computer-based interface for an integrated solid waste management

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Environmental Modelling & Software 19 (2004) 11511164www.elsevier.com/locate/envsoft

Computer-based interface for an integrated solid waste managementoptimization model

M. Abou Najm, M. El-Fadel

Department of Civil and Environmental Engineering, Faculty of Engineering and Architecture, American University of Beirut, P.O. Box 11-0236,Bliss Street, Beirut, Lebanon

Received 22 August 2002; received in revised form 5 September 2003; accepted 24 December 2003

Abstract

Planning a regional waste management strategy is a critical step that, if not properly addressed, will lead to an inefficient inte-grated solid waste management (ISWM) system. Regional planning affects the design, implementation, and efficiency of the over-all ISWM scheme. Consequently, decision-makers must look for optimized regional waste management planning to achieve asuccessful strategy. The optimization of an ISWM strategy for an area requires the knowledge of available solid waste manage-ment alternatives and technologies, economic and environmental costs associated with these alternatives, and their applicability tothe specific area. Decision-makers often have to rely on optimization models to examine the impacts of mass balance, capacitylimitations, operation, and site availability as well as to analyze different alternative options in the selection of a cost effective,environmentally sound waste management alternative. In this context, the complexity associated with the formulation of optimi-zation models may hinder its use, and consequently, user friendliness is a major concern. This paper presents an interface thatwas developed to address this concern, that is to formulate the matrices associated with an integrated waste management optimi-zation model.# 2004 Elsevier Ltd. All rights reserved.

Keywords: Optimization; Linear programming; Modeling; Solid waste management

1. Introduction

In the absence of a single optimal waste managementalternative that can handle municipal solid waste(MSW), the concept of integrated solid waste manage-ment (ISWM)1 has evolved with the philosophy of inte-grating all available waste management options withexisting geographic, environmental, and socio-economic

conditions, in an attempt to better manage our waste.Decision-makers and waste management planners are

currently faced with the increase in complexity, uncer-tainty, multi-objectivity, and subjectivity of ISWM. Thedecision process of MSW management has developedfrom simple comparison between few single-waste-management alternatives, to a larger number of combi-nations through ISWM. Accordingly, the decisionprocess of ISWM must follow a more scientific and sys-tematic approach to improve the quality of the resulting

decisions.At this stage, decision-makers must be able to dis-

tinguish between an optimum decision, a gooddecision, and a lucky outcome. The first provides theoptimum feasible solution that satisfies all the pre-determined constraints, and optimizes the requiredobjective function using operations research (OR) tech-niques. The second is based on experience, trial anderror techniques, sensitivity analysis, and/or compari-son of various ISWM combinations. It might lead tonear optimal decisions, however, with the increase inthe number of combinations in the decision process,

Corresponding author. Tel.: +961-3-228-338; fax: +961-1-744-462.

E-mail address: [email protected] (M. El-Fadel).1 An ISWM is reached when the use, effectiveness, and economics

of its functional elements (collection, transport/transfer, processing,treatment, and disposal) have been assessed with corresponding inter-faces and connections. It can thus be defined as the selection andapplication of suitable techniques, technologies and managementoptions to achieve specific waste management objectives and goals(Tchobanoglous et al., 1993).

1364-8152/$ - see front matter # 2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.envsoft.2003.12.005


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these techniques can no longer be used with the same

efficiency. The third follows a non-scientific approach,

and outcomes, whether lucky or unlucky, are not

dependent on the decision quality.Various issues of ISWM have been addressed

through OR methods (Table 1). A linear programming

(LP) waste management and planning optimizationtool was developed to assist decision-makers in provid-

ing an optimum waste management policy given the

available data (Abou Najm et al., 2002a,b). It presents

the information required for making a factual, analyti-

cal decision about the optimum waste management

alternative taking into consideration the economic and

environmental costs, along with various constraints

adopted to account for implemented or suggested poli-

cies, mass balance, capacity limitations, operation,

finance, and site availability. The interface developed in

this paper allows the use of this model by decision-

makers without the need of acquiring the knowledge ofLP optimization. The interface will automatically buildthe essential matrices by just entering the requireddata. Once the matrices are ready, specialized solvers(Excel, Matlab, Lindo, etc.) can obtain the optimumsolution with no further complication.

