solve large, or even medium sized, problems. An improved

version of the algorithm (Kiuchi, Shinano, Hirabayashi and Saruwatari,

1995) exploits the use of multiple computers in parallel to reach a

solution more rapidly.

As we have seen above in Section 5.5.2, the initial lower bound for the

NDLB bound is obtained by summing up the costs on the arcs in the

initial optimal matching. This lower bound is a lower bound on the sum of

the costs or traversal times for the optimal vehicle route given the matrix

that is sent down to the MCPM function. The Node Duplication

Transformation now provides significant advantages for the operation of

the branch and bound procedure.


136

The presence (or absence) of a feasible solution is based on the concept of

an alternating path. Because of the characteristics of the node-duplicated

graph, we can identify paths whose arcs are alternately an MCPM

solution arc (dotted lines) and a demand arc (solid lines). An alternating

path which starts and ends at the depot node and which does not violate

either the time capacity constraint or the volume capacity constraint of

the vehicle is called a postman path. A collection of mutually disjoint

postman paths where all demand arcs are contained in some postman

path is called a postman tour.

1 2

3

4 5

7

6

8

9

10 11

12 13

14

15

16

17

18

19 20 21 22 23 24 25 26

1,3

1,3 1,1

1,1

2,3 2,3

3,2

1,2

Cost, Volume

1,2

1,2

0,0 0,0 2,2 2,2

2,2

2,2

0,0 0,0

1,2

0,0

1,3

1,3

1,1

Figure 6-3 : Postman paths on the 9-arc example


137

In the example in Figure 6-3, there are four alternating paths. Dotted

lines are used to identify artificial arcs found by the MCPM on the

complete transformed graph. When calculating the total time of the

alternating paths, we use the traversal times for MCPM solution arcs (or

artificial arcs) and the service time for demand arcs. The total costs for

the four alternating paths above are 2, 4, 6, and 14. This would be a

postman tour if postman capacity were 14 or more. If capacity was less

than 14, then the alternating path of length 14 is not a feasible postman

path, so a postman tour would not exist.

A branch and bound algorithm proceeds by bringing the upper bound (the

feasible solution) closer to the lower bound (a lower limit on the optimal

solution). Initially the algorithm sets the upper bound to the maximum

total length of time possible to service the network, which is the product

of the number of vehicles by the time capacity per vehicle. One unit of

time is added to this and the total service time subtracted in order to give

the upper bound. In many cases, this does not provide a very tight bound,

as one of vehicles may be largely empty in the optimal solution.

The tour construction algorithm splits each sub-problem into two further

sub-problems (Figure 6-4). The left sub-problem has the characteristic

that the branching arc can never be in the MCPM solution, while the

right sub-problem has the characteristic that the branching arc must be

in the MCPM solution. For each arc (i,j) in the MCPM solution, the lower

bound of the sub-problem with (i,j) prohibited from being in the MCPM

solution is found. The branching arc (k,l) is the arc that returns the

highest lower bound, when prohibited.

Starting from the original problem, at each iteration work is carried out

on the right sub-problems, while saving the left sub-problems. Movement

down the right hand side is continued until the sub-problem becomes

infeasible or the sub-problem’s lower bound is greater than or equal to

the upper bound. As the algorithm proceeds, additional restrictions are

placed on the solution, by the addition of definite arcs. Therefore, the


138

lower bound of each sub-problem is always greater than or equal to lower

bound of its parent.

The other occasion at which the algorithm stops at a sub-problem is when

we have a postman tour. When this occurs, the upper bound is set to the

lower bound of the current sub-problem, and this sub-problem is stored as

the banker. The banker is defined as being the best solution found so far.

As the upper bound has been decreased, all stored left sub-problems

whose lower bound is greater than or equal to the upper bound are

deleted (We ignore sub-problems whose lower bounds are equal to the

upper bound, as we are looking for one optimal solution).

A

B C

D

F

E

G

Figure 6-4 : Branch and Bound Sub-Problems

A

B C

D

F

E

G

Optimal Solution

Figure 6-5 : Fathomed Sub-Problems and Optimal Solution, Sub-

Problem G


139

When all of the remaining sub-problems have been deleted, all branches

have been fathomed (Figure 6-5). At this point, the current feasible

solution (banker) is thus the optimal solution (Sub-Problem G).

Alternatively, if a sub-problem existed with a lower bound less than the

upper bound, then that sub-problem would be treated in the same way as

sub-problem A.

A definite arc is a set of arcs that form a particular artificial arc. This

artificial arc is a path of two or more arcs, which are guaranteed to form

part or all of a postman path in the final solution. Initially, at the

beginning of the algorithm, the definite arcs are all the demand arcs.

When we branch from a sub-problem to its right sub-problem, the

branching arc is forced to be in the solution. This has the effect of making

two definite arcs into one definite arc. For example if arc (9, 12) is the

first branching arc in the nine-arc example, we now have a definite arc

from Node 5 to Node 8. Arcs (5, 9) and (8, 12) are demand arcs and arc (9,

12) must be in the solution. We also notice that the length of the definite

arc has become 7 hours. An advantage of this is that Nodes 9 and 12 are

excluded when finding the MCPM solutions to sub-problem C (when

finding the branching arc for sub-problem C) as they are automatically in

the MCPM solution. As we progress further down the right hand side, we

need to look at fewer arcs when finding an MCPM solution. We also have

less definite arcs but the definite arcs are getting longer. Therefore, at

each right sub-problem we look at the new definite arc formed and see if

we can prohibit more arcs from being in the MCPM solution.

When we examine the transition from sub-problem C to sub-problem E, if

the new definite arc causes an arc in the MCPM solution of C (and

therefore A) to be prohibited, it becomes necessary to find a new lower

bound and MCPM for sub-problem E. It is clear that until a new lower

bound is calculated, the right sub-problems’ lower bounds will remain the

same, and less than the upper bound. A summary of the procedure for the

TC algorithm can be found in Table 6-3.


140

6.2.3 Practical feasibility of branch and bound algorithm

The computational experiments by Hirabayashi, Saruwatari, and Nishida

were on relatively small well-connected graphs with large demands per

arc. This type of network suited the techniques used in this algorithm.

These results indicated that the solve time increased with the number of

demand arcs |R|. However, the computational demands of the algorithm

Table 6-3 : Outline Code of the Tour Construction Algorithm:

Set U := ∅ ;

Transform network using Node Duplication;

Find Lower Bound and MCPM of the original problem;

Add original problem (Lower Bound and MCPM) to U;

Set Upper Bound := maximum possible lower bound + 1;

WHILE ( U is NOT Empty ) DO

Choose Sub-Problem with smallest Lower Bound from U.

WHILE ( LB < UB ) AND (sub-problem is feasible) DO

IF Postman Tour exists THEN

Upper Bound := Lower Bound;

Banker := Postman Tour;

Delete any Sub-Problems whose Lower Bound ≥ Upper Bound;

ELSE REPEAT

Select Branching arc (x, y);

Add Sub-Problem to U where arc (x, y) is prohibited;

Make definite arc and do prohibit arcs;

UNTIL (Sub-Problem is feasible) OR (Arc in MCPM is prohibited);

IF Arc in MCPM was Prohibited THEN

Find new Lower Bound and MCPM.

ENDIF;

ENDWHILE;

ENDWHILE;

Optimal Solution is in Banker;

ENDALG;


141

are also reflected in the number of sub-problems generated and this tends

to increase greatly as the size of the problem increases. The

representation of each sub-problem requires additional machine memory.

Two MMangtSc students in UCD (Montwill and Naughton, 1994),

working with the author, implemented the branch and bound algorithm

and tested a number of minor modifications. Their experiments identified

excessive use of computer memory as an important limitation on the

ability of this algorithm to solve larger problems. As the algorithm uses a

complete representation of the network and as a large number of sub-

problems are generated, large amounts of memory are used in the

solution procedure

Montwill and Naughton identified a number of strategies that could be

used to improve the performance of the branch and bound algorithm. An

estimate of the matching could be used, by not updating the matching for

every small change in the solution. This would tend to improve solution

time without addressing the problem of excessive memory use. Another

approach used generates more lower bounds, increasing the computation

time, but possibly reducing the number of sub-problems. The use of a

heuristic approach to identify a good initial upper bound is also a means

by which the number of sub-problems could be reduced.

The experiments on a parallel branch and bound algorithm for CARP

(Kiuchi, Shinano et al., 1995) provides a method of approaching

somewhat larger problems, although in this paper only problems

previously solved were attempted. The use of multiple machines in this

example means that greater computing power was used. This makes it

difficult to assess fully the contribution of parallelisation to solution of

CARP. Further improvement in performance is probable if superior

algorithmic and computer science techniques are employed. However, the

branch and bound approach seems unlikely to be easily extended to solve

large practical problems.


142

Chapter 7 : CARP on Irish Rural networks

7.1 Postal delivery of rural networks

7.1.1 Irish Rural Road Networks

Earlier chapters of this dissertation have reviewed the DSS field,

identifying routing DSS as an important application. Within the routing

field, this research has placed a particular emphasis on arc routing

problems. This chapter discusses the focus of this dissertation, arc

routing for large sparse networks, a problem has not been discussed

substantially in the literature. The particular application is rural postal

delivery, which is an interesting TCARP.

The problems discussed in this dissertation are characterised the use of

large sparse networks, such as the Irish rural road network. By European

standards, Ireland has a substantial rural population that is dispersed

over an extensive network of rural roads. For each one thousand

population, Ireland has roughly twice as many kilometres of road as in

Belgium, Denmark, and France, and over three times as many as in Italy,

the Netherlands, and Spain (Dept of the Environment, 1999). It is

estimated that there is 87,149 km of non-national roads in the Republic of

Ireland, almost all in rural areas.

The extensive rural road network partly reflects the fact that, by western

European standards, Ireland still has an above average proportion of the

population engaged in agriculture. The current situation also reflects the

historical situation in Ireland, where in the nineteenth century the rural

population was several times its present size. This large population was

served by an extensive network of rural roads. Subsequent population

change has reduced the population size, but has left the comprehensive

road network in place. This has created a large network of rural roads

with scattered small populations living on each road segment.


143

The road network for CARP can be examined by reference to the ratio of

arcs to nodes (sparsity) and the proportion of odd degree vertices. In

theory a network could have an arc-node ratio of 2, as in Figure 7-1. This

network also has only odd degree vertices. At the other end of the

spectrum, extremely high arc-node ratios could exist (Figure 7-2), many of

the artificially generated networks used in testing routing algorithms are

of this type. In real-world networks, the arc/node ratio lies between 2

(Figure 7-1) and around 4, the latter case would imply a uniform grid

with four-way crossroad junctions.

Rural roads give rise to a mathematical graph that differs from one

derived from urban road networks. Eglese and Li (1992) note the high

frequency of T-junctions (nodes of degree 3) in rural road networks, and

discuss the need for consideration of the network characteristics in

assessing the quality of any routing solution. The tractability of arc

routing problems is largely a function of the number of odd degree

Figure 7-1 : Network with arc-node ratio of 2

Figure 7-2 : Network with high arc/node ratio


144

vertices. As there are few junctions with more than four incident roads,

odd degree vertices typically arise from T-junctions (nodes of degree 3)

and cul-de-sacs (nodes of degree 1). Both of these features are very

common in rural road networks.

Consequently, the Irish rural road network gives rise to a graph that is

extremely sparse compared to the networks usually encountered in the

routing literature (Figure 7-3). This arises because roads leading to

individual houses are frequently part of the public road network. If we

assume replacement of bi-directional arcs with unidirectional arcs in each

direction, the arc/node (arc/vertex) ratio is between 2.3 and 2.8. This

Figure 7-3 : Extract from Irish Rural road network


145

implies that on average each node is connected to two or three other

nodes. As there are hundreds of nodes in a typical rural network , this

implies that only a small proportion of nodes are directly connected by a

single arc, less than 1% for a real world problem.

This sparse nature of rural road networks is in contrast to most of the

examples in the literature, which use artificially created networks that

are almost completely connected (see Section 6.1.1). Harrison and Wills

(1983) refer to Irish road networks at a regional scale; these networks are

significantly less sparse than the rural networks. Mtenzi (2000) examined

the operation of TSP algorithms on similar Irish road networks. In

Ireland the national and regional road network gives rise to a graph with

an arc/node ratio of 3.1. Zhan and Noon (1998) tested shortest path

algorithms on real road networks from the USA and found a similar

arc/node ratio of 2.68 to 3.28.

Figure 7-4 : Extract from Dublin City main road network


146

The sparsity of urban road networks varies, depending on the road layout

in the city. Suburban areas are frequently deliberately designed with

many cul-de-sacs, which would give rise to a low arc/node ratio.

Nevertheless, the main urban road network is typically well connected,

the main road network in Dublin city has an arc/node ratio of 3.24

(Figure 7-4). North American cities laid out in a block structure could

have an arc/node ratio of close to 4. The Manhattan network in Figure 7-5

has an arc/node ratio of 3.68, reflecting the comparative lack of T-

junctions and cul-de-sacs.

7.1.2 Rural Postal Delivery

The main example used in this dissertation is that of postal delivery on

these rural networks. The author has had considerable experience, over a

ten-year period, working with An Post (Irish Post Office) on routing

problems. This work in turn benefited from experience gained as a

summer relief postman on rural routes, while the author was an

undergraduate student. While the research undertaken for this

Figure 7-5 : Extract from New York City road network


147

dissertation was not directly conducted with An Post, the proposals for

decision support presented are directed at the type of problems faced by

that organisation. The relatively large rural population in Ireland means

that servicing this population is expensive for Irish organisations. This

differs from many other developed countries, where the rural population

is such a small proportion of the overall customer base of an organisation

as to be of little importance in the overall cost structure.

In Ireland, unlike many other countries, almost all rural households

receive a postal delivery to the doorstep. This is true even if such houses

are located at the end of cul-de-sac laneways. Rural delivery takes place

from delivery offices situated in a village or small town. Such offices

service deliveries to a small urban area (in the village/town) and a larger

rural area. A delivery office may have only a single postman, but most

have between three and six delivery routes. If the urban area is large

enough, one or more postmen may deliver on foot in that area. This

situation is not of direct interest here. However, in a practical solution

the presence of foot deliveries may mean that a van route represents only

part of the postman’s working day. Postmen are required to sort their

deliveries before setting out to deliver the day's post. Consequently, a

typical working day of eight hours would have approximately six or six

and a half hours available for travel in the delivery van. This time would

include any travel time from the post office to the first and last deliveries.

7.2 CARP on large sparse networks

7.2.1 The Large Sparse Capacitated Arc Routing Problem (LSCARP)

This dissertation uses the example of the Large Sparse Capacitated Arc

Routing Problem (LSCARP) on Irish rural road networks. The LSCARP

represents an economically important CARP on a sparse network. The

problem of visiting all houses in a given area will be a CCPP, as the roads

to be serviced will generally form a connected network. However, in some

sparsely populated districts, the arcs to be visited might not be initially


148

connected and a CRPP is encountered. In the practical solutions

discusssed later in this dissertation we assume that all arcs are to be

visited.

Because of Ireland’s dispersed population distribution, Irish rural postal

delivery is such that few houses are serviced on each road segment (arc).

In the LSCARP the route is serviced by van, this differentiates the

problem from many others found the literature. Many arc routing

examples discuss pedestrian routes, for instance postal delivery (Bodin

and Levy, 1991) or meter reading (Stern and Dror, 1979). Other examples

in the literature discuss routing problems where the vehicles must travel

slowly to operate machinery, for instance road sweeping (Eglese and

Murdock, 1991), refuse collection (McBride, 1982) or snow clearance

(Gendreau, Laporte et al., 1997). Most of these examples are capacitated

by volume restrictions, for instance the amount of refuse that can be

carried on a vehicle.

Unlike these applications, rural postal deliveries are undertaken by vans

that can travel relatively quickly between houses. These vehicles have no

effective volume restriction, as they can carry much more mail than could

be feasibly delivered in one day. The only effective capacity restriction is

the total time for the route, including travel to the first delivery and from

the last delivery to the post office. The service time for each arc is related

to the length of the arc and the number of houses to be serviced on it. The

traversal time for an arc is related only to its length (assuming a constant

speed of travel). In general, arcs can be traversed or serviced relatively

quickly, as vehicles travel comparatively fast and there are few houses.

Consequently, the service time for each arc is typically a small proportion

of the capacity of a vehicle. A postman working a six-hour day in a van

could service more than two hundred road segments in some cases. A

typical rural delivery area might have approximately one thousand arcs

to be serviced by three or four vehicles. This means that each vehicle


149

visits some two or three hundred arcs, which is a much larger network

than is typical in arc routing problems.

Rural postal delivery also differs from many other arc routing problems,

in that each road segment need only be serviced once, as it is possible to

service customers on both sides of the road. Many of the complications

found in urban areas do not arise on rural roads. These include problems

with crossing the road, no right or left turns, traffic restrictions, etc.

Therefore, from an algorithmic point of view, arc routing in a rural Irish

context presents a problem that is relatively free of constraints in

comparison to other real world problems. Consequently, this problem is

differentiated from most of the examples in the literature by the much

larger problems encountered and the sparsity of the networks used.

7.2.2 Time Capacitated Arc Routing Problems

TCARP represents a problem where a time rather than volume

limitation provides capacity restraints for the problem. This typically

arises in problems where volume constraints are not relevant, for

instance meter reading. Postal delivery problems may be volume

constrained if delivery takes place on foot, as the postman cannot easily

carry all the mail. This dissertation is concerned with rural postal

delivery by van, and so is a time-capacitated problem. In this class of

problem, the length of the working day is the main factor in the

clustering of distinct routes.

A simple approach to a TCARP problem is to substitute units of time for

units of volume and apply techniques devised for volume constrained

problems. However, this approach does not recognise the specific

characteristics of TCARP. In a volume-based problem the capacity of the

vehicle is used up by servicing arcs, mere transit of an arc does not add

any volume to the route. In TCARP, either traversing or servicing an arc

will exhaust the time capacity of a route. Volume based solution

procedures are likely to give good solutions to TCARP, as any technique


150

designed to minimise distance will obviously tend to reduce arc traversals

and consequently will reduce the overall time spent in making these

traversals. Nevertheless, superior solutions can be identified by

procedures that exploit the distinct characteristics of TCARP.

7.3 Modified bounds for LSCARP

7.3.1 Lower bounds for the LSCARP

The complexity of CARP precludes the use of optimal techniques for large

problems, such as those arising in rural postal delivery. The absence of

optimal solutions makes it difficult to assess the efficiency of heuristic

approaches. Lower bounds provide such a basis for comparison. In this

section we propose a lower bound procedure for CARP that is based on

those in Chapter 5, in particular on the LB1 and LB2 bounds (Benavent,

Campos et al., 1992) in Sections 5.5.3 and 5.5.4. Our revised bounds

incorporate some improvements on LB1 and LB2. The following sections

propose some modifications specifically directed at time based problems.

Section 7.3.4 identifies a modification to the way LB2 generates

successive cutsets, this change should improve the bound generated for

both volume and time based problems. Section 7.4 provides

computational examples of the revised lower bounds. These bounds are

used subsequently as the basis of comparison for the heuristic techniques

for the LSCARP discussed in this dissertation.

7.3.2 Depot based lower Bounds for TCARP

In this section, we propose modified versions of the NDLB (Saruwatari,

Hirabayashi et al., 1992) and the LB1 and LB2 bounds (Benavent,

Campos et al., 1992) discussed in Chapter 5. These modifications reflect

the differences between time and volume constrained problems. These

bounds, which we will call TNDLB, TLB1 and TLB2 respectively, provide

bounds appropriate to time constrained problems.


151

The original NDLB and LB1 approaches calculate bounds by adding

additional traversals at the depot to reflect the fact that multiple vehicles

must travel along the arcs leading to the depot. The number of traversals

required is twice the number of vehicles required to service the network.

The number of vehicles required reflects vehicle capacity and the demand

in the network. In a time based problem this relationship is slightly more

complex as the vehicle capacity is consumed both by traversing and by

servicing an arc. A straightforward modification of a volume-based lower

bound could include traversal time in service time and calculate a bound

on this basis, using time units instead of volume units. A time-based

approach needs to recognise that vehicle capacity is also consumed by arc

traversals generated by the matching procedure.

The modified version of NDLB, known as TNDLB, calculates the number

of vehicles required by reference to the time taken to traverse all arcs, to

service all arcs and to make any additional traversals needed to generate

an Euler tour. The time based bound TLB1 contains similar

modifications. In some cases, the calculation of the lower bound might

indicate that additional traversals are required, and this might entail a

higher number of vehicles. In this case, the bound is recalculated based

on the increased number of vehicles.

The time modified bounds, TLB1 and TNDLB, can be expected to reflect

the relationship between their original counterparts, where LB1 was

superior to NDLB (see Section 5.5.3). This implies that TNDLB is not

especially useful for comparison purposes. However, as we discuss below,

the development of TNDLB allows the use of a modified version of the

optimal branch and bound procedure based on that bound (see Section

6.2.2). Li and Eglese (1992) proposed a bound similar to TLB1, which

they called Time Constrained Lower Bound (TCLB). In addition to

modifications for time constraints, this bound improves on LB1 by

incorporating some changes in the method of calculating the paths to the

depot. However, TCLB only examines cuts at the depot and we believe


152

that in large sparse networks it is important to use a bound that

examines cuts away from the depot. Consequently, in this research this

dissertation has concentrated on developing a time-based bound based on

those bounds that examine parts of the graph away from the depot.

Further examination of the implications for cuts away from the depot of

the ideas introduced by Li and Eglese would constitute a useful extension

of the work presented in this dissertation.

7.3.3 Bounds for TCARP based on the entire graph

In Section 5.5.4 we saw that the LB2 bound improves on LB1 by looking

at any additional traversals needed at all points in the graph, and not

just at the depot. The additional traversals needed are assessed at a

number of cuts in the graph distant from the depot. For each cut in the

graph, the algorithm identifies the number of vehicles required to service

the area beyond the cut, and LB2 then calculates any additional

traversals required for this number of vehicles crossing the cut. LB2

represents an effective bound, which can be calculated in reasonable

time. As LB2 was originally designed with volume constrained problems

in mind, the calculation of the number of vehicles crossing a cut is made

by comparing the volume to be serviced beyond the cut and the capacity

of each vehicle. The calculation of the bound for volume constrained

problems assumes that the vehicle travels to the cut without servicing

any arcs along the way. Therefore for volume constrained problems the

entire capacity of the vehicle is available to service arcs beyond the cut.

In deriving a modification of LB2 for TCARP, alterations are made to

both the calculation of the vehicle capacity and the calculation of the

capacity required to service beyond the cut. In TCARP when a vehicle

reaches a distant part of the graph, its potential capacity will have been

reduced by the time taken to travel to and from the depot. Therefore, the

available capacity of a vehicle depends on where in the graph the cut is

located. The capacity needed to service beyond the cut must include both

the service time and any unavoidable traversal time beyond the cut. Both


153

of these amendments to the basic LB2 tend to increase the number of

vehicles required. The increased number of vehicles leads to an increased

number of traversals of the cut and therefore provides a tighter lower

bound for TCARP than the simple substitution of time for volume.

The original LB2 calculations assume that the number of vehicles

crossing the cut is known. For the time-based problem, traversal times

beyond the cut must be calculated exactly in advance to establish the

effective vehicle capacity. Identifying the traversals requires a

computationally intensive matching algorithm, a process that could make

TLB2 much slower than LB2. An exact approach would mean that a

matching procedure would be used to calculate the number of vehicles

and then a second MCPM procedure used to calculate the bound itself. In

order to avoid calling the MCPM procedure twice, an estimate of the

traversal time beyond the cut is used. This provides an estimate of the

number of vehicles required, which can be revised when the full MCPM

calculations take place as part of the lower bound calculations. If the

estimate proves to be incorrect the number of vehicles can be revised and

the lower bound calculated a second time. If this occurs infrequently, the

use of an estimate is less computationally intensive than using a MCPM

at each iteration to calculate an accurate number of vehicles.

In TLB2 a MCPM is performed initially on the entire network, this

provides a measure of the additional traversals required in the

uncapacitated problem. The uncapacitated problem provides a lower

bound for the traversal time on the network as a whole. A ratio between

the time taken to visit all network arcs and this additional traversal time

is calculated. This ratio is then used to estimate the additional traversal

time for any cutset in the network. This ratio will differ somewhat from

network to network depending on the proportion of odd degree vertices.

At each cut, the vehicle capacity for that cutset is defined as the original

vehicle capacity (in time units), less the time taken to travel from the

cutset to the depot and back again. For TLB2, this reduced vehicle


154

capacity is compared with the estimated traversal time and total service

time for arcs beyond the cut. From this calculation, the number of

vehicles is derived and this is used in the lower bound calculations, which

are otherwise similar to those for LB2.

7.3.4 Modification to LB2 cutset strategy

As described in Section 5.5.4 above, LB2 generates a cutset by taking all

nodes adjacent to nodes in the existing U to form the set U′. These nodes

are then added to those in U to form a new set U at each iteration. The

resulting cut is formed by including all arcs from the existing graph

which connect the new U set and the component, V′, formed by removing

the nodes in U from the original graph. This adds a complete set of

adjacent nodes to U at each iteration, thereby ignoring a large number of

possible cutsets. Our proposed bounding techniques incorporate a

modification to LB2 that adds nodes individually to the set U,

consequently generating a larger number of cutsets. This larger number

of cutsets may contain a superior solution to that obtained with the more

computationally efficient LB2. This strategy was first tested by two

MMangtSc students working with the author (Breslin and Keane, 1997)

and was found to improve the LB2 bound in some circumstances.

As the set U′ generally contains more than one node, the revised selection

procedure must choose between these (Figure 7-6). The revised procedure

selects nodes from U′ in increasing order of degree and adds them to U.

The selected node is marked to ensure that it will not be considered again

and an iteration of LB2 is carried out as before. The unmarked node in U′

U ′′′′

U

Figure 7-6 : Multiple nodes in U′′′′ at each iteration


155

with the next lowest degree is selected and included in U. This procedure

is repeated until all nodes from U′ are included in U. Once all the nodes

from U′ are included in U, then a new U′ is identified in the same manner

as used in the original LB2, where U′ is the set of nodes adjacent to nodes

in U. The calculation of L1 remains similar to the approach used in LB2,

L1 is recalculated only when all of the nodes in U′ have been added to U.

7.4 Computational Results for TLB2

7.4.1 Example of new cutset strategy

The modifications to LB2 can be illustrated by the example shown in

Figure 7-7. This example is used as the degree of the nodes in each

successive set U′ are not all the same. The first cut in Figure 7-7 is Cut

(1-2, 1-3). The basic LB2 calculations would use this as the basis of

calculating a lower bound and would then proceed by adding all adjacent

nodes to the set V at each iteration (Table 7-1). Our alternative strategy

can be seen by looking at the graph in Figure 7-8. At the initial step we

select Node 3 as having the lowest degree and include it in U.

2

3

5

4

6

7

9

8

1 2, 7

2, 4

3, 7

5, 6

5, 9

4, 5

4, 5

7, 9

3, 5

2, 5

2, 5

3, 5

3, 7

Cut 1

Cut 2

Cut 3

Cut 4

Traversal Time , De mand

Figure 7-7 : Original LB2 cutsets


156

Therefore U′ = {i ∈ V | i is adjacent to a vertex in U}. U = U ∪ Node b,

such that Degree[b] = Min(Degree[i]) where i ∈ U′ and i is not already

included in U.

For the example in Figure 7-7, the iterations will add nodes one at a time

in increasing order of connectivity and will produce sets U, U′ and V′ as

in Table 7-2 and Figure 7-8.

Table 7-1 : The sets at each iteration using the original LB2

procedure

IterationNumber

U U′′′′ V′′′′

1 {1} {2, 3} {2, 3, 4, 5, 6, 7, 8, 9}

2 {1, 3, 2} {4, 5} {4, 5, 6, 7, 8, 9}

3 {1, 3, 2, 4, 5} {6, 7,9} {6, 7, 8, 9}

4 {1, 3, 2, 4, 5, 7, 6, 9} {8} {8}

2 3

5 4

6 7

9 8

1 2, 7 2, 4

3, 7 5, 6 5, 9

4, 5 4, 5 7, 9

3, 5

2, 5 2, 5 3, 5

3, 7

Cut 1

Cut 2

Cut 4

Cut 1a

Cut 2a

Cut 3a

Traversal Time , Demand Cut 4a

Cut 1b

Cut 2b

Figure 7-8 : Selecting Nodes one at a time, in increasing order of

connectivity


157

7.4.2 Simple Computational Example for TCARP

This example is based on the graph shown in Figure 7-8 and uses the

cutset selection modification discussed in Section 7.2.2 above. The first

iteration adds node 1 to set U. The bound TLB1 can then be calculated,

based on the number of vehicles required to enter and leave the depot.

Subsequent iterations examine cuts away from the depot, providing our

bound TLB2. In this example, we use a vehicle capacity of 50 minutes.

The overall network has a total of 9 nodes, 13 bi-directional arcs, a total

travel time of 45 minutes and a service time of 79 minutes (including the

travel time for each arc).

TLB1 starts with an estimate of the number of vehicles, found by adding

the total time required to traverse the network arcs and the additional

traversal time required for the arcs added by the MCPM. In this case,

only nodes 2 and 4 are of odd degree, so there is an additional traversal of

Table 7-2 : The sets at each iteration using the modified cutset

selection

IterationNumber

U U′′′′ V′′′′

1 {1} {2, 3} {2, 3, 4, 5, 6, 7, 8, 9}

2 {1, 3} {2} {2, 4, 5, 6, 7, 8, 9}

3 {1, 3, 2} {4, 5} {4, 5, 6, 7, 8, 9}

4 {1, 3, 2, 4} {5} {5, 6, 7, 8, 9}

5 {1, 3, 2, 4, 5} {6, 7,9} {6, 7, 8, 9}

6 {1, 3, 2, 4, 5, 7} {6,9} {7, 8, 9}

7 {1, 3, 2, 4, 5, 7, 6} {9} {8, 9}

8 {1, 3, 2, 4, 5, 7, 6, 8} {8} {8}


158

the arc between them, giving an additional time of 3 minutes. This figure

is used to calculate a matching ratio for use later in the calculation of

TLB2, in this case the matching ratio is 3/(45+3) = 0.063 (matching

/(traversal + matching)). The estimated number of vehicles is therefore

(79+3)/50 = 2 ((service+matching)/capacity). The remaining calculations

required for the bound are similar to those for LB1 (see Section 5.5.3).

This gives a lower bound of 7, reflecting two additional traversals to the

depot. For this vehicle capacity, TLB1 is the same as LB1, as the

additional traversal time is not sufficient to warrant the use of another

vehicle.

We tested two versions of the TLB2 bound, TLB2a and TLB2b. TLB2a

uses the same cutset procedure as the original LB2 bound. For this

example TLB2a gives a lower bound of 7, which is identical to that found

by TLB1. This outcome is not unexpected given the small size of the

Table 7-3 : TLB2 example

Iteration

Number

(Table

7-2)

Service

time

beyond

cut

Available

Vehicle

Capacity

Estimated

matchingEstimatedVehiclescrossing

cut

Actual

Vehicles

TLB2

1 79 50 2.56 2 2 7

2 75 50 2.25 2 2 7

3 68 46 1.75 2 2 7

4 55 46 1.50 2 2 7

5 46 40 0.63 2 2 8

6 36 36 0.31 2 1 8

7 27 36 0.19 1 1 8

8 10 32 0.00 1 1 8


159

network. TLB2b proceeds by using the revised cutset selection procedure

discussed in Section 7.3.4 and selects nodes in the sequence shown above

in Table 7-2.