2. Why optimization?

It is essential at the onset that decision-makers andwaste management planners differentiate between therelatively new concept of optimization, in comparisonto the more commonly used life cycle assessment(LCA) computer modeling. Technically, the two con-cepts are completely different. Optimization tools pro-vide decision-makers with optimum ISWM policies forany region based on economic and environmentalcosts, mass balance, capacity limitations, operations,

Table 1A literature review on the use of OR in MSW management

Reference Description

Nema and Modak (1998) An integer linear programming model was developed as a strategic design approach for the optimization of regionalhazardous waste management systems. The objective was to minimize total costs and risks

Haith (1998) An Excel spreadsheet, MSWFLOW, was developed as an accounting procedure for the exploration of MSWmanagement decisions

Daskalopoulos et al. (1998) A simple LP model that accounts for both the economic and environmental impacts of an IMSW system was used.The model optimizes the waste management process for a single generation source. Environmental costs are thoseassociated with emissions of greenhouse gases, expressed in terms of equivalent global warming potential (GWP)

Huang et al. (1997) A solid waste decision support system (SWDSS) was developed based on an inexact mixed integer linearprogramming (IMILP) to incorporate different types of uncertainties within its optimization process

Sundberg and Ljunggren(1997)

A methodology was suggested for the integrated analysis of cost and environmental impacts by linking two modelingapproaches for the strategic ISWM planning: the MIMES/waste model and the LCA model

Rubenstien (1997) A multiple attribute decision system (MADS) was developed. The MADS model is a simulation-planning model thatis composed of two modules: screening and evaluation. The screening module assists in selecting feasible MSWmanagement alternatives based on constraints set by decision-makers. The evaluation module builds on the previousmodule and economic and environmental impacts of MSW management and policy. The model accounts for onlyenvironmental transportation costs in terms of vehicle emissions

Charnpratheep et al. (1997) The fuzzy set theory and the analytic hierarchy process (AHP) were coupled into a raster-based geographicinformation system (GIS) for the preliminary screening of landfill sites

Kao et al. (1997) A prototype network GIS was developed for landfill siting. Improving the prototype is currently underway throughintroducing expert systems. That include a fuzzy expert system and a mixed-integer liner optimization subsystems toimplement multi-objective analysis

Ljunggren and Sundberg(1997)

A one-period nonlinear programming model (MWS) was developed. This model analyzes SWM systems for a singletime period and optimizes the system for a defined objective function. The objective is to minimize the total cost ofMSW management systems. Environmental considerations are addressed through integrating emission constraintsand fees

Chang et al. (1996) MIP model was applied with the framework of dynamic optimization considering economic and environmentalfactors

Barlishen and Baetz (1996) A mixed integer linear programming (MILP) was used in the optimization study with dynamic, multi-period modelformulation for facility location, timing, and sizing

Powell (1996) A multi criteria model was developed to evaluate six waste disposal options in a two dimensional matrix. Assessingdata was conducted in two ways: numerical or cardinal valuation when numerical data are present, and ordinalranking method when data are absent or unreliable

Bhat (1996) A simulation-optimization model was developed to obtain the optimal allocation of trucks for MSW management byreducing traveling and waiting time costs. The simulation model estimates the waiting time of trucks and theoptimization model uses heuristic approach to find the optimal allocation of trucks

Gottinger (1991) A fixed charge mixed integer programming model which views regional waste management systems as network flowswas suggested. The mathematical formulation of the long range planning of locations and expansion of facilities forregional waste management was also explored

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location, and site availability. On the other hand, LCAmodels are not inherently structured to advise decision-makers on what they must do with their waste. Theyare assessment tools that present the environmentaland economic impacts of various ISWM policies sothat decision-makers can make more informed deci-

sions. In other words, the output of an optimizationtool is an ISWM policy, whereas that of an LCAmodel is impact and total life cycle burden resultedfrom an ISWM policy (which is part of the input to theLCA model). This means that decision-makers usingonly LCA models can only obtain the optimum ISWMpolicy among the ISWM policies that they were able tothink of, by simply selecting the option with the leastimpact (since LCA models only assess predeterminedpolicies). However, the optimum ISWM policy mightbe a combination that was not thought of, and thuswas not assessed and analyzed by the LCA model.