The operation of the algorithm is shown in Table 7-3. An estimate of the

additional traversals is obtained by multiplying the matching ratio

(0.063) by the cost of travelling the arcs beyond the cut. This is shown in

Table 7-3 in the column headed estimated matching. The estimated

matching is added to the cost of servicing the arcs to obtain an estimate of

the total time needed for the region beyond the cut. This estimated total

time is used to determine the number of vehicles needed, and to calculate

a bound, based on the LB2 calculations. The number of vehicles needed is

verified when this bound has been calculated. The operation of this

feature can be seen from iteration 6 in Table 7-3. At this point nodes

{7,8,9} are beyond the cut. Vehicles crossing this cut have a maximum

capacity of 36(50-14), this reflects the fact that vehicles must travel for a

minimum of 7 minutes (to node 5) to reach and return from the cut. There

are 36 minutes of service time beyond the cut and the estimate for the

matching required is 0.31 (0.063 * 5). This is added to the service time,

implying that two vehicles are required. In this case, each of these nodes

is of even degree, so there is no actual matching required. Consequently,

only the service time of 36 is relevant and the actual number of vehicles

required is one. The bound is then recalculated with one vehicle.

On this small example, the TLB2 bound gives a bound of 8. This offers

some improvement over the standard LB2 bound of 7 as a result of the

use of modified cutset strategy. This is a result of the modified cutset

strategy rather than the time-based alterations. In iteration four the

revised cutset procedure leads to a situation where two arcs cross a cut

and two vehicles are required to service the arcs beyond the cut. This

means that two extra traversals are added, giving a higher bound. The

original cutset strategy used in LB2 would not have examined this cut, so

the best bound would have been 7.


160

Table 7-4 : Summary of Time based bound

units) time (in cut at vehicle ofcapacity adjustedunits) time (in vehicle of capacity

distance (over node to node from travel totime

(deadleg) servicingwithout arc traverse to time

time traversal including arc service to time

==

==′=

s

ijij

e

e

WW

djitet

et

)

Set U = { 1 }, L = L1 = L2 = 0;

∑∑

∈

∈

+=

Gee

Gee

estt

tMR

MCPM(G) (calculation of matching ratio)

WHILE U <> V DO

Let V' = V - U and G' be the graph induced by V'. Find the connectedcomponents of G'. Suppose G' has ‘k’ components G's = (V's , E's ) and

},:),({)(cutsetedge UjViEjieV ∈′∈∈==′δSet V'' = V' – U' and G'' be the graph induced by V''

Set Uc = U

WHILE U'' <> U' DO

U'':= U'' ∪ i {i ∈ V | i is adjacent to a vertex in U, i ∉ U'' }

FOR s := 1 TO k DO

)(set and LB2 tosimilar

Hgraphweightedaconstruct thenorIf

Let

},{max

min

:)({

)(

capacity) vehicle adjusted( }min{*

s

.

)(

)(e

ss

ss

ss

sests

eves

ess

ests

VEeest

is

HMPm

rS

VS

tpr

tt

tVet

MRW

t

p

tWW

s

ss

=>≠′

′=′−=

=>′∈=

+×

=

−=

′∈

′′∈∑

0

20

0

1

2 1

φ

δ

δ

δ

ENDFOR s.

U := Uc ∪ U''

},max{ 1221

LLttLL

mL

Gee

Gee

t

ss

++′+=

=

∑∑∑

∈∈

=

ENDWHILE

s

t

SstrLL ∑

=

+=1

11

Set U' = the set of nodes {i ∈ V | i is adjacent to a vertex in U }.

ENDWHILE.

Set LB2 = L2.


161

In this example, most of the cuts identified by LB2 have three arcs

crossing the cut, implying that few additional traversals are needed. In

this extremely small network, the time modification does not provide a

superior lower bound. However, the greater number of cuts examined by

TLB2 leads to a significant improvement on the large sparse networks

discussed subsequently. The operation of the time-based bounds is

summarised in Table 7-4.

7.5 Comparison of lower bound and optimal results

7.5.1 Time based branch and bound procedure

In order to assess the lower bound procedures introduced above we used a

time-based version of the branch and bound procedure introduced in

Section 6.2.2. Our algorithm uses 32-bit Windows 95 code in Borland

Delphi and is derived from the Pascal code built in UCD by Montwill and

Naughton (1994). This code embodies a matching procedure derived from

the FORTRAN code used by Derigs (1981). Our algorithm is similar to

the original procedure (Hirabayashi, Saruwatari et al., 1992) with a

modification for time. Previously only relatively small networks have

been solved with this procedure, the largest network solved in the

original paper contained fifty demand arcs. Montwill and Naughton were

also able to solve a fifty-arc problem. However, this problem could be

solved only for the two-vehicle situation; using a larger number of

vehicles increased the number of subproblems to the point where it

became computationally impossible to solve the problem. This suggests

that time-based problems are more difficult to solve on sparse rural

networks, in comparison to the complete networks examined by the

Japanese designers of the optimal branch and bound procedure.

The difficulty of solving an arc routing problem optimally was confirmed

by our experiments, despite our use of a much more powerful computer

than that used by Montwill and Naughton. Intuitively it might seem that

the use of modern computers with more RAM might allow larger


162

problems be solved. In fact, the exponential increase in the number of

subproblems meant that the use of more memory had little practical

effect on the ability of this procedure to solve problems of practical size to

optimality.

The branch and bound procedure starts with a complete representation of

the original graph and generates artificial nodes so that the number of

nodes in the completed graph is twice the number of undirected arcs in

the original. Each subproblem generated contains a cost matrix between

the artificial nodes, therefore a 50 arc problem would have 100 nodes and

would have a 100 x 100 cost matrix. If floating-point numbers were used

this would mean that each subproblem would typically occupy more than

60KB of RAM. This would make such a problem very difficult to solve.

For the work recorded in this dissertation, we tested this algorithm on a

Pentium III 500Mhz PC with 256MB of RAM running the Windows NT

4.0 operating system. By storing only the changes from one sub problem

to another and by using single byte storage structures we were able to

reduce the marginal storage required for each subproblem to around 100

bytes. This configuration typically allowed 750,000 subproblems be

generated before the machine ran out of RAM. This larger number of sub-

problems did not greatly improve the ability of the procedure to reach an

optimal solution, indicating that memory use remains an important

constraint on the operation of this algorithm.

The Tour Construction algorithm uses the NDLB lower bound, which is

inferior to the LB2 bound (see Section 5.5.2). This is potentially

important, as the algorithm is generally unable to find a solution when

the solution is above the lower bound. It would be quite difficult to devise

a branch and bound procedure based on the LB2 approach and beyond

the scope of this dissertation. The systematic approach of the branch and

bound technique is likely to provide a good feasible solution and therefore

to provide a useful basis for comparison for the lower bounds, even if the

optimal solution has not been identified.


163

number of nodes 27

number of demand arcs 35

total demand (inc service) 139 minutes

total service time 47 minutes

Arc Weights (demand, cost) in minutes (rounded off to nearest integer)

Figure 7-9 : 35 arc network


164

7.5.2 Computational experiments

In order to assess the TLB2 procedure we used a 35-arc network derived

from the Irish rural road network (see Figure 7-9). This network is still

much smaller than a real world problem, but is around the largest size

that allows the calculation of an optimal solution for some vehicle

combinations. All of the arcs in this network are demand arcs. We tested

this network with various vehicle capacities, so that from two to five

vehicles would be needed (Table 7-5). We tested TNDLB, TLB1 and TLB2

using the original LB2 cut procedure (TLB2a) and our proposed

individual arc cut procedure (TLB2b) (see Section 7.2.2). These bounds

were programmed in Borland Delphi and employ a matching procedure

derived from the FORTRAN code used by Derigs (1981).

In this 35-arc example, the results for TLB2a and TLB2b were the same.

TNDLB and TLB1 gave the same results, as would be expected from the

results reported in Section 5.5. The branch and bound procedure

identified the TNDLB solution as the optimal one where two or three

vehicles were used. Where more vehicles were used, the depot-based

bound was not optimal and the branch and bound procedure failed to

converge on a solution.

Table 7-5 : Computational results for 35 arc network

VehicleCapacity

Numberof

VehiclesTNDLB TLB1 TLB2a TLB2b

BranchAnd

Bound

80 2 16 16 16 16 16

55 3 18 18 18 18 18

45 4 20 20 22 22 24#

35 5 22 22 26 26 28#

TLB2a : arc cut strategy of original LB2TLB2b : individual arc cut strategy# best solution when machine ran out of memory


165

The difference between TLB1 and TLB2 can best be seen if a larger

number of vehicles is used. For instance if five vehicles are used, each

with a vehicle capacity of 35. TNDLB and TLB1 give a value of 22 for the

cut at the depot alone. This reflects the fact that five vehicles (ten trips)

must pass along three arcs (1-10), (1-13) and (1-9). Consequently, seven

additional traversals are needed (Table 7-5).

TLB2 gives a higher bound for the cut shown in Figure 7-10, across arcs

(10-11), (10-14), (9-5), (9-2), (13-25) and (13-27). At this cut the vehicle

capacity is reduced to 33, after deduction of the time taken for vehicles to

travel to and from the cut. The path taken to reach the cut is

unimportant in this network as arcs 1-9, 1-10, and 1-13 each require one

minute to transit. In this case, node 11 and node 5 form two separate

components and the algorithm identifies the additional traversals of arcs

(10-11) and (9-5). The rest of the network is reached along arcs (10-14),

(9-2), (13-25) and (13-27). Five vehicles are still needed to service the arcs

beyond the cut, so six additional traversals are needed along these four

arcs. The algorithm calculates these extra traversals as 17 minutes,

which is added to the two extra minutes incurred traversing arc (10-11)

and arc (9-5). The TLB2 procedure then adds an estimate of the

additional traversals between the cut and the depot. In this example, this

is 7 minutes, reflecting the fact that 5 vehicles make 10 trips (inward and

outward) along only 3 arcs. The TLB2 bound is therefore 26, which

provides a much superior bound to TLB1 in this case.

1

95

10

11

13

27

25

14

2

Figure 7-10 : Maximum TLB2 cut for vehicle capacity of 35


166

7.5.3 Implications of computational results

The above examples indicate that the TLB2 bound is much superior to

the TLB1 bound and the both outperform the TNDLB approach. Later in

this dissertation, we look at larger real world network examples. These

larger networks cannot be feasibly solved to optimality. In this situation

lower bounds provide the only means of assessing the quality of a

heuristic solution. The following chapter introduces heuristic approaches

to TCARP. In Chapter 9 these approaches are applied to real world

networks and their performance is compared to the TLB2 bound

discussed in this Chapter.


167

Chapter 8 : Solution procedures for TCARP

8.1 Introduction

8.1.1 Solutions for TCARP

In the previous chapter, we introduced a time-based formulation and

proposed modified lower bounding procedures to make them suitable for

time capacitated routes. The objective of this dissertation is to examine

large networks. Currently available optimal procedures, such as those

discussed in Section 6.2, do not solve these problems to optimality; only

heuristic approaches are likely to be successful. This chapter discusses

these heuristic techniques.

Solution procedures for TCARP can be assessed by comparison with the

lower bounding methods introduced in the previous chapter. However, in

the context of the focus on decision support in this dissertation, any

algorithmic techniques must also be evaluated with respect to the real

world requirements of the problem. In a DSS context, the output from

routing models is subject to further manipulation by the decision-maker

(see Section 2.2.1). From a DSS point of view the mathematical objective

function used in the model is only one dimension of the quality of the

solution.

8.1.2 Algorithm requirements for the LSCARP

A number of specific decision support issues arise in the context of

routing postal deliveries on Irish rural networks. Customer service is

improved if deliveries are completed early in the day. This may be

especially important for particular businesses or other premises on the

route. However, by definition, some of the customers must be visited at

the end of the route. In the context of an eight-hour day, this means that

deliveries take place in the afternoon. While customers are unlikely to be


168

happy about this late delivery, they are more likely to accept it if it

appears to be an inevitable consequence of geography.

One component of user acceptability is the perception of the overall shape

of the route and whether it appears to be ‘logical’. Human perception of

route design is largely a spatial one; if a route appears to be a logical

shape, then it will be acceptable to all parties involved, including drivers

and customers. Practical routing projects often note the loss of goodwill

that results from the fact that routes do not appear to be logical (Bocxe

and Tilanus, 1985). Some solutions generated by automated procedures

meet this requirement better than others. A second concern for

acceptability is that deliveries are completed as early as possible. Service

considerations dictate that if a route passes along a road more than once,

then the deliveries should occur on the first pass and that deadleg

traversals of the road should occur later in the day. Customers do not

wish to see a postal van passing their door early in the day, if they have

to wait until afternoon for their deliveries.

In the context of the algorithms discussed in this chapter, the overall

spatial distribution of the route is of interest. A spatially compact route is

more likely to meet service needs and is easier for the decision-maker to

manipulate in the DSS. Routing techniques need to be assessed with

respect to the ease of user intervention in the process. A facility for user

intervention will allow any specific circumstances be taken into account.

8.2 Heuristic approaches

8.2.1 CARP solution techniques

As previously discussed in Chapter 6, three basic approaches to solving

CARP exist. Many arc routing procedures have been based on Single-Pass

heuristics where a single iteration provides both a clustering of arcs and

a sequence for each route (Section 6.1.1). An alternative is to separate the

clustering and routing phases, using either RFCS approach (Section

6.1.2) or the CFRS approach (Section 6.1.3).


169

8.2.2 Route-First Cluster-Second approach

In the context of LSCARP the RFCS approach generates a large Euler

tour. This requires that odd degree vertices are initially matched. In a

multi-vehicle problem this large route is infeasible, as it is longer than a

single vehicle can service. This large infeasible route is then split up into

routes within the maximum service time for the vehicle. In this approach,

a matching algorithm is initially used to make the network Eulerian.

Within this matched network, a large number of possible Euler tours

exist. Consequently, the large infeasible tour needs to be suitable for

splitting into smaller tours. Therefore, a number of heuristics are used

when building the large tour to ensure that suitable routes result from

the splitting of this large tour. The large Euler tour may be decomposed

into sub-clusters or cycles, and are then combined into new feasible

routes (Eglese, 1994).

8.2.3 Cluster-First Route-Second Approaches

CFRS approaches follow an intuitively appealing sequence of first

choosing the grouping of the routes and then dealing with the sequence to

be followed within each route. This seems especially appropriate for arc

routing where the Euler tour provides an optimal sequence within a

route. Cluster-first techniques are widely used in point based vehicle

routing, where the technique is seen to provide compact routes. Initial

clustering would seem to address the requirement in the LSCARP for

compact routes that are easily understood. We examined this approach

for LSCARP as an alternative to the less successful RFCS discussed

below in Section 8.3.

The objective of clustering techniques in routing is to achieve a compact

and easily routed grouping of arcs or nodes. Vehicle routing problems

often employ a coordinate-based approach, for example that of Gillett and

Millar (1974) discussed in Section 6.1.3. In the context of arc routing on

sparse networks, the coordinate based approach would appear to be


170

inappropriate. In this context, we sought to retain some of the motivation

underlying other clustering techniques, but to employ a method that took

full account of the actual road layout.

Our investigations revealed the CFRS method to be the most appropriate

approach and we discuss in detail two techniques based on this approach.

We also discuss our less successful experiments with the RFCS approach.

8.3 Route first, cluster second algorithm

8.3.1 Tour construction

In our RFCS algorithm, phase one uses a matching algorithm to allow a

single vehicle Euler Tour to be generated. The algorithm proceeds by

adding arcs to the Euler tour, on the matched network, giving preference

to demand arcs. The route is built in a direction generally moving away

from the depot. This phase continues until approximately half of the

route time of a vehicle has been allocated. In the second phase of the

algorithm, we attempt to keep the algorithm in the region of the most

distant point routed in phase one. This attempts to ensure that routes are

reasonably compact. A third phase begins when the route has completed

more than three-quarters of the route time for a single vehicle. In this

phase, the large route makes its way back towards the depot. When the

route time for a single vehicle is exhausted, the algorithm goes back to

phase one (Table 8-1).

At the end of the routing process, when the large route has returned to

the depot, checks are made to ensure that all sections of the network have

been routed. If the large route returns prematurely to the depot, the

addition of these unallocated arcs may affect the quality of the routes

generated. When the large route is completed, it is subdivided into routes

within the vehicle capacity. While the multi-vehicle solution will

inevitably introduce additional traversals, the design of the large tour

was such that these should not add unnecessarily to the solution.


171

8.3.2 Computational example for the RFCS algorithm

The operation of the RFCS algorithm can be demonstrated using the

(extremely simplified) network in Figure 8-1. Assume that the vehicle has

Table 8-1 : Pseudo code for RFCS approach

Matchnodes(network)

Currpoint := 0;

While all arcs not routed do

If currpoint < vehcapacity*.45 then

AddEulerOutwards

If currpoint > vehcapacity*0.45 and < vehcapacity*0.75 then

AddEulerRegion;

If currpoint < vehcapacity*.75 and vehcapacity <= 1 then

AddEulerToDepot;

If currpoint > vehiclecapacity then currpoint := 0;

EndWhile;

Splitroutes(routenet);

For i := 1 to numroutes do

Matchnodes(routenet[i];

Eulertour(routenet[i]

Endfor

Table 8-2 : Infeasible route for RFCS procedure

Sequence of nodes visited

1-S-2-S-4-S-5-S-2-T-1-S-3-S-6-S-8-S-9-S-6-S-10-S-12-T-10-T-6–T-3-S-7-S-11-T-7-T-3-T-1

T = traversal of arcS= service of arc


172

a capacity of 24 time units. The first step is to perform a MCPM on the

network, adding additional arcs between the nodes of odd degree. This

adds additional traversals for arcs (1-2), (1-3), (3-6) (3-7) (7-11), (6-10) and

(10-12), giving an uncapacitated solution time of 62. A large route is

devised on this matched network, arbitrarily starting at arc 1-2. The

infeasible route generated is shown in Table 8-2. This route is then

subdivided into feasible routes. Route 1 in this solution is the same as in

the other approaches. Route 2 is then built from the remaining arcs on

the large infeasible route until a point is reached where the vehicle must

return to the depot. This means that route 2 can visit arc (6-10) and then

return to the depot, giving a route of exactly the vehicle capacity of 24

units. However arc (10-12) is not visited, leaving this isolated arc to be

visited by another route. The final route visits this arc and the remaining

arcs, giving a route of 23 units (Table 8-3).

1,3

2,4

1,3

1,2

2,4

1,2

2,3

2,3

2,5

2,4 2,5

1,3

4,6

9

12

8

6

10

11 7

3

1

5

4

2

(cost, demand)

Figure 8-1 : Simplified network for heuristic examples


173

8.3.3 Evaluation of the RFCS algorithm

This strategy should ensure that the routes are reasonably compact and

that the split points on the large infeasible route occur close to the depot.

In the above example the heuristic worked fairly well, but inefficiencies

can result from particular network configurations. Any amendments to

overcome this deficiency would need to recognise the structure of the

network.

8.4 Tree based Approach to clustering for the LSCARP

8.4.1 Clustering on rural road networks

Our first CFRS is based on observation of the characteristics of the

problem. A typical LSCARP features deliveries from a small town or

village, this is typically a central point on the local road network.

Generally, five or six roads will converge at a village, providing a well-

connected node on the road network. Deliveries radiate out along these

roads to the more sparsely connected rural road network, where

deliveries take place. Any algorithm designed to cluster routes needs to

recognise these characteristics in the road network (see Figure 8-2). A

network constrained equivalent to the coordinate-based approaches is to

regard delivery routes as a tree routed at the depot node (in the village).

Recent work by New Zealand based researchers (Basnet, Foulds and

Table 8-3 : Routes generated by RFCS algorithm

Route Sequence of nodes Volume

1 1-S-2-S-4-S-5-S-2-T-1 222 1-S-2-S-3-S-6-S-8-S-9-S-6-S-10-T-6–T-3-T-1 243 1-T-3-T-6-T-10-S-12-T-10-T-6-T-3-S-7-S-11-T-7-T-3-T-1 23



174

Wilson, 1999) has also recognised the importance of the tree-like

structure of rural roads in designing clusters for milk collection routes.

8.4.2 The shortest path tree clustering algorithm

This first phase of our algorithm starts by identifying the shortest path to

every node in the delivery area. We identify nodes near the depot where

some of the shortest paths diverge. These are known as split nodes. The

next phase identifies the set of nodes whose shortest path passes through

a split node. A matching is performed on the set of arcs linking these

nodes. This provides a measure of the service time required to visit this

set of nodes. If this is less than the capacity of a route then this set of arcs

forms the basis of a cluster for one route. If the service time required

exceeds the capacity of a single vehicle, then split nodes further away

from the depot are examined. For more distant split nodes the aim is to

identify clusters of approximately one hour. When such clusters have

been defined, adjacent clusters are combined to give a cluster close to the

size of the vehicle. An abbreviated pseudocode version of the algorithm

can be seen in Table 8-4.

Figure 8-2 : Treelike structure of rural road network


175

8.4.3 Computational example of tree clustering algorithm

In this example, we again use the simple network in Figure 8-1, with a

vehicle capacity of 24 time units. In the first phase, shortest paths are

calculated to each node. The nodes nearest the depot are examined. The

shortest paths from nodes 8, 9, 12, 10, 6, 7, 11 pass through node 3. The

shortest paths from nodes 5, 4 pass through node 2. Beyond node 2 there

are only even degree nodes, so no matching arcs are required.

Consequently, to service beyond node 2 requires a service time of 3+4+5 =

12. A vehicle travelling to node 2 could service arc (1-3), with a service

time of 6 and must travel along arc (1-3) on its return journey, adding an

additional traversal of 4. This indicates a total time of 22, which is close

to the vehicle capacity.

Table 8-4 : Pseudo code of tree clustering algorithm

While Not all arcs routed do

Next splitnode ∈ U

Calculate_cluster_routetime

While cluster-routetime > minclustersize do

SubCluster

EndWhile

While cluster-routetime < vehicle_capacity do

Amalgamate Subclusters

Endwhile

Buildroute

Endwhile


176

We now look at the other split node. Beyond node 3 there is a total service

time of 25 (3+3+2+3+4+2+5+3). There are also additional matching

traversals of arcs (3-7) (7-11) (6-10) and (10-12). Therefore the total time

required is 32 (25 + 7), which exceeds vehicle capacity. Therefore we move

to node 6, which now becomes a split node. Beyond this node, there is

total service time of 14 and traversal time of 3. If we look at the arcs

linking node 6 to the depot, we see that these arcs cannot be serviced

within the vehicle capacity. Even if we do not service these arcs, vehicles

must at least travel from the depot to and from node 6, adding an

additional traversal of 6. This is within the vehicle capacity, so the region

beyond node 6 can form a cluster, with the arcs between node 6 and the

depot being traversed but not serviced by this route.

At this point, a third route is generated to service these arcs and arcs (3-

7) and (7-11). This vehicle has a total service time of 15 and additional

traversals of 6. This gives a total route time of 21. Consequently, in this

example the shortest path tree clustering approach provides a solution

with three routes of 21, 23 and 22 units respectively (see Table 8-5 and

Figure 8-3 below). This is in fact the optimal solution for this problem.

Table 8-5 : Routes from Tree Clustering approach

Route Sequence of nodes visited Volume

1 1-S-2-S-4-S-5-S-2-T-1 222 1-T-3-T-6-S-10-S-12-T-10-T-6-S-8-S-9-S-6-T-3-T-1 233 1-S-3-S-6-T-3-S-7-S-11-T-7-T-3-T-1 22



177

8.4.4 Evaluation of shortest path tree clustering approach

This approach meets many of the requirements for achieving a practical

solution for LSCARP. Routes are compact in keeping with user

expectations, this also simplifies sorting of the mail before the delivery.

The clustering reflects the actual configuration of the road network.

Unlike a coordinate-based approach, a tree-based technique is likely to

perform adequately even in unusual situations where a river or sea inlet

unbalances the road network. As far as possible different vehicles serve

roads leading out of the village where the depot is located. This means

that there are few unnecessary traversals on the approach to the depot,

and this is likely to provide a near optimal solution.

1,2

1,2 9

12

8

6

10

11 7

3

1

5

4

2 Route 1

Route 2

Route 3

Figure 8-3 : Routes derived from clusters


178

Inevitably, this approach also has some limitations. As it combines

relatively large clusters together, it does not fill vehicles very precisely.

This may not be entirely inappropriate in a DSS context, as the user can

refine the solution interactively. In some cases, routes can more closely

match vehicle capacity, but only if non-adjacent clusters are joined. This

compromises the compact nature of the routes. In addition, while the user

can easily adjust the route at the edges, it could be argued that this

clustering approach does not facilitate radical re-sequencing of the route.

This may be needed to meet non-geographic constraints, and this type of

flexibility is inherent in the DSS approach.

8.5 Insertion heuristic for clustering for the LSCARP

8.5.1 Justification for using insertion procedure

The clustering techniques discussed above are influenced by those found

in vehicle routing problems, an alternative approach might be derived

from techniques specifically developed for arc routing problems. The arc

routing techniques discussed in Section 6.1.1 have generally been

designed for small and well-connected networks (see Table 6-1). Pearn

(1991) tested somewhat larger networks and found the best performing

heuristic to be the augment-insert algorithm. The networks on which

these results were achieved are much smaller than those discussed here,

although they have more in common with those discussed in this

dissertation than most of the other examples in the literature. A common

approach of arc routing algorithms is to attempt to identify cycles in the

network and to form routes from those cycles including the depot. We feel

that this approach is extremely difficult to implement for the LSCARP, as

routes may have hundreds of arcs and travel quite far from the depot.

Instead we have tested a simpler arc insertion algorithm that identifies

arcs in a region of arcs surrounding a seed arc, this was originally tested

by two MMangtSc students working with the author (Brady and Murphy,

1998).


179

8.5.2 Operation of the algorithm

In the spirit of the augment-insert heuristic, our modified heuristic

begins by identifying a seed arc (Table 8-6). In this case, the seed arc is

the unserviced demand arc with the greatest total time for service and

travel to and from the depot. This approach constructs routes around

those arcs that are most difficult to service, as any inefficiency in

servicing these arcs will have a significant impact on the overall solution

efficiency. When a seed arc has been identified a demand arc is inserted

into the cluster if its distance from the demand arc is less than a certain

amount. This criterion is selectively altered to ensure that the arcs added

Table 8-6 : Pseudo code for insertion algorithm

While Not all arcs routed do

Selectseedarc

While Not converged do

converged := (abs(a-b)<tolerance)

If Not converged then

mid := a+(b-a)/2

GetCluster

If (clustersize > capacity) then

b:= mid

Else begin

a:= mid

EndIf;

EndIf

EndWhile

Topuproute

EndWhile


180

provide a route that is close to the overall route time. If the resulting

cluster does not include the depot, then copies of the depot are added to

the route. A matching algorithm is then used to identify the appropriate

paths to the depot (this approach is similar to that used in developing

lower bounds in Section 5.5).

8.5.3 Computational example

The operation of this procedure can be seen by reference to the problem

discussed above (Figure 8-1) with a vehicle capacity of 24 (as before). We

start the process by choosing the arcs most distant from the depot, (Max

cij+d1i+d1j) in this case arc (4-5) (Figure 8-4). We then accumulate arcs

near the seed arc until we reach a figure close to vehicle capacity. In this

case, we add arcs (2-4) and (2-5) and (1-2). This gives a route time of 22

1,3

2,4

1,3

1,2

2,4

1,2

2,3

2,3

2,5

2,4 2,5

1,3

4,6

12

8

6

10

11 7

3

1

5

4

2

9

Figure 8-4 : Seed Arcs for Insertion heuristic


181

units, the next possible arc (1-3) has a service time of 4 and cannot be

added to the route. Therefore, the first route is the same as route 1

generated previously by the tree based procedure.

We then proceed by looking at the remaining arcs to identify the next

seed arc, this gives a tie between arcs (8-9) and (10-12) (see Figure 8-4). If

we select arc (10-12) then we next add arc (6-10) and subsequently arcs

(6-8) (6-9) and (6-3). This gives a route with a total time of 24, which is

exactly the vehicle capacity (Figure 8-5).

However, this route is slightly problematic, as arc (8-9) is traversed but

not serviced by this route. This inefficiency is a consequence of the

relatively myopic criteria used to add arcs to the cluster. Arc (8-9) now

becomes the seed for third route. Demand arcs (1-3) and (3-7) are now

1,3

2,4

1,3

1,2

2,4

1,2

2,3

2,3

2,5

2,4 2,5

1,3

4,6

9

12

8

6

10

11 7

3

1

5

4

2

Figure 8-5 : Routes 1&2 using insertion heuristic


182

added, and arcs (3-6) (6-8) and (6-9) are traversed without service. Arc (7-

11) cannot be serviced within the vehicle capacity by this route and so a

fourth route is needed (Table 8-7).

8.5.4 Evaluation of Insertion heuristic

In some ways, this approach has the opposite characteristics from the

tree-based approach discussed in Section 8.3. This approach proceeds arc

by arc, this allows vehicles be filled accurately. However this approach is

myopic and is not based on the actual network structure. Consequently,

this technique may not perform well on actual networks, as in the

example above. In its current form, this approach does not provide a

particular shape of route and this may be a problem. Nevertheless, it

could be argued that the arc selection procedure could be refined to

provide a more flexible route structure more in keeping with the DSS

approach. For instance, the user might be allowed to select the seed arc

and thereby direct the routing process.

8.6 Refinements to heuristic algorithms

8.6.1 Network simplification

The rural networks used in this dissertation are not only extremely

sparse but, for routing purposes, there is also some redundancy in the

Table 8-7 : Insertion heuristic route

Route Sequence of nodes visited Volume

1 1-S-2-S-4-S-5-S-2-T-1 222 1-T-3-T-6-S-10-S-12-T-10-T-6-S-8-T-9-S-6-T-3-T-1 223 1-S-3-T-6-T-8-S-9-T-6-T-3-S-7-T-3-T-1 214 1-T-3-T-7-S-11-T-7-T-3-T-1 12



183

road network. This leads to a situation where a number of nodes of degree

two divide a single road section into multiple arcs (see Figure 8-6). For

routing purposes, these arcs can be combined into a single arc by

combining the service and demand values for the individual arcs. This

reduces the number of arcs in the problem and might reduce the solution

time for the problem.

Many forms of CPP contain regions connected to the rest of the network

by a bridge and this property can be exploited in a problem solution

(Hamers, Borm, van de Leensel and Tijs, 1999). In a sparse rural

network, there are many cul-de-sac road sections. A route visiting these

cul-de-sacs must inevitably travel back the way it came, leading to

predictable additional traversals. These additional traversals are

foreseeable in advance if a single route visits the cul-de-sac.

Figure 8-6 : Multiple arcs in a single road section

1,2

2,3

1,2

1,2

2,4

2,4

2,3

2,4 1,2 2,3

(cost, demand)

Figure 8-7 : Complex Cul-de-sac road section


184

Consequently, the cul-de-sac could be routed in advance, reducing the

complexity of the ultimate problem to be solved. The demand and service

time required for the cul-de-sac can be added to the arcs at the base of

cul-de-sac. This may also allow a single road section be combined into

one. For instance in the network in Figure 8-7 the arcs could be combined

into a single arc with an equivalent “demand” of 40 and a service time of

5. This can greatly simplify the network and reduce the number of the

arcs, but it effectively leads to clustering of arcs and may reduce the

flexibility of algorithms dealing with the network.