Optimization tools comprise the approach to obtainthe optimum waste management policy whether pre-determined or not.

3. The model

This section briefly describes the mathematical for-mulation of the LP model to be used in the systematicanalysis of the ISWM problem. In the model, the flownetwork of the waste stream is divided into three mainsets (Fig. 1). The first set consists of the generationsources. The second is the intermediate facilities includ-ing the processing facilities, the biological treatmentfacilities, and the thermal treatment facilities. The lastset is the landfills.

Let I, J, K, R, U, and T be the total number of gen-

eration nodes, processing facilities, biological treatment

facilities, thermal treatment facilities, landfills, and time

intervals, respectively. The decision variables in the

model are the waste amounts transported from one

node, or location, to another (Table 2). They cover the

transport of waste in the eight possible paths (Fig. 1).

For simplicity, the term x was introduced to account

for all waste generation nodes and management facili-

ties. Similarly, the term y represents all waste manage-

ment facilities. Consequently, the term Wdxyt includes

any of the following terms: W1ijt, W2irt, W

3iut, W

4jkt, W

5jrt,

W6jut, W7kut, and W

8rut. All the remaining symbols rep-

resent predetermined parameters that can be changed

only once for every run.

3.1. Objective functionThe general form of the objective function considers

the minimization of the amortized difference between

Fig. 1. Waste stream flow network.

Table 2Models decision variables

Decision variable Waste transported

From To At

W1ijta Generation node, i Processing facility, j Time interval, t

W2irtb Generation node, i Thermal treatment facility, r Time interval, t

W3iutc Generation node, i Landfill, u Time interval, t

W4jktd Processing facility, j Biological treatment facility, k Time interval, t

W5jrte Processing facility, j Thermal treatment facility, r Time interval, t

W6jutf Processing facility, j Landfill, u Time interval, t

W7kutg Biological treatment facility, k Landfill, u Time interval, t

W8ruth Thermal treatment facility, r Landfill, u Time interval, t

a i 1; . . . ; I, j 1; . . . ; J, t 1; . . . ; T.b i 1; . . . ; I, r 1; . . . ; R, t 1; . . . ; T.c i 1; . . . ; I, u 1; . . . ; U, t 1; . . . ; T.d j 1; . . . ; J, k 1; . . . ; K, t 1; . . . ; T.e j 1; . . . ; J, r 1; . . . ; R, t 1; . . . ; T.f j 1; . . . ; J, u 1; . . . ; U, t 1; . . . ; T.g k 1; . . . ; K, u 1; . . . ; U, t 1; . . . ; T.h r 1; . . . ; R, u 1; . . . ; U, t 1; . . . ; T.

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costs and benefits of the whole ISWM system:

MinimizeXTt1

btCt Bt 1

where Ct is the costs associated with ISWM stream attime t($); Bt is the benefit associated with ISWMstream at time t($); bt is the discount factor, accountsfor the inflation rate, f, and the nominal interest rate, ras expressed in Eq. (2).

bt 1f

1 r

t12

The cost component of the objective function consists

of two major cost categories: conventional andenvironmental (Tables 3 and 4).

4. Model constraints

The basic model constraint set consists of mass bal-ance, capacity and material limitations, and policyimplementation constraints (Table 5).

Note that the last three sets of equations can be tes-ted through the sensitivity analysis by simulating theoptimized solution with the targeted composting quan-

tities, material recycling percentages, and householdrecycling material percentages, respectively.

4.1. Number of variables and equations in the model

The number of constraints and number of non-zeroterms for every constraint-equation is summarized inTable 6. Let p and q denote the total number ofdecision variables and constraints, respectively. Theywill have the following values:

p T IJ IR IU JK JR JU KU RU

q T 2I 5J 3R 3K 2U 1

5. The need for an interface

The objective is to prepare and solve the followinggeneral linear programming problem:

Objective function : minATxSubject to : Bx C

where A is a vector that constitutes the set of coeffi-cients of the linear objective function. The matrix B

Table 3Summary of the conventional and environmental cost component

Total cost of Mathematical representation (equation)

Transportation X8d1

TCxyt Wdxyt

3

OperationX8d1

OCdy Wdxyt

4

RemediationX8d1

RCdyt Wdxyt

5

Fixed constructionXTt1

CCxt 6

Fixed expansion XTt1

ECxt 7

TCxyt, unit cost of waste transported from x to y at time t ($/ton);

Wdxyt, amount of waste transported from x to y at time t (tons); OCd

y ,

unit operating cost at facility y ($/ton); RCdyt, unit remediation cost

of pollution at facility y at time t ($/ton); CCxt, construction cost ofa new facility x at time t ($); ECxt, fixed expansion cost of facility xat time t ($).Note: The fixed construction and expansion costs are not decisionvariables. They are numbers that should be added to the objectivefunction. To consider them as decision variables, integer linear pro-gramming (ILP) should be introduced.