8.6.2 Route refinement

Clustering algorithms of the type described above provide routes that

approximately meet the requirements of the problem. These techniques

may provide close to optimal solutions. However, even better solutions

can be obtained by refining the solutions obtained. When all routes have

been generated, a number of instances will occur where different routes

pass along the same road section. One of these routes will service the arc

while the others will merely traverse it. Where this occurs, any of the

routes may service the arc without an increase in the overall time for the

problem. In a similar way, the sequence of an Euler tour can be altered

within a set of matched arcs without affecting the overall solution time.

Other refinements to the overall route may improve the solution time

(Hertz, Laporte and Hugo, 1999). The LSCARP solutions are

characterised by a small number of routes that typically do not greatly

overlap, so it seems probable that these techniques would only lead to

modest improvements. Some of the new general local search heuristic

techniques (Section 6.1.4) could be used to improve an arc routing

solution. A combination of clustering and refinement algorithms is likely

to prove the best strategy for practical problems.


185

Chapter 9 : Decision Support for the LSCARP

on Irish road networks.

9.1 Specific DSS Characteristics

9.1.1 Network characteristics

The specific program of rural postal routing in Ireland has a number of

distinct characteristics (Harrison and Deegan, 1992). As outlined in

Chapter 7, the mathematical graph used in the LSCARP on rural roads

in Ireland is quite different from the networks generated from urban road

networks. This difference in network structure has implications for the

algorithms used, and requires an appropriate representation in the DSS.

This chapter discusses the design of a comprehensive SDSS for arc

routing and tests the heuristic procedure introduced in Chapter 8 on

realistic networks.

9.1.2 Management Requirements

The specific DSS discussed in this dissertation is directed at the

operations of the Irish post office rural delivery service (although without

their direct involvement). For the purposes of postal delivery, rural

customers are serviced by a large number of delivery offices (DO) situated

throughout the country. Consequently, each DO is responsible for quite a

small area. A smaller DO may be responsible for one or two routes

serving four or five hundred houses. A larger DO might serve a region

with two thousand houses and eight or nine routes.

9.1.3 Address structure

However, we must also consider an important difference in the address

structure of the postal routes in rural areas in Ireland. Urban routes in

Ireland, as is the case in most countries with a few exceptions such as


186

Japan, are based on numbered houses along streets. The address

structure is therefore congruent with the mathematical representation of

the routing problem. In rural Ireland this straightforward relationship

between network arcs and addresses does not hold true. Addresses are

based on small spatial regions, known as townlands. A typical townland

will have between three and twenty-five houses, with an average of about

seven. This distinctive arrangement is slightly at odds with the

structures expected by computerised databases and routing software. In

Northern Ireland, the Post Office has attempted to redefine addresses

based on road names, but this has met with considerable public

resistance. As the Post Office in the Republic is more responsive to local

concerns, there is a recognition that any technology must adapt to the

address structure, rather than the other way around.

The separation between the address structure and the network

representation used for arc routing has several implications for an arc

routing DSS. Population data is collected on spatial units, rather than

any given collection of streets. This could affect any attempt to use

demographic data as the basis of an arc routing DSS. Delivery areas are

defined as a block of townlands, rather than being directly defined as a

set of arcs to be visited. The lack of easy correlation between the

addresses and the route structure could lead to a situation where two

sections of road in the same townland are located on different routes. The

division of the demand in the same townland across different delivery

routes would make postal sorting difficult. Therefore, one objective of a

routing system would be to devise routes where this did not occur. In

Figure 9-1 there are several road sections in Townland A, yet there are no

intersections there. Each of these road sections is in more than one

townland, which may have implications for how the populations

(demands) are distributed on the arcs. GIS techniques, discussed in

Chapter 4, can greatly facilitate this interaction between line and polygon

structures (Table 9-1).


187

Townland B

Townland A

Figure 9-1 : Overlay of townland boundaries and road network

Table 9-1 : Examples of GIS operations to facilitate use of

townland structure

GIS Operation Application in rural postal routing

Data editing Splitting arcs at townland boundaries

Polygon-Line Identifying roads within townland

Distributing population over road segments

Line-Polygon Identifying townlands visited by route


188

9.2 ROMC approach

9.2.1 Principles of the ROMC approach

The ROMC approach (Sprague and Carlson, 1982) introduced in Section

1.3.3 is one well-established approach that can provide useful guidelines

for the design of a DSS for the LSCARP. This approach is largely based

on the user interaction with the system and can be contrasted with the

more traditional OR/MS approach of describing the system in terms of

the modelling component. Our approach to designing the DSS reflects our

belief in the importance of visual interaction, reflecting some of the issues

discussed in Section 2.2.2.

We also propose a system built around the use of a GIS as a DSS

generator (Section 3.4.2). GIS provides the rich interface necessary to

implement our DSS, and contributes useful database functionality for

such a system. While our proposed system does not fully exploit the

modelling possibilities of SDSS, outlined in Chapter 4, it does indicate

how a GIS based system can enrich support for arc routing problems.

9.2.2 Representations

Figure 9-2 : Removal of irrelevant detail in interface and

algorithmic representations


189

In a routing DSS the problem representation must allow the user access

to the problem definition and input data, in addition to the problem

solution. A variety of visualisation techniques can convey the nature of

the input data. The display of the road network is an obvious

representation for a routing DSS. For an arc routing problem, the DSS

might offer the option of highlighting cul-de-sacs or of displaying the

fundamental network with cul-de-sac sections removed (Figure 9-2

above). The values associated with each arc could be represented visually.

Population density or demand is an important factor and this can be

represented on the interface by different colours or line weights (Figure

9-3).

The solution of the routing problem is a series of routes and these can be

displayed visually. For an arc routing problem, the number of extra

traversals largely determines the quality of the solution. A customised

Figure 9-3 : Representation of arc attributes in different colours

and line weights


190

arc routing DSS could have mechanisms for the display of deadleg

traversals on arcs (Figure 9-4) and could highlight where more than one

route passed along a section of road. Customer service considerations

could be facilitated by using different colours on screen to represent

approximate delivery times. These techniques allow easy user

understanding of the solution presented by the system and this facilitates

user intervention in the solution process.

9.2.3 Operations

In our DSS a number of fundamental operations are required. We need to

be able to assign arcs to vehicles, the clustering phase of the process. We

need to sequence the arcs being serviced on any particular route, the

sequencing phase. Finally, we need to be able easily to alter the routes,

moving arcs from one route to another. These logical operations may

require quite complex mathematical processing; a well-designed DSS will

conceal complexity this from the user, while still allowing the user

maximum control over the process.

In the case of the LSCARP, clustering procedures such as those discussed

in Section 8.2.3 can be used. For arc routing problems, an optimal Euler

tour procedure can be used for the sequencing phase. In principle, the

system might facilitate considerable user intervention in these

procedures.

Figure 9-4 : Only sections of road visited more than once are

shown


191

9.2.4 Memory Aids

Memory aids provide additional information to the user without intro-

ducing any fundamental new problem representations. This would in-

clude the ability to query the database and examine the characteristics of

particular arcs or routes. The variety of text based information boxes

found in modern DSS software would be an example of this. Another

desirable feature in this category is context sensitive help, allowing the

user to receive relevant assistance in operating the system. Modern DSS

generators should provide customised help for all system operations,

including those added by the user. In a SDSS, modern GIS software

allows a variety of labels and text boxes to be displayed on the maps.

9.2.5 Controls

A successful DSS must be convenient to use and this can be achieved by

the use of modern interfaces. Current software features the user-friendly

features such as the use of menus, dialog boxes and toolbars. In an SDSS,

visual techniques can be used to select regions of the map that can then

be processed by the algorithmic techniques. These methods typically

include the ability to select individual road segments or junctions and

sections of the map within a square or circular area. Combined with the

other elements of the DSS the ROMC design framework allows a

comprehensive system to be developed (Table 9-2).

Table 9-2 : Summary of ROMC features

ROMC feature Feature in DSS for LSCARP

Representations Visual displays of data values

Elimination of unnecessary detail

Operations Route resequencing

Memory Aids Context sensitive access to data values

Controls Command Menus


192

9.3 TransCAD GIS

9.3.1 TransCAD Software characteristics

The construction of a comprehensive DSS to fully implement the ideas

discussed above would necessarily require many man years of

programming and is therefore beyond the scope the this dissertation.

However some of the ideas discussed in this Chapter have been

implemented in the form of a SDSS built from a synthesis of TransCAD

GIS software and the heuristic based solution techniques discussed in

Chapter 8. The TransCAD software is well suited to this purpose as it is

designed with transportation applications in mind. TransCAD is

developed by the Caliper Corporation, and comes from the same software

family as the Maptitude and GIS+ products. These are designed to

provide substantial GIS functionality on the PC platform and have a

user-friendly graphic user interface.

While the other Caliper products are aimed at general business

applications of GIS, the TransCAD software adds features for the display

of routes and their interactive manipulation by the user. TransCAD

comes in two basic varieties, the basic version provides standard GIS

functionality and the ability to display routes, although without an

algorithms to generate such routes. The full version additionally contains

a variety of pre-programmed routing algorithms to generate routes. The

full version can be used as a very capable routing DSS for many classes of

problem.

Built-in features of the GIS allow the user to easily query the attributes

associated with each arc or to display arc attributes as different colours or

line weights (Figure 9-5). This allows implementation of some of the

mechanisms discussed in the ROMC approach in Section 1.3.3 above. The

academic version of TransCAD (version 3.0), which was employed for this

work, has essentially the same functionality as the full version (although

it is much cheaper!).


193

9.3.2 GDK

The full and academic versions of TransCAD contain an arc routing

procedure. However the allocation approach used is based on urban street

networks and is not suitable for the rural applications discussed in this

dissertation. TransCAD provides a Geographic Developers Kit (GDK)

which allows access to almost eight hundred GIS and routing related

functions through a macro language known as Caliper Script . The GDK

allows construction of customised applications and GDK macros were

combined with Delphi programs for our work. This provides a simple

prototype of a DSS for the LSCARP, although more work is needed to

make it a useable DSS. A particular limitation is that only simple line

data was available for building the system. We did not have access to

datasets with polygon data (e.g. townlands) which would have allowed

Figure 9-5 : TransCAD interface with TransCAD arc routing data


194

the full capability of SDSS to be demonstrated (Chapter 4). Therefore,

this dissertation has not implemented the interaction between the road

network and the townland data discussed in Section 9.1.3.

Our prototype arc routing DSS is one where the GIS software provides

the system interface and operations within the GIS call the customised

programs. This structure means that the GIS provides the interface,

rather than the alternative approach of using the programs to provide the

interface and call the GIS routines where appropriate (Keenan and

Brodie, 2000). Our customisation of the GIS was largely concerned with

interaction with the routing algorithms. A macro is used to generate data

files for use by the routing algorithm and the routing program builds the

data tables needed for the display of an onscreen route. The routing

program then calls a GIS macro using a DDE link to display the results

onscreen.

9.3.3 User Interface Features

TransCAD provides the ability to build a customised interface and the

menu structure provided is just one example. Interface customisation s

allows the users be presented with an interface that is appropriate for

their needs, concealing functionality that is no of interest for the specific

application. The main interface components available for customisation

in TransCAD are

! Dialog Boxes

! Toolboxes

! Toolbars

! Menus

In our prototype SDSS, we did not consider it necessary to build a

sophisticated interface, and therefore did not fully exploit these features

of TransCAD.


195

9.4 Initial Computational Experiments with routing algorithms

9.4.1 Early testing of RFCS and Tree based approaches

The initial phase of our investigations sought to devise heuristic solutions

and compare their results with optimal solutions obtained using the

branch and bound procedure introduced in Section 6.2.2. It quickly

became clear that even medium size problems (around 100 arcs) could not

be solved optimally. For larger problems (more than 100 arcs), we

therefore found it more useful to compare the heuristic solution to a lower

bound. Early testing compared the algorithms to the NDLB lower bound

(Section 5.5.2) for different sizes of networks (Keenan and Naughton,

1996), some results are presented in Table 9-3. These results are

expressed in distance (KM) rather than the time units used in the

presentation of later results.

9.4.2 Assessment of initial testing

Our early work on the RFCS approach (Section 8.3) indicated that it is

inferior to the tree clustering approach (Section 8.4) in routing efficiency

and that it also provided less compact routes from a DSS viewpoint.

While Table 9-3 indicates that the RFCS approach can be marginally

better than the tree clustering approach in some circumstances, this

difference is only of the order of one percent. On those routes where the

Table 9-3 : Initial computational results

Area No of arcs Vehicles NDLB LB RFCS TreeClustering

1 649 4 269.7 288.4 292.8

2 600 3 307.1 330.2 322.5

3 483 3 168.7 183.7 184.26

4 362 3 203.8 224.8 213.8


196

tree clustering approach is superior, the solution can be up to five percent

better, as in Area Four.

As optimal solutions proved impossible to calculate, we implemented the

superior bounds to the NDLB (Section 7.3). We also noted at this stage

that the clustering algorithms could not be easily adjusted to make full

use of vehicle capacity. Consequently, we went on to develop the Insertion

clustering algorithm (Section 8.5). This provided the possibility of testing

improved heuristics against improved lower bounds. Unfortunately, much

of this early work reported in Table 9-3 was lost owing to a computer

failure. Given the problems with the RFCS approach it was decided not to

recreate this algorithm, but to proceed instead with the CFRS procedures

and these approaches were incorporated in the DSS. The solution

procedures incorporated in our prototype DSS apply the tree clustering

algorithm and the Insertion clustering algorithm

9.5 Final Computational Experiments with routing algorithms

9.5.1 Data sets used.

In order to test the algorithms, we have derived three cases from the

rural road network. These do not correspond exactly to particular

administrative areas or postal delivery regions, but are broadly similar in

characteristics. While the road networks are drawn from real data, the

population distribution on these roads is randomly distributed to

approximate the actual population distribution. Every arc has a

population of at least one, so that every arc must be visited. If real data

were available, the algorithmic techniques could be readily applied to it.

Each region comprises a sparse road network of hundreds of nodes and

arcs. Some of the road sections in the digital map are divided into several

arcs, giving rise to nodes of degree two. Each arc has a length in metres,

and as we are working with a time based problem we calculate a travel

time based on an approximate speed of 35 KM/H. For convenience, travel

times are rounded up to the nearest integer value (minutes), so each arc


197

has a minimum travel time of one minute. This rounding up slightly

overstates the time take to travel the network. In a realistic situation, a

more sophisticated calculation of time per arc might be used. The basic

data for each region is given in Table 9-4.

9.5.2 Case One

Case One is a region with a road network of 221 nodes and 245 arcs. Its

population of 820 implies an average population of 3.34 per arc (Figure

9-6). The depot in this region is located centrally, close to the only bridge

on a river. Manual route clustering would probably use the existence of

the river as the starting point for logical clusters. This situation often

arises in practical routing problems as delivery offices are often situated

in towns on villages located at a river crossing. This network has a

distinct structure and an efficient route is likely to exploit this structure.

The existence of the bridge is likely to lead to a higher lower bound.

The road network has many nodes of degree two and three and a network

reduction can reduce the network (Figure 9-7). Of the population of the

region, 341 live on the West Side of the river, with the remaining 479 on

the East Side of the river. This has implications for the routing heuristics

used, as an efficient route will probably stay on one or other side of the

river.

Table 9-4 : Region data

Case No of

Nodes

No of

Arcs

Population ServiceTime

(mins)

One 221 245 820 1073

Two 382 424 1211 1655

Three 508 550 1224 1828


198

Figure 9-6 : Case One - road network with population density

Depot

Figure 9-7 : Case One - reduced network


199

9.5.3 Case One solutions

We ran computational tests for this region using the Tree clustering

approach (Section 8.4) and the Insertion clustering approach (Section

8.5). On this network, these heuristics provided a solution with

approximately one minute of computation time (on a 500 MHz Pentium

III PC). We compare the heuristic results with lower bounds generated

using the procedures discussed in Section 7.3.

Our experiments indicated that the heuristics provided solutions that

were comparable with the lower bound. In all cases, the additional

traversals required by the heuristic solution are less than 45% above the

Table 9-5 : Case One - total time summary

Capacity (mins)

Algorithm 360 420 480

Uncapacitated 1192 1192 1192

TLB1 1196 1194 1194

LB2 Volume 1198 1198 1194

TLB2a 1202 1200 1198

TLB2b 1202 1200 1198

Tree 1227 1211 1207

Insertion 1247 1253 1254

Insertion with top-up 1248 1243 1258

Uncapacitated – lower bound with single vehicleTLB1 – depot based lower boundLB2 volume – original LB2TLB2a : time based bound with arc cut strategy of original LB2TLB2b : time based bound with individual arc cut strategyTree – Tree clustering heuristicInsertion – Basic insertion clustering heuristicInsertion –Insertion clustering heuristic with top-up to fill capacity


200

traversal distance of the lower bound solution. When total route time is

compared, including service time, all solutions were less than 6% above

the lower bound. The tree based clustering approach provided solutions

with a total time only 1% greater than the lower bound (which itself

might not be optimal). It is clear that these procedures have the potential

to provide routes close with close to optimal efficiency.

If we examine the detail of the routes (see Appendix A), the tree heuristic

provided more efficient routes than the insertion approach. This reflects

the fact that it exploits the inherent shape of the network. However, the

insertion approach, especially with the use of the top-up procedure, made

better use of the vehicle capacity. This was especially noticeable at a

vehicle capacity of 420, when the insertion procedure with top-up was

able to solve the problem in three vehicles rather than the four needed by

the tree heuristic. Consequently, the relative efficiencies of the two

procedures appears to be partly dependent on the relationship between

overall demand and vehicle capacity.

9.5.4 Case Two

The second case is region with 382 nodes, 424 arcs and a population of

1211, giving an average population density of 3.85 per arc. The depot in

this region is situated slightly off-centre in a well-connected part of the

network (Figure 9-8).

The solutions for Case Two follow a similar pattern to the first example

(Table 9-6 and Appendix B). The tree based heuristic generated routes

with fewer additional traversals but did not always make optimal use of

the vehicle capacity. Where a capacity of 480 minutes was used, the

insertion procedure with top-up was able to fill four vehicles to 98%

capacity and have a small route of 79 minutes remaining. The tree

procedure in this case generated routes that were only 80%-90% full and

the remaining route was 242 minutes.


201

However, for a capacity of 420 minutes (7 hours) the tree approach was

able to derive very effective routes and cover the region with only five

vehicles in circumstances where the basic insertion heuristic required six

vehicles. This indicates that the tree approach is capable of identifying

excellent clusters if they exist in the network. The insertion heuristic

with top-up also achieved a five-vehicle solution, indicating the value of

this post-processing. The gap between the heuristic solutions and the

lower bound is a little higher in this case, reflecting the larger number of

Depot

Figure 9-8 : Case Two - road network and reduced network


202

vehicles used and that the lower bound is not as tight on a better

connected network. On this network, the TLB2b bound gives an identical

performance to the TLB2a bound. As the TLB2b bound examines more

cuts, it takes much longer to calculate, in this case thirteen minutes as

against one minute for the TLB2a bound.

9.5.5 Case Three

The third example has the largest road network with 508 nodes and 550

arcs. This region has a population of 1224, implying an average of 2.2

people per arc. This region requires a basic service time of 1828 minutes

and therefore around six routes are required. The depot is situated in a

relatively central and well-connected location, with about seventeen

minutes driving time needed to reach the outer arcs on the network

(Figure 9-9).

Table 9-6 : Case Two - total time summary

Capacity (mins)



TLB1 1838 1836 1836

LB2 Volume 1844 1838 1838

TLB2a 1859 1848 1844

TLB2b 1859 1848 1844

Tree 1926 1931 1908

Insertion 2055 2008 2001



203

Testing of this Case resulted in a similar pattern of results as the other

examples (Table 9-7 below and Appendix C). The time based lower bound

(TLB2a) provided a significantly higher bound than the volume-based

approach. The use of the modified cutset strategy in bound TLB2b, which

took one hour to calculate, did not lead to a higher bound than TLB2a.

This result is similar to the other networks and seems to suggest that the

TLB2b approach does not offer a higher bound on this type of real

network.

Depot

Figure 9-9 : Case Three - road network and reduced network


204

The tree based routing heuristic performed well on this network, with few

extra traversals needed. However, this efficiency was achieved at the

expense of inefficient use of vehicles. In the solution for a vehicle capacity

of 360 minutes, the tree-based approach required eight vehicles. This

meant that each vehicle on average used only 80% of the time available to

it. The solutions for the tree and insertion approaches for a capacity of

420 minutes required seven vehicles, although the insertion with top-up

approach reached a feasible solution with six vehicles. These differences

reflect the existence of particular patterns in the network. One approach

to achieving a feasible solution with the minimum number of vehicles

would be to relax slightly the capacity constraints and then to move arcs

between the resulting routes to bring them within capacity. This

emphasises the need for an automated procedure to refine the clusters

generated.

Table 9-7 : Case Three - total time summary

Capacity (mins)



TLB1 2149 2149 2144

LB2 Volume 2160 2156 2147

TLB2a 2178 2166 2158

TLB2b 2178 2166 2158

Tree 2294 2228 2234

Insertion 2363 2459 2449



205

9.6 Conclusion

9.6.1 Decision Support for Routing

This dissertation is concerned with decision support for routing problems.

This represents a relatively popular type of DSS application and an

important area of OR/MS modelling research. This dissertation has

indicated that the field continues to develop, with increasing emphasis on

integrated systems that associate the algorithmic techniques with

sophisticated database and user interface features. This dissertation has

suggested that routing DSS needs to continue to take advantage of

continuing developments in IT. We identified GIS and the growth for

spatial data as one such important trend. This dissertation has suggested

that existing routing applications do not fully exploit the potential of GIS

and has argued for the better integration of OR/MS modelling techniques

and GIS.

9.6.2 Modelling issues

This dissertation has examined large sparse arc routing problems, which

is presently an under-researched area of OR/MS. Modified lower bound

procedures are proposed for this type of problem and these have been

validated for small networks against our implementation of an optimal

procedure. As it proved impossible in this dissertation to extend the

optimal approach to larger networks, we have developed three heuristic

solution procedures. One of these was initially tested, and discarded as

not being a promising line of research. We extensively tested the other

two heuristics in comparison to our revised lower bonds. This research

demonstrates that heuristic solutions can provide close to optimal

solutions for this class of problem. These heuristic solutions require a

minimal amount of computation time on a modern machine and are

therefore quite suitable as the basis for a DSS where real time solutions

are required.


206

The proposed solutions were also examined from the point of view of their

probable user-acceptability in the context of a DSS. The two heuristics

tested had different strengths; the tree based clustering procedure offered

efficient and acceptable solutions, but did not use up vehicle capacity very

well. In some cases an extra vehicle was required for solutions generated

by this heuristic, because each vehicle was not completely filled. The

insertion heuristic did allow all of the vehicle capacity to be used, but did

not provide very efficient or compact routes. The routes generated by this

approach did not take full advantage of the geographic layout of the

network. This could lead to routes that were quite different from those

that a human scheduler would choose, such routes were not likely to be

very acceptable to users.

9.6.3 Further Research on Modelling Techniques

The work presented in this dissertation provides a solid foundation for a

successful implementation of a DSS for large sparse arc routing problems.

Further research in the field might usefully combine the tree based

clustering approach and the insertion approach. A superior synthesis of

these approaches might use an initial clustering that reflected the

network structure and that used other heuristics to extend the basic

routes to the full capacity of the vehicle.

Another approach to improving our work might be a modification in the

way that the tree-based heuristic generates routes from the depot. The

current strategy grows a tree along a single path; this neglects the

possibility of the vehicle returning by a different route from its outward

journey. There is scope for further testing of the parameters of the tree

heuristic, alternative strategies for combining neighbouring clusters

might lead to an improved performance. Greater attention to these

details might lead to a heuristic that could generate very close to optimal

solutions in a few seconds of computer time. Such an algorithm would be

ideally suited to practical applications, where strict optimality is not

essential.


207

This dissertation presents potentially important time based modifications

to the existing volume based lower bounds. The examination of more cuts

discussed in Section 7.3.4 doesn’t seem in practice to represent an

advance in sparse networks. The graph theory based lower bounding

approaches discussed here might be further improved by reference to

other work; notably the TCLB discussed in Section 7.3.2. The enhanced

lower bounds and the optimal branch and bound procedure could be used

to provide guidelines for the design of a close to optimal heuristic. If

critical cuts in the network can be identified and if routes are designed to

pass through these critical points in an optimal way, then the end-result

will be close to the lower bound. This would provide good solutions, and

might make the use of a branch and bound approach feasible for larger

problems.

One obvious area of further development is the post feasibility

improvement of the routes. A systematic automated swapping procedure

is needed to move arcs to and from routes where two routes pass close to

each other. Such a procedure might have an important role in balancing

the routes produced and in ensuring the vehicle capacity was fully used.

A relatively straightforward post-processing approach might greatly

improve the performance of the heuristics. While conceptually simple,

such a procedure would require significant programming effort and this

work is left to future researchers.

A further requirement for a comprehensive DSS solution to this problem

is the implementation of modelling support for manual intervention in

the solution. Such intervention would include the ability to identify

manually the appropriate seed points required to direct the clustering

procedure. It should be possible to re-solve all or part of the route where

the user has made manual changes. A fully developed approach would

require the integration of this type of facility with appropriate user

interface features in a SDSS.


208

9.6.4 Developments in SDSS

In our examination of existing applications of GIS based systems for

routing, this dissertation has found that the field is a fragmented one and

that many systems make only a trivial use of GIS techniques. This

dissertation has looked at a range of routing problems with respect to

three types of constraint; locations, paths and vehicles. This dissertation

suggests that the first two of these are inherently spatial in nature, and

that path restrictions have been given less attention in traditional

routing applications. This dissertation identified some of the interactions

that can take place between these different types of spatial parameters.

This dissertation identified the type of problems where we believe that a

SDSS may contribute. We further went on to discuss one specific

application, that of a DSS for large sparse capacitated arc routing

problems. We discussed how such a system might be developed using the

TransCAD GIS.

The specific system discussed in this dissertation reaches only a small

part of the potential of routing SDSS in general. It is the firm belief of the

author that more sophisticated SDSS will continue to be developed as

researchers realise the importance of this type of system. Routing will be

one, of many, applications to benefit from advances in SDSS design.


209

References

1. Abraham, T. and Wankel, C. (1995). “Supporting decision support: Whereinformation on DSS is located”, Decision Support Systems 14(4): 299-312.

2. Adenso-Diaz, B., González, M. and García, E. (1998). “A hierarchical approach tomanaging dairy routing”, Interfaces 28(2): 21-31.

3. Alter, S. (1980). Decision Support Systems: Current Practice and ContinuingChallenges. Reading, USA, Addison-Wesley.

4. Amberg, A., Domschke, W. and Voß, S. (2000). “Multiple center capacitated arcrouting problems: A tabu search algorithm using capacitated trees”, EuropeanJournal of Operational Research 124(2): 360-376.

5. Angehrn, A. A. (1991). “Modelling by Example: A link between users, models andmethods in DSS”, European Journal of Operational Research 55(3): 296-308.

6. Angehrn, A. A. and Lüthi, H.-J. (1990). “Intelligent Decision Support Systems: AVisual Interactive Approach”, Interfaces 20(6): 17-28.

7. Anonymous (2000a). “Europe's Celtic Tiger turns green into gold”, GEOEurope9(10): 37-40.

8. Anonymous (2000b). “OSI: Challenging times for the nation's mapmakers”,GEOEurope 9(10): 34-36.

9. Assad, A. and Golden, B. (1982). “A categorised bibliography of survey articles inmanagement science and operations research”, Management Science 28(4): 425-438.

10. Assad, A., Pearn, W. L. and Golden, B. (1987). “The Capacitated ChinesePostman Problem: Lower bounds and solvable cases”, American Journal ofMathematical and Management Science 7(1): 63-88.

11. Assad, A. A. and Golden, B. L. (1995). Arc Routing Methods and Applications.Handbooks in OR & MS. M. O. Ball, T. Magnanti, C. Monma and G. Nemhauser.Amsterdam, North-Holland, Elsevier. 8: 375-483.

12. Avis, D. (1983). “A survey of heuristics for the weighted matching problem”,Networks 13: 475-493.

13. Barbosa, L. C. and Hirko, R. G. (1980). “Integration of Algorithmic Aids IntoDecision Support Systems”, MIS Quarterly 4(March): 1-12.

14. Basnet, C., Foulds, L. and Igbaria, M. (1996). “FleetManager: a microcomputer-based decision support system for vehicle routing”, Decision Support Systems16(3): 195-207.

15. Basnet, C., Foulds, L. and Wilson, J. (1999). “Heuristics for vehicle routing ontree-like networks”, Journal of the Operational Research Society 50(6): 627-635.

16. Beasley, J. E. (1983). “Route First - Cluster Second methods”, Omega 11(4): 403-408.

17. Begur, S. V., Miller, D. M. and Weaver, J. R. (1997). “An integrated spatial DSSfor scheduling and routing home-health-care nurses”, Interfaces 27(4): 35-48.

18. Belenguer, J. M. and Benavent, E. (1997). A cutting plane algorithm for theCapacitated Arc Routing problem, Valencia, Spain., Universidad de Valencia.


210

19. Belenguer, J. M. and Benavent, E. (1998). “The Capacitated Arc RoutingProblem: Valid Inequalities and Facets”, Computational Optimization andApplications 10(2): 165-187.

20. Bell, P. C. (1985). “Visual interactive modelling as an Operations Researchtechnique”, Interfaces 15(4): 26-33.

21. Bell, P. C. (1994). “Visualization and Optimization : The future lies together”,ORSA Journal on Computing 6(3): 258-260.

22. Bell, W. J., Dalberto, L. M., et al. (1983). “Improving the distribution ofindustrial gases with an online computerized routing and scheduling optimizer”,Interfaces 13(6): 4-23.

23. Beltrami, E. (1974). “Networks and Vehicle Routing for Municipal WasteCollection”, Networks 4(1): 65-94.

24. Benavent, E., Campos, V., Corberan, A. and Mota, E. (1992). “The CapacitatedArc Routing Problem. Lower Bounds”, Networks 22(7): 669-690.

25. Benavent, E. and Soler, D. (1999). “The Directed Rural Postman Problem withTurn Penalties”, Transportation Science 33(4): 408-418.

26. Beroggi, G. E. G. (1994). “A real time routing model for hazardous materials”,European Journal of Operational Research 75(3): 508-520.

27. Beroggi, G. E. G. and Wallace, W. A. (1994). “A prototype decision supportsystem in hypermedia for operational control of hazardous material shipments”,Decision Support Systems 12(1): 1-12.

28. Bertsimas, D. and Simchi-Levi, D. (1996). “A New Generation of Vehicle RoutingResearch: Robust Algorithms, Addressing Uncertainty”, Operations Research44(2): 286-304.

29. Bocxe, M. A. G. and Tilanus, C. B. (1985). “Testing vehicle scheduling programsfor milk collection”, European Journal of Operational Research 20(1): 25-33.

30. Bodin, L., Fagan, G. and Levy, L. (1992) The Geomod system. The 5th AdvancedPostal Technology Conference Proceedings, Washington, USA., ProInfo

31. Bodin, L., Fagan, G. and Levy, L. (1997). Street routing and schedulingproblems, presented at EURO/INFORMS 97 conference Barcelona.

32. Bodin, L. and Golden, B. (1981). “Classification in Vehicle Routing andScheduling”, Networks 11(2): 97-108.

33. Bodin, L. and Levy, L. (1991). “The arc partitioning problem”, European Journalof Operational Research 53(3): 393-401.