Table 4Summary of the conventional and environmental benefit component

Total income from Mathematical representation (equation)

Resource recovery(recyclable) am PCm W

1ijt

UCm 8

Biological treatmentrevenues

W4jkt1VRkC 9

Thermal treatmentrevenues

W2irt Thir

or W5jrt Thjr

10

Household recyclingincome

XTt1

nm PCm RIm XIi1

Git 11

am, percent of material m in waste, sold as recyclable raw material attime t (% ratio) (model parameter not variable); PCm, percent ofmaterial m in SW (% ratio); UCm, unit selling price of material m ($);VRk, volume reduction ratio at compost facility k; C, revenues frombiological treatment facilities, for composting, it is the compost unit

price ($/ton of waste); Thir, revenues from thermal treatment facili-ties with waste received directly from generation sources (withoutseparation or treatment), for incineration, it is the energy recoveryrevenues from one ton of waste ($/ton of waste); Thjr, revenues fromthermal treatment facilities with waste received from processing facili-ties (i.e. with higher energy content than Thir) ($/ton of waste); nm,percent material m sold as recyclable raw material from household(% ratio) (model parameter not variable); RIm, recycling income formaterial m ($/ton of waste); Git, generation amount at source i attime t (ton).Note: The household recycling income is not a decision variable. It isa number that should be added to the objective function. To considerit as a decision variable, ILP should be introduced.



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Table 5Models constraints

Constraint (equation)

Mass balance constraints

XJ

j1

W1ijt XR

r1

W2irt XU

u1

W3iut GIT 1 XM

m1

nm PCm

!with i 1; . . . ;I; and t 1; . . . ;T 12

XIi1

W1ijt 1 XMm1

am PCm

!" #XRr1

W5jrt XKk1

W4jkt XUu1

W6jut with j 1; . . . ;J; and t 1; . . . ;T 13

XIi1

XMm1

am;maxGit XIi1

XJj1

W1ijt with t 1; . . . ;T 14

am,max, maximum percent of material m in waste, sold as recyclable raw material at time t (% ratio).

Capacity limitation constraint

Capmin;t;j XIi1

W1ijt Capmax;t;j with j 1; . . . ;J and t 1; . . . ;T 15

Capmin;t;k XJj1

W4jkt Capmax;t;k with k 1; . . . ;K and t 1; . . . ;T 16

Capmin;t;r XJj1

W5jrt XIi1

W2irt Capmax;t;r with r 1; . . . ;R and t 1; . . . ;T 17

Capmin;t;u XIi1

W3

iut XJj1

W6

jut XRr1

W8

rut XKk1

W7

kut Capmax;t;u with u 1;

. . .

;

U and t 1;

. . .

;

T 18

Capmin,t,x, minimum capacity for facility x at time interval t; Capmax,t,x, maximum capacity for facility x at time interval t.

Material limitation constraints

XKk1

W4jkt PCcompXIi1

W1ijt with j 1; . . . ;J and t 1; . . . ;T 19

XRr1

W2irt PCinc:GIT with i 1; . . . ;I and t 1; . . . ;T 20

XRr1

W5jrt PCinc:XIi1

W5ijt with j 1;::::::;J and t 1;::::::;T 21

XUu1

W7kut ! PCret;bXJj1

W4jkt with k 1; . . . ;K and t 1; . . . ;T 22

(continued on next page)



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and vector C comprise the coefficients of the linearconstraints, accounting for both equality andinequality constraints. Table 7 summarizes the sizes ofthe optimization problem components: A, B, and C.