34. Bodin, L. and Levy, L. (1994). “Visualization in Vehicle Routing and SchedulingProblems”, ORSA Journal on Computing 6(3): 261-268.

35. Bodin, L. D., Golden, B. L., Assad, A., A. and Ball, M. O. (1983). “Routing andScheduling of Vehicles and Crews: The State of the Art”, Computers andOperations Research 10(2): 67-211.

36. Bodin, L. D. and Kursh, S. J. (1979). “A Detailed description of a ComputerSystem for the Routing and Scheduling of Street Sweepers”, Computers andOperations Research 6(4): 181-198.

37. Bonczek, R. H., Holsapple, C. W. and Whinston, A. B. (1981). Foundations ofdecision support systems. Orlando, Academic Press.


211

38. Bott, K. and Ballou, R. (1986). “Research Persepectives in Vehicle Routing andScheduling”, Transportation Research Part A 20A(3): 239-243.

39. Braca, J., Bramel, J., Posner, B. and Simchi-Levi, D. (1997). “A computerisedapproach to the New York City school bus routing problem”, IIE Transactions29(8): 693-702.

40. Brady, E. and Murphy, B. (1998). The Time Capacitated Arc Routing Problem:Feasible solutions for real world problems, MMangtSc Thesis, Dept. of MIS,University College Dublin.

41. Breslin, P. and Keane, A. (1997). The capacitated arc routing problem: Lowerbounds, MMangtSc Thesis, Dept. of MIS, UCD.

42. Camm, J. D., Chorman, T. E., et al. (1997). “Blending OR/MS, Judgement andGIS: Restructuring P&G's Supply Chain”, Interfaces 27(1): 128-142.

43. Chang, Y.-H., Yeh, C.-H. and Cheng, J.-H. (1998). “Decision support for busoperations under uncertainty : A fuzzy expert system approach”, Omega 26(3):367-380.

44. Chapleau, L., Ferland, J. A., Lapalme, G. and Rousseau, J. M. (1984). “A ParallelInsert Method for the Capacitated Arc Routing Problem”, Operations ResearchLetters 3(2): 95-99.

45. Chapleau, L., Ferland, J.-A. and Rousseau, J.-M. (1985). “Clustering for routingin densely populated areas”, European Journal of Operational Research 20(1):48-57.

46. Chrisman, N. (1997). Exploring Geographic Information Systems. New York, J.Wiley and Sons.

47. Christodes, N. (1973). “The Optimum Traversal of a Graph”, Omega 1(6): 719-732.

48. Clarke, G. and Wright, G. (1964). “Scheduling of vehicles from a central depot toa number of delivery points”, Operations Research 12: 568-581.

49. Clossey, J., Laporte, G. and Soriano, P. (2001). “Solving arc routing problemswith turn penalties”, Journal of the Operational Research Society 52(4): 433-439.

50. Cook, W. and Rohe, A. (1999). “Computing minimum-weight perfect matchings”,INFORMS Journal on Computing 11(2): 138-148.

51. Corberán, A. and Sanchis, J. M. (1994). “A polyhedral approach to the ruralpostman problem”, European Journal of Operational Research 79(1): 95-114.

52. Cortez, E., Meek, R. and Koger, J. (1994) GIS to support vehicle routing in publiceducation. Annual Conference of the Urban and Regional Information SystemsAssociation (URISA) Proceedings: 387-399.

53. Coutinho-Rodrigues, J., Rodrigues, N. and Climaco, J. (1993). “Solving an urbanrouting problem using heuristics and a successful case study”, Belgian Journal ofOperational Research, Statistics and Computer Science 33(1): 19-32.

54. Cova, T. and Goodchild, M. (1994) Spatially Distributed Navigable Databases forIntelligent Vehicle Highway Systems. GIS/LIS '94 Proceedings, AmericanSociety for Photogrammetry and Remote Sensing, American Congress onSurveying and Mapping: 191-200.


212

55. Crossland, M. D., Wynne, B. E. and Perkins, W. C. (1995). “Spatial DecisionSupport Systems: An overview of technology and a test of efficacy”, DecisionSupport Systems 14(3): 219-235.

56. Dantzig, G. B. and Ramser, J. H. (1959). “The Truck Dispatching Problem”,Management Science 6: 80-91.

57. de Silva, F., Gatrell, T., Pidd, M. and Eglese, R. (1993) Spatial Decision SupportSystems for Emergency Planning. European Conference on GeographicalInformation Systems Proceedings: 1276-1285.

58. de Silva, F. N. and Eglese, R. W. (2000). “Integrating simulation modelling andGIS: Spatial decision support systems for evacuation planning”, The Journal ofthe Operational Research Society 41(4): 423-430.

59. Dennis, A. R. and Carte, T. A. (1998). “Using Geographical Information Systemsfor Decision Making: Extending cognitive fit theory to map based presentations”,Information Systems Research 9(2): 194-203.

60. Densham, P. J. (1991). Spatial Decision Support Systems. GeographicalInformation Systems, Volume 1 : Principles. D. J. Maguire, M. F. Goodchild andD. W. Rhind, Longman,. 1: 403-412.

61. Dept of the Environment (1999). Irish Department of the Environment(http://www.environ.ie), Dublin, Ireland.

62. Derigs, U. (1981). “A shortest augmenting path method of solving minimalperfact matching problems”, Networks 11(4): 379-390.

63. DeSanctis, G. (1984). “Computer graphics as decision aids: directions forresearch”, Decision Sciences 15(4): 463-487.

64. Desrochers, M., Jones, C. V., et al. (1999). “Towards a model and algorithmmanagement system for vehicle routing and scheduling problems”, DecisionSupport Systems 25(2): 109-133.

65. Ding, Y., Baveja, A. and Batta, R. (1994). “Implementing Larson and SadiqsLocation Model in A Geographic Information System”, Computers andOperations Research 21(4): 447-454.

66. Djokic, D. (1996). Toward a general-purpose decision support system usingexisting technologies. GIS and Environmental Modeling: Progress and ResearchIssues. M. F. Goodchild, L. T. Steyaert, B. O. Parkset al. Fort Collins, CO, USA,GIS World Books: 353-356.

67. Dror, M., Ed. (2000). Arc routing : theory, solutions, and applications. Boston,MA, Kluwer Academic.

68. Duchessi, P., Belardo, S. and Seagle, J. P. (1988). “Artifical Intelligence and theManagement Science Practitioner: Knowledge Enhancements to a DecisionSupport System for Vehicle Routing”, Interfaces 18(2): 85-93.

69. Edmonds, J. (1965). “The Chinese Postman's problem”, ORSA Bulletin 13: 73.

70. Edmonds, J. and Johnson, E. (1973). “Matching, Euler Tours and the ChinesePostman”, Mathematical Programming 5(1): 88-124.

71. Eglese, R. and Murdock, H. (1991). “Routeing Road Sweepers in a Rural Area”,Journal of the Operational Research Society 42(4): 281-288.

72. Eglese, R. W. (1990). “Simulated Annealing: A tool for operational research”,European Journal of Operational Research 46: 271-281.


213

73. Eglese, R. W. (1994). “Routing Winter Gritting Vehicles”, Discrete AppliedMathematics 48(3): 231-244.

74. Eglese, R. W. and Li, L. Y. O. (1992). “Efficient Routing for Winter Gritting”,Journal of the Operational Research Society 43(11): 1031-1034.

75. Eiselt, H. A., Gendreau, M. and Laporte, G. (1995a). “Arc Routing Problems. PartI:The Chinese Postman Problem.”, Operations Research 43(2): 231-242.

76. Eiselt, H. A., Gendreau, M. and Laporte, G. (1995b). “Arc Routing Problems. PartII: The Rural Postman Problem”, Operations Research 43(3): 399-414.

77. Eom, H. and Lee, S. (1990). “Decision support systems applications research: Abibliography (1971-1988)”, European Journal of Operational Research 46(3): 333-342.

78. Eom, S., Lee, S. and Kim, J. (1993). “The intellectual structure of DecisionSupport Systems (1971-1989)”, Decision Support Systems 10(1): 19-35.

79. Eom, S., Lee, S., Somarajan, C. and Kim, E. (1997). “Decision support systemsapplications - a bibliography (1988-1994)”, OR Insight 10(2): 18-32.

80. Eom, S. B., Lee, S. M., Kim, E. B. and Somarajan, C. (1998). “A survey ofdecision support applications (1988-1994)”, Journal of the Operational ResearchSociety 49(2): 109-120.

81. Er, M. C. (1988). “Decision Support Systems: A Summary, Problems and FutureTrends.”, Decision Support Systems 4(3): 355-363.

82. Erkut, E. (1996). “The road not taken”, ORMS Today 23(6).

83. ESRI ESRI Corp (http://www.esri.com), Redlands, CA , USA.

84. Euler, L. (1736). “Solutio Problematis ad Geometrian Situs Pertinentis”,Commentarii Academiae Scientarum Petropolitanae 8: 128-140.

85. Evans, J. R. and Minieka, E. (1992). Optimization Algorithms for Networks andGraphs. New York, Dekker.

86. Fernandez de Córdoba, P., Garcia Raffi, L. M. and Sanchis, J. M. (1998). “Aheuristic algorithm based on Monte Carlo methods for the Rural PostalProblem”, Computers and Operations Research 25(12): 1097-1106.

87. Fisher, M. (1995). Vehicle Routing. Handbooks in OR & MS. M. O. Ball, T.Magnanti, C. Monma and G. Nemhauser. Amsterdam, North-Holland, Elsevier.8: 1-33.

88. Fisher, M. and Jaikumar, R. (1981). “A generalized assignment heuristic forvehicle routing”, Networks 11(2): 109-124.

89. Fisher, M. L., Greenfield, A. J., Jaikumar, R. and Lester, J. T. (1982). “Acomputerized vehicle routing application”, Interfaces 12(4): 42-52.

90. Fölsz, F., Mészáros, C. and Rapcsák, T. (1995). “Distribution of gas cylinders”,European Journal of Operational Research 87(3): 613-623.

91. Forgionne, G. A. (1999). “An AHP model of DSS effectiveness”, EuropeanJournal of Information Systems 8: 95-106.

92. Franklin, C. (1992). “An Introduction to Geographic Information Systems:Linking Maps to Databases”, Database 15(2): 12-21.


214

93. Freckmann, P. (1993) Route Calculation for Dangerous Goods Transports with aGraphical Information System. European Conference on GeographicalInformation Systems Proceedings: 1132-1138.

94. Fung, D. S. and Remsen, A. P. (1997). “Geographic Information Systemstechnology for business applications”, Journal of Applied Business Research13(3): 17-23.

95. Gamma Geographical and Multimedia Applications Ltd(http://www.gamma.ie), Dublin, Ireland.

96. Garey, M. R. and Johnson, D. S. (1979). Computers and Intractibility: a guide tothe theory of NP-Completeness. San Francisco, Freeman.

97. Gendreau, M., Laporte, G. and Yelle, S. (1997). “Efficient routing of servicevehicles”, Engineering Optimization 28(4): 263-271.

98. Georoute (1998). GIRO Inc (http://www.giro.ca), Montréal , Canada.

99. Ghiani, G. and Improta, G. (2000). “An efficient transformation of thegeneralized vehicle routing problem”, European Journal of Operational Research122(1): 11-17.

100. Gillet, B. and Miller, L. (1974). “A heuristic algorithm for the vehicle-dispatchproblem”, Operations Research 22(2): 340-349.

101. Golden, B. L., Bodin, L. and Goodwin, T. (1986). “Microcomputer-Based VehicleRouting and Scheduling Software”, Computers and Operations Research 13(2):277-285.

102. Golden, B. L., DeArmon, J. S. and Baker, E. K. (1983). “ComputationalExperiments With Algorithms for a Class of Routing Problems”, Computers andOperations Research 10(1): 47-59.

103. Golden, B. L., Hevner, A. R. and Power , D. J. (1986). “Decision Insight Systemsfor Microcomputers: A Critical Evaluation”, Computers & Operations Research13(2): 287-300.

104. Golden, B. L. and Wong, R. T. (1981). “Capacitated Arc Routing Problems”,Networks 11(3): 305-315.

105. Gorry, A. and Scott-Morton, M. (1971). “A Framework for Information Systems”,Sloan Management Review 13(Fall 1971): 56-79.

106. Grace, B. F. (1977). “Training Users of a prototype DSS”, Data Base 8(3): 30-36.

107. Greistorfer, P. (1994). Computational Experiments with heuristics for aCapacitated Arc Routing Problem, University of Graz - Working Paper 32.

108. Grimshaw, D. J. (1996) Towards a Taxonomy of Geographical InformationSystems. 29th Hawaii International Conference on System Sciences (HICSS-29)Proceedings, Hawaii: 547-556.

109. Grimshaw, D. J. (2000). Bringing Geographical Information Systems intoBusiness, Wiley.

110. Grimshaw, D. J. and Clarke, M. (1996). “The use of spatial models to supportdecision making: an empirical investigation of financial services and retailsectors”, Journal of Targeting, Measurement and Analysis for Marketing 4(4):314-325.


215

111. Grimshaw, D. J., Mott, P. L. and Roberts, S. A. (1997). “The role of context indecision making: some implications for database design”, European Journal ofInformation Systems 6(2): 122-128.

112. Hall, R. W. and Partyka, J. G. (1997). “On the Road to Efficiency”, Or/MS TodayOnline 24(3).

113. Hamers, H., Borm, P., van de Leensel, R. and Tijs, S. (1999). “Cost allocation inthe Chinese postman problem”, European Journal of Operational Research119(3).

114. Harding, S. M. and Wilkinson, G. G. (1996). A strategic view of GIS research andtechnology development for Europe, Ispra, European Space ApplicationsInstitute.

115. Harrison, H. (1979). “A Planning System for Facilities and Resources inDistribution Networks”, Interfaces 9(2): 6-22.

116. Harrison, H. C. and Deegan, A. J. D. (1992) A geographical database approach tothe optimization of the Irish postal networks. USPS Advanced TechnologyConference Proceedings, United States Postal Service: 981-990.

117. Harrison, H. C. and Wills, D. R. (1983). “Product assembly and distributionoptimization in an agribusiness cooperative”, Interfaces 13(2): 1-9.

118. Hertz, A., Laporte, G. and Hugo, P. H. (1999). “Improvement procedures for theundirected rural postman problem”, INFORMS Journal on Computing 11(1): 53-62.

119. Hertz, A., Laporte, G. and Mittaz, M. (2000). “A tabu search heuristic for thecapacitated arc routing problem”, Operations Research 48(1): 129-135.

120. Hirabayashi, R., Saruwatari, Y. and Nishida, N. (1992). “Tour ConstructionAlgorithm for the Capacitated Arc Routing Problem”, Asia-Pacific Journal ofOperational Research 9(2): 155-175.

121. Hobieka, A., Kim, S. and Beckwith, R. (1994). “A Decision Support System forDeveloping Evacuation Plans around Nuclear Power Stations”, Interfaces 24(5):22-35.

122. Holsapple, C. W. and Whinston, A. (1996). Decision Support Systems: AKnowledge Based Approach, West Publishing.

123. Hong, Y. and Thompson, G. L. (1998). “Finding postal carrier walk paths inmixed graphs”, Computational Optimization and Applications 9(3): 229-247.

124. Hurrion, R. D. (1986). “Visual interactive modelling”, European Journal ofOperational Research 23(3): 281-287.

125. Imielinski, T. and Navas, J. C. (1999). “GPS-based geographic addressing,routing, and resource discovery”, Communications of the ACM 42(4): 86-92.

126. IMO (1995). Geographic Information Systems in Europe : Problems andPotential, IMO Working Paper 95/2, Information Market Observatory (IMO),European Commission, Luxembourg.

127. IRIS Irish Regional Information Systems Ltd (http://www.iris.ie), Dublin,Ireland.

128. Ives, B. (1982). “Graphical user interfaces for business information systems”,MIS Quarterly(Dec. (special issue)): 15-47.