As Table 7 indicates, the preparation of the optimi-

zation components is a complex task that requires time

and professional expertise. An interface was developedto assemble these components given the user inputs.Input to the interface includes detailed informationabout the specific region of interest.

6. The interface

The interface was developed using an ExcelVisualBasic environment. It is completely generic and

designed to request the required data input from theuser. It is composed of a set of Excel worksheets. TheMain Menu worksheet, which starts the interface, looksfor the major model parameters: I, J, K, R, U, and T(Fig. 2). The call for data is generated by the model asthe user shifts between the worksheets (using the com-mand buttons in the Main Menu). Worksheets respon-sible for generation quantities, distances, and capacitiesare: Generation Nodes (Fig. 3), Processing Facilities(Fig. 4), Biological Treatment Facilities (Fig. 5), Ther-mal Treatment Facilities (Fig. 6), and Landfills (Fig. 7).The main input information required by these work-

sheets is described in Table 8.Operational costs, benefits, and waste management

alternatives properties are required by Cost and PolicyData worksheet (Fig. 8). Costs include the operatingcost of every waste management facility in $/tondepending on its capacity, policies, and technologyused. Consequently, the model accounts for differentoperating costs for the same waste management alter-native. Ratios of compostable (PCcomp) and combust-ible (PCinc.) materials, as well as ratio of returnablematerial from biological (PCret,b) and thermal (PCret,t)treatment facilities are also expressed in this worksheet.

Table 5 (continued)

Constraint (equation)

XUu1

W8rut ! PCret;tXIi1

W2irt XJj1

W5jrt

!with r 1; . . . ;R and t 1; . . . ;T 23

PCcomp and PCinc., percentages of compostable or combustible waste (% ratio); PCret,b and PCret,t, percentages for returnable materials to landfillsfrom biological and thermal facilities, respectively (% ratio).

Policy implementation constraints

nmin;m nm nmax;m 24

amin;m am amax;m 25

W4jkt;min W4

jkt W4

jkt;max 26

nmin,m and nmax,m, minimum and maximum percent material m sold as recyclable raw material from household (% ratio).

Table 6Number of equations and non-zero terms for constraints

Equation number Number ofequations

Number ofnon-zero terms

(12) IT JRU(13) JT IRKU(14) T IJ(15) 2JT I(16) 2KT J(17) 2RT IJ

(18) 2UT IJRK(19) JT IK(20) IT I(21) JT IJ(22) KT UJ(23) RT IUJ

Table 7Sizes of the optimization problem components

Component Number ofrows

Number ofcolumns

Comments

A p 1 VectorB q p MatrixC q 1 Vector

p TIJIRIUJKJRJUKURU;q T2I5J3R3K2U1.



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Environmental costs of prevention, treatment, health,

land depreciation, ecosystem and others in $/ton are

placed for every waste management facility in the

Detailed Environmental Costs worksheet (Fig. 9). Waste

composition, recycling and household separation poli-

cies and costs are pointed out in the Recycling and

Household Data worksheet (Fig. 10).

7. Main Menu worksheet

The Main Menu in the interface (Fig. 2) calls for the

main parameters in the model. The user needs to input

the following:

. The number of generation nodes, I

. The number of processing facilities, J

. The number of biological treatment facilities, K

. The number of thermal treatment facilities, R

. The number of landfills, U

. The number of time periods, T

The user will directly see the number of decision vari-

ables and number of constraints for the specified prob-

lem. Command buttons designed in the Main Menu

worksheet are to direct the user for data entry. A set of

generic worksheets will open to instruct the user of

what data needs to be input. Data required includes

the following:

Fig. 2. Main Menu worksheet.

Fig. 3. Generation Nodes Data worksheet.



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. Generation quantities

. Distances from generation nodes to waste treatmentand disposal facilities

. Distances from intermediate facilities to intermedi-ate and ultimate disposal facilities

. Capacities of waste treatment and disposal facilities

. Conventional and environmental costs

. Waste management policies

The data-entry worksheets are generated in a format

that looks for data given the users input for the mainparameters.

8. Input worksheets

Data input worksheets will appear as the user pressesthe corresponding command button in the Main Menu

worksheet. The naming of generation nodes, time inter-

vals, processing facilities, thermal treatment facilities,

composting plants, and landfills is generic using the

major inputs of the Main Menu. The representation of

a node or facility in all the interface worksheets is sim-

ply the index of that node or facility (I, T, J, R, K, or

U) and its number. It is completely generic using theinputs of the Main Menu worksheet.

Fig. 4. Processing Facilities Data worksheet.

Fig. 5. Biological Treatment Facilities Data worksheet.



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8.1. Generation Nodes Data worksheet

In this worksheet (Fig. 3), the user enters the gener-

ation quantities for each time interval and generation

node. The user needs also to input the distances from

every generation node, I, to each processing facility, J,

thermal treatment facility, R, and landfill, U.

8.2. Processing Facilities Data worksheet

In this worksheet (Fig. 4), the user enters the mini-

mum and maximum capacities for each processing

facility, J, at every time interval T. The user needs alsoto input the distances from every processing facility, J,to each biological treatment facility, K, thermal treat-ment facility, R, and landfill, U.

8.3. Biological Treatment Facilities Data worksheet

In this worksheet (Fig. 5), the user enters the mini-mum and maximum capacities for each biological

treatment facility, K, at every time interval T. The userneeds also to input the distances from every biologicaltreatment facility, K, to each landfill, U.

Fig. 6. Thermal Treatment Facilities Data worksheet.

Fig. 7. Landfilling Data worksheet.



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Table 8Required input data for the model by the interface worksheets

Worksheet Required input (unit)

Main Menu (Fig. 2) Models main parameter: I, J, K, R, U, and TGeneration Nodes (Fig. 3) Waste generation quantities, Git, for every generation node, i (ton/day).

Distance between every generation node, i, and all other facilities: j, r, and u (km).Multiply distances by unit transportation cost ($/ ton km) to get TCijt, TCirt, TCiut.

Input-worksheetsProcessing Facilities (Fig. 4) Minimum and maximum capacities (Capmin,t,j and Capmax,t,j) for all processing facilities, j(ton/day).

Distance between every processing facility, j, and all other facilities: k, r, and u (km).Multiply by unit transportation cost ($/ ton km) to get TCjkt, TCjrt, TCjut.

Biological Treatment Facilities (Fig. 5) Minimum and maximum capacities (Capmin,t,k and Capmax,t,k) for all biological treatment facilities,k (ton/day).Distance between every biological treatment facility, k, and all other landfills, u (km).Multiply by unit transportation cost ($/ ton km) to get TCjkt, TCjrt, TCjut.

Thermal Treatment Facilities (Fig. 6) Minimum and maximum capacities (Capmin,t,r and Capmax,t,r) for all thermal treatment facilities, r(ton/day).Distance between every thermal treatment facility, r, and all other landfills, u (km).Multiply by unit transportation cost ($/ton km) to get TCrut.

Landfills (Fig. 7) Minimum and maximum capacities (Capmin,t,u and Capmax,t,u) for all landfills, u (ton/day).Cost and Policy Data (Fig. 8) Unit transportation cost ($/ton km).

Operational costs (OCj, OCk, OCr, OCu) for all waste management alternatives ($/ton).Benefits from biological treatment facilities (C) ($/ton).Benefits from thermal treatment facilities (Thir, Thjr) for waste coming directly from generationsources and waste coming from processing facilities ($/ton).Ratio of returnable material (PCret,t, PCret,b) from thermal and biological treatment facilities (%ratio).Ratio of compostable and combustible material (PCcomp, PC inc.) (% ratio).

Detailed Environmental Costs (Fig. 9) Looks for all possible environmental costs: prevention, treatment, health, land depreciation,ecosystem and others ($/ton) for:Processing facilities, j (sum of all environmental costs gives RCj).Biological treatment facilities, k (sum of all environmental costs gives RCk).Thermal treatment facilities, r (sum of all environmental costs gives RCr).Landfills, u (sum of all environmental costs gives RCu).

Recycling and Household Data (Fig. 10) Percent of material m in solid waste (% ratio) (PCm).Percent of material m sold as recyclable raw material (% ratio) (am,max).Policy of recycling for material m sold as recyclable raw material (% ratio) (a

m).

Policy of household recycling for material m sold as recyclable raw material (% ratio) (nm).Recycling income from material m ($/ton of waste) (RIm).

Note: If unit other that ton/day was used, consistency should be considered in all other terms.

Fig. 8. Cost and Policy Data worksheet.