216

129. Jansen, K. (1993). “Bounds for the general capacitated routing problem”,Networks 23(3): 165-173.

130. Jones, C. (1991). User Interface Development and Decision Support Systems.Recent Developments in Decision Support Systems. C. Holsapple and A.Whinston, Nato ASI Series, Springer-Verlag: 181-209.

131. Jones, C. (1994a). “Anchoring and Cross-Fertilization”, ORSA Journal onComputing 6(3): 278-280.

132. Jones, C. (1994b). “Visualization and Optimization”, ORSA Journal onComputing 6(3): 221-257.

133. Jones, C. V. (1999). “Visualization and Modeling”, Interactive Transactions ofOR/MS 2(1).

134. Keen, P. (1986). Decision Support Systems: The Next Decade. Decision SupportSystems: a decade in perspective. E. McLean and H. G. Sol, North-Holland.

135. Keen, P. (1998). Puzzles and Dilemmas: An agenda for value adding IS research,Keynote Address at ECIS 98, Aix-en-Provence,(http://www.peterkeen.com/Downloads/ecis.ppt).

136. Keenan, P. and Naughton, M. (1996). Arc routing for rural Irish networks.System Modelling and Optimization. J. Dolezal and J. Fidler. London, ChapmanHall.: 599-606.

137. Keenan, P. B. (1997) Geographic Information Systems : Their contribution to theIS mainstream. AIS Americas Conference on Information Systems Proceedings,Indianapolis, USA, Association of Information Systems: 691-693.

138. Keenan, P. B. (1998a). “Spatial Decision Support Systems for Vehicle Routing”,Decision Support Systems 22(1): 65-71.

139. Keenan, P. B. (1998b) Spatial Decision Support Systems: Extending thetechnology to a broader user community. Context Sensitive Decision SupportSystems Proceedings, Bled, Slovenia: 21-30.

140. Keenan, P. B. (1998c). “When the Question is 'Where'? Integrating geographicinformation systems and management science”, OR Insight 11(1): 23-28.

141. Keenan, P. B. and Brodie, S. (2000) A Prototype Web-based Carpooling System.Americas Conference on Information Systems (AMCIS) Proceedings, Long Beach,California, USA, Association for Information Systems: 362-364.

142. Kiuchi, M., Shinano, Y., Hirabayashi, R. and Saruwatari, Y. (1995) An exactalgorithm for the Capacitated Arc Routing Problem using the Parallel Branchand Bound method. 30th SSOR, The Operations Research Society of JapanProceedings, Japan: 18-23.

143. Kwan, M.-K. (1962). “Graphic programming using odd or even points”, ChineseMathematics 1: 273-276.

144. Lang, L. (1999). Transportation GIS. Redlands, CA, Environmental SystemsResearch.

145. Lapalme, G., Rosseau, J.-M., et al. (1992). “Georoute : A Geographic InformationSystem for Transportation Applications”, Communications of the ACM 35(1): 81-88.


217

146. Laporte, G., Asef-Vaziri, A. and Sriskandarajah, C. (1996). “Some applications ofthe generalized travelling salesman problem”, Journal of the OperationalResearch Society 47(12): 1461-7.

147. Laporte, G. and Osman, I. (1995). “Routing Problems: A bibliography”, Annals ofOperations Research 61: 227-262.

148. Lee, Z., Gosain, Sanjay and Im, I. (1999). “Topics of interest in IS: evolution ofthemes and differences between research and practice”, Information &Management 36(5): 233-246.

149. Lenstra, J. K. and Rinnooy Kan, A. H. G. (1976). “On general routing problems”,Networks 6(3): 273-280.

150. Lenstra, J. K. and Rinnooy Kan, A. H. G. (1981). “Complexity of vehicle routingand scheduling problems”, Networks 11(2): 221-227.

151. Letchford, A. and Eglese, R. (1998). “The rural postman problem with deadlineclasses”, European Journal of Operational Research 105(3): 390-400.

152. Letchford, A. N. (1999). “The general routing polyhedron: A unifyingframework”, European Journal of Operational Research 112(1): 122-133.

153. Levy, L. and Bodin, L. (1989). “The arc oriented location routing problem”,INFOR 27(1): 74-94.

154. Li, L. Y. O. (1992). Vehicle routeing for winter-gritting, PhD Thesis, Dept. ofManagement Science, Lancaster University.

155. Li, L. Y. O. and Eglese, R. W. (1992). A lower bound for the time constrainedrouting problem.

156. Li, L. Y. O. and Eglese, R. W. (1996). “An interactive algorithm for vehiclerouteing for winter-gritting”, Journal of the Operational Research Society 47(2):217-228.

157. List, G., Mirchandani, P., Turnquist, M. and Zografos, K. (1991). “Modeling andAnalysis for Hazardous Materials Transportation: Risk Analysis,Routing/Scheduling and Facility Location”, Transportation Science 25(2): 100-114.

158. Little, J. D. C. (1971). “Models and managers: the concept of a decision calculus”,Management Science 16(8): 466-485.

159. Maguire, D. J. (1991). An Overview and definition of GIS. GeographicalInformation Systems, Volume 1 : Principles. D. J. Maguire, M. F. Goodchild andD. W. Rhind, Longman. 1: 9-20.

160. Malandraki, C. and Daskin, M. S. (1993). “The maximum benefit ChinesePostman problem”, European Journal of Operational Research 65(2): 218-234.

161. Mallach, E. G. (1994). Understanding Decision Support Systems and ExpertSystems, Irwin.

162. Mapinfo MapInfo Corp (http://www.mapinfo.com), Troy, NY, USA.

163. Marakas, G. M. (1998). Decision Support Systems in the 21st Century, PrenticeHall.

164. Martell, D. L., Gunn, E. A. and Weintraub, A. (1998). “Forest managementchallenges for operational researchers”, European Journal of OperationalResearch 104(1): 1-17.


218

165. McBride, R. (1982). “Controlling left and U-turns in the routing of refusecollection vehicles”, Computers and Operations Research 9(2): 145-152.

166. McCosh, A. M. and Scott Morton, M. S. (1978). Management decision supportsystems. London, Macmillan.

167. Mejia-Navarro, M. and Garcia, L. A. (1995). Integrated Planning DecisionSupport System (IPDSS). R. Report, Integrated Decision Support Group,Colorado State University.

168. Mennecke, B. E. (1997). “Understanding the Role of Geographic InformationTechnologies in Business: Applications and Research Directions”, Journal ofGeographic Information and Decision Analysis 1(1): 44-68.

169. Mennecke, B. E., Crossland, M. D. and Killingsworth, B. L. (2000). “Is a mapmore than a picture? The role of SDSS technology, subject characteristics, andproblem complexity on map reading and problem solving”, MIS Quarterly 24(4):601-4, 625-9.

170. Mentzas, G. (1994). “A functional taxonomy of computer based informationsystems”, International Journal of Information Management 14(6): 397-410.

171. Minieka, E. (1979). “The Chinese postman problem for mixed networks”,Management Science 25(7): 643-648.

172. Mole, R. H. (1979). “A survey of local delivery vehicle routing methodology”,Journal of the Operational Research Society 30(3): 245-252.

173. Montwill, P. and Naughton, M. (1994). The Capacitated Chinese PostmanProblem, MMangtSc Thesis, Dept. of MIS, University College Dublin.

174. Mtenzi, F. J. (2000). The sparse travelling salesman problem, PhD Thesis, Dept.of Management Information Systems, University College Dublin.

175. Muller, J.-C. (1993). “Latest developments in GIS/LIS”, International Journal ofGeographical Information Systems 7(4): 293-303.

176. Murphy, L. (1996) Competing in Space: The Strategic Roles of GeographicInformation Systems. The conference of the Association of Information SystemsProceedings, Las Vegas

177. Navtech (1999). Navigation Technologies Corp, Rosemont, Illinois, USA.

178. Naylor, T. (1982). “Decision support systems or whatever happened to MIS?”,Interfaces 12(4): 92-97.

179. Newcomb, M. and Medan, J. (1993) Data Requirements for Route Guidance.Annual Conference of the Urban and Regional Information Systems AssociationProceedings: 200-211.

180. Önal, H., Jaramillo, B. M. and Mazzocco, M. A. (1996). “Two formulations of theVehicle Routing Problem: An empirical application and computationalexperience”, Logistics and Transportation Review 32(2): 177-190.

181. Orloff, C. S. (1974). “A fundamental problem in vehicle routing”, Networks 4: 35-64.

182. Partyka, J. G. and Hall, R. W. (2000). “On the Road to Service”, OR/MS Today27(4).

183. Patel, M. and Horowitz, A. (1994). “Optimal routing of hazardous materialsconsidering risk of spill”, Transportation Research: Part A 28A(2): 119-132.


219

184. Pearn, W. L. (1988). “New Lower Bounds for the Capacitated Arc RoutingProblem”, Networks 18(3): 181-191.

185. Pearn, W. L. (1989). “Approximate solutions for the capacitated arc routingproblem”, Computers and Operations Research 16(6): 589-600.

186. Pearn, W. L. (1991). “Augment-Insert Algorithms for the Capacitated RoutingProblem”, Computers and Operations Research 18(2): 189-198.

187. Pearn, W. L., Assad, A. and Golden, B. L. (1987). “Transforming Arc Routing intoNode Routing Problems”, Computers and Operations Research 14(4): 285-288.

188. Pearn, W. L. and Chou, J. B. (1999). “Improved solutions for the ChinesePostman problem on mixed networks”, Computers and Operations Research26(8): 819-827.

189. Pearn, W. L. and Li, M. L. (1994). “Algorithms for the Windy Postman Problem”,Computers and Operations Research 21(6): 641-651.

190. Pearn, W. L. and Wu, T. C. (1995). “Algorithms for the rural postman problem”,Computers and Operations Research 22(8): 819-828.

191. Portier, M. A., Berthet, P. and Moreno, J. (1994) Optimized Network Modellingfor Route Planning. European Conference on Geographical Information SystemsProceedings: 1807-1816.

192. Potvin, J., Lapalme, G. and Rousseau, J. (1989). “ALTO:A computer system forthe design of vehicle routing algorithms”, Computers and Operations Research16(3): 451-470.

193. Potvin, J.-Y., Lapalme, G. and Rousseau, J.-M. (1994). “A microcomputerassistant for the development of vehicle routing and scheduling heuristics”,Decision Support Systems 12(1): 41-56.

194. Power, D. J. and Kaparthi, S. (1998). The changing technological context ofDecision Support Systems. Context Sensitive Decision Support Systems. D.Berkeley, G. Widmeyer, P. Brézillion and V. Rajkovic, Chapman Hall: 41-54.

195. Psaraftis, H. N. (1995). “Dynamic Vehicle Routing : Status and Prospects”,Annals of Operations Research 61: 143-164.

196. Ralston, B. and Zhu, X. (1991) Interfacing Stand Alone Transport AnalysisSoftware with GIS. GIS/LIS '91 Proceedings: 209-218.

197. Rasmussen, L. H. (1997). “GIS in the military,yesterday, today and tomorrow”,GIS Europe 6(1): 26-28.

198. Rolland, E. and Gupta, R. (1996) New linkages between GIS and combinatorialoptimization. AIS Americas Conference on Information Systems Proceedings,Phoenix, Arizona, USA

199. Roy, S. and Rousseau, J.-M. (1989). “The Capacitated Canadian PostmanProblem”, INFOR 27(1): 58-73.

200. Sahay, S. and Walsham, G. (1996). “Implementation of GIS inIndia:organizational issues and implications”, International Journal ofGeographical Information Systems 10(4): 385-404.

201. Santana, M. (1995) Managerial learning: A neglected dimension in decisionsupport systems. 28th Annual Hawaii International Conference on SystemSciences Proceedings


220

202. Saruwatari, Y., Hirabayashi, R. and Nishida, N. (1992). “Node Duplication LowerBounds for the Capacitated Arc Routing Problem”, Journal of the OperationsResearch Society of Japan 35(2): 119-133.

203. Sauder, R. L. and Westerman, W. M. (1993). Computer aided train dispatching:decision support through optimization. Decision Support Systems: Putting theoryinto practice. R. H. Sprague and H. J. Watson, Prentice Hall: 85-95.

204. Sauter, V. (1997). Decision Support Systems. New York, John Wiley & Sons.

205. Silver, M. S. (1991). “Decisional guidance for computer-based decision support”,MIS Quarterly 5(1): 105-22.

206. Simon, H. A. (1977). The new science of management decision, Prentice-Hall.

207. Smelcer, J. B. and Carmel, E. (1997). “The effectiveness of differentrepresentations for managerial problem solving: Comparing maps and tables”,Decison Sciences 28(2): 391-420.

208. Sprague, R. (1980). “A Framework for the development of Decision SupportSystems”, MIS Quarterly 4(1).

209. Sprague, R. H. and Carlson, E. D. (1982). Building Effective Decision SupportSystems, Prentice Hall International.

210. Stabell, C. B. (1986). Decision Support Systems: Alternative Perspectives andSchools. Decision Support Systems: a decade in perspective. E. McLean and H. G.Sol, North-Holland: 173-182.

211. Stern, H. I. and Dror, M. (1979). “Routing electric meter readers”, Computersand Operations Research 6(4): 209-223.

212. Stocx, C. F. M. and Tilanus, C. B. (1991). “Deriving route lengths from radialdistances: Emphirical evidence”, European Journal of Operations Research 50(1):22-26.

213. Sussams, J. (1984). “The future for computerised vehicle-load planning systems”,Journal of the Operational Research Society 35(11): 963-966.

214. Swink, M. and Speier, C. (1999). “Presenting geographic information: Effects ofdata aggregation, dispersion, and users' spatial orientation”, Decision Sciences30(1).

215. Sylvan Sylvan Ascent, Inc., Santa Fe, NM, USA.

216. Tactician “Tactician Corporation (http://www.tactician.com)”, .

217. Teng, J. T. C. and Galletta, D. F. (1990). “MIS research directions: A survey ofResearchers' Views”, Data Base 21(3-4): 1-10.

218. Thill, J.-C. (2000). “Geographic information systems for transportation inpersepective”, Transport Research Part C 8C(1-6): 3-12.

219. Tracey, M. and Dror, M. (1997). “Interactive graphical computer application forlarge-scale cattle feed distribution management”, Decision Support Systems19(1): 61-72.

220. Transcad (1996). Transcad User's Guide Version 3.0 for Windows, Newton, Mass.USA, Caliper Corporation.

221. Turban, E. (1995). Decision Support and Expert Systems, Prentice-HallInternational.


221

222. Turban, E. and Aronson, J. E. (1998). Decision Support and Intelligent Systems,Prentice-Hall International.

223. van der Knapp, W. (1993) GIS and Planning of Route Selection made by TouringCyclists. European Conference on Geographical Information Systems '93Proceedings: 1580-1581.

224. Walsham, G. and Sahay, S. (1999). “GIS for district-level administration inIndia: Problems and opportunities”, MIS Quarterly 23(1): 39-65.

225. Watson, H. J. and Hill, M. M. (1983). “Decision Support Systems or what didn'thappen with MIS”, Interfaces 13(3): 81-88.

226. Weigel, D. and Cao, B. (1999). “Applying GIS and OR techniques to solve Searstechnician dispatching and home delivery problems”, Interfaces 29(1): 112-130.

227. Wilson, R. D. (1994). “GIS & decision support systems”, Journal of SystemsManagement 45(11): 36-40.

228. Win, Z. (1988). Contributions to Routing Problems, PhD Thesis, UniversitätAugsburg.

229. Wunderlich, J., Collette, M., Levy, L. and Bodin, L. (1992). “Scheduling meterreaders for Southern California Gas Company”, Interfaces 22.(3): 22-30.

230. Zhan, F. B. and Noon, C. E. (1998). “Shortest Path Algorithms: An evaluationusing real road networks”, Transportation Science 32(1): 65-73.

spatial decision support systems for large arc routing...

Documents