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8.4. Thermal Treatment Facilities Data worksheet

In this worksheet (Fig. 6), the user enters the mini-mum and maximum capacities for each thermal treat-ment facility, R, at every time interval T. The userneeds also to input the distances from every thermaltreatment facility, R, to each landfill, U.

8.5. Landfilling Data worksheet

In this worksheet (Fig. 7), the user enters the mini-mum and maximum capacities for each landfill, U, atevery time interval T.

8.6. Cost and Policy Data worksheet

In this worksheet (Fig. 8), the user enters the trans-portation cost in $/km, as well as the operational costsin $/ton for every processing facility, J, biologicaltreatment facility, K, thermal treatment facility, R, andlandfill, U. Benefits from the biological and thermaltreatment alternative are also required in $/ton. Theinterface allows for two benefit values for the thermal

treatment alternative since waste that is thermallytreated without any pretreatment (in a processingfacility) is usually characterized by a lower BTU con-tent than that of a processed waste. Other important

Fig. 9. Detailed Environmental Costs worksheet.

Fig. 10. Recycling and HouseholdData worksheet.



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policy parameters for biological and thermal treatment

alternatives as well as household separation and recy-

cling are introduced.

8.7. Detailed Environmental Costs worksheet

In this worksheet (Fig. 9), the user enters thedetailed environmental costs for every processing

facility, J, biological treatment facility, K, thermal

treatment facility, R, and landfill, U. The detailed

environmental costs include the cost of prevention,

treatment, health impacts, land depreciation, and eco-

system degradation. Any additional factor that the user

wants to add can be entered in the others row for every

facility.

8.8. Recycling and Household Data worksheet

In this worksheet (Fig. 10), the user needs to provide

the percent material composition of waste. For every

waste material (or component), the user must input the

maximum allowable recycling range depending on the

material and waste properties as well as the recycling

and processing available technologies. Recovery bene-

fits from recycling and household separation must also

be supplied. Finally, recycling and household separ-

ation policies are entered by the decision-maker. Note

that for every waste component material, the sum-

mation of waste to be recycled and household-separatedmust be greater than or equal to the maximum allow-

able recycling range.

9. Output sheets

As the user inputs all the required data in the pre-viously described sheets, the Run button in the MainMenu sheet will generate three sheets that provides theobjective function A, the matrix B, and the right handside matrix C. Fig. 11 shows a sample output of thematrix B of a typical simulation.

10. Interface limitations

The interface design was completely generic. Thecoding encountered is supposed to generate therequired matrices for a problem of any size. However,given the fact that it was built using the ExcelVisualBasic environment, the limitations of the interface areconsequently those of Excel and Visual Basic. Since themost recent version of Excel allows the use of only 256

columns, the interface will be limited to a total numberof 256 decision variables.

11. Model application

The region of Northern Lebanon (Fig. 12) was con-sidered as a case study in an attempt to demonstratethe capability of the model (Abou Najm et al., 2002b).Data were collected for the regions six counties, withestimated population of 893,000, and daily waste gen-eration of about 624 tons. The model provided as an

output, the optimum waste management policy for sixwaste generation centers, six processing facilities, twocomposting plants, one incinerator, and six landfills

Fig. 11. Sample output of the matrix B.



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Fig. 12. Layout of case study application.

Fig. 13. Typical model output.



14/14

(Fig. 13). In other words, one simulation provided the

optimum solution for a problem of 150 decision vari-

ables, and a large number of possible waste manage-

ment combinations.

12. Conclusion

This tool was developed for the generation of the

optimization models three main matrices. This is con-

sidered a very time-effective tool as it saves decision-

makers, adopting this or similar model, all the time

required for building the model matrices. One step fur-

ther is to link this tool to an optimization solver thatwill take the matrices from this tool and solve the opti-

mization problem. The output from the solver is an

array with a number of elements equal to the number

of the decision variables. The output from the solver

provides the optimum value for every decision variable.One solver that can work perfectly well with this tool is

Matlab optimization toolbox, which is an excellent sol-

ver for LP problems.

Acknowledgements

Special thanks are extended to the United States

Agency for International Development for its continu-

ous support to the Water Resources Center and

Environmental Engineering and Sciences Programs at

the American University of Beirut.

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