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Intelligent Modeling for Decision Making

Katta G. MurtyIndustrial and Operations Engineering

University of Michigan Ann Arbor, Michigan 48109-2117 USA

murty@umich.edu

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Operations Research (OR) Deals With Making Optimal Decisions

Main strategy: Construct math model for decision problem

List all relevant decision variables, bounds and constraints on them (from the way the system operates), objective function(s) to optimize

Solve model using efficient algorithm to find optimal solutions

Make necessary changes and implement solution

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Math Modeling

OR theory developed efficient algorithms to solve several single objective decision models

But practitioners find no model in OR theory fits their problem well Real world problems usually multi-objective and lack nice structure

of models discussed in theory, there is a big gap between theory and practice.

The gap between practice and theory and its bridge

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Math Modeling (continued)

To get good results, essential to model intelligently using heuristic modifications, approximations, relaxations, hierarchical decomposition

Will illustrate this using work done at Hong Kong Container Port, and a bus rental company in Seoul

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“Achieving Elastic Capacity Through Data-intensive

Decision Support System (DSS)”

Professor Katta G. Murty

Industrial and Operations EngineeringUniversity of Michigan, Ann Arbor

Hong Kong University of Science & Technology

Work done at Hong Kong Container Port

 

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HHong Kong ng Kong International TerminalsInternational Terminals

The largest privately owned terminal in the world’s busiest container port

Operating under extremely limited space and the highest yard density yet achieving one of highest productivity amongst ports

Key FacilitiesQuay Crane: 41Yard Crane: 116Internal Trucks: > 400Yard Stacking Capacity: >

80,000 boxes (= 111 football stadiums)

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The Container Storage Yard

Storage yard (SY). Containers in stacks 4 - 6 high. RTGCs (Rubber Tired Gantry Cranes), stack and retrieve containers. SY divided into rectangular blocks.

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Storage Block

RTGC has 7 rows in block between its legs. 6 for container storage, 7th for truck passing.

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QCs on Dock

QCs unload containers, place them on ITs. ITs take them to SY for storage until consignee picks them. ITs bring export containers from SY to QCs to load into vessel.

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The flow of outbound containers

SY=Storage Yard

Underneath each location or operation, we list the equipment that handles the containers there

Customer Quayside Vessel Terminal

Gate Storage

Yard External Tractor

Internal Tractor

Quay Crane

Arrival at terminal and storage

Retrieval and loading into vessel

Documentation Inspection Storage space

assignment

External Tractor Yard

Crane

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Arrival, Storage and Retrieval of Import Containers

Flow of inbound containers

Customer Quayside Vessel Terminal

Gate Storage

Yard External Tractor

Internal Tractor

Quay Crane

Retrieval, pickup by customer

Unloading, storage

External Tractor Yard

Crane

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Top View of a Block B1 Being Served by an RTGC

The RTGC

Road

Road

Road

Truck

Truc

k la

neSt

orag

e lan

es

B 1

B 3

B 2

1 2632

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Land Scarcity for Terminal Development in Hong Kong

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The Highest Land UtilizationTerminal in the World

HK handles more throughput with less landHK handles more throughput with less land

CTB

Hamburg

HIT

Hong Kong

Pier T

Long Beach

Land Area / Number of Berth

Throughput (2003)

39.5 acre 25.1 acre 72.0 acre

2.3m TEU 6.4m TEU 1.2m TEU

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Key Service Quality Metrics

HIT

TruckTruck

TurnaroundTurnaround

TimeTime

VesselVessel

TurnaroundTurnaround

TimeTime

QuayQuay

CraneCrane

RateRate

ReshuffleReshuffleraterate

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Objectives of the Study

Minimize congestion on terminal road system

Reduce internal truck cycle time Increase yard crane productivity Minimize reshuffling Improve quay crane rate Enhance vessel operating rate

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D1: Route trucks and allocate storage spaces to arriving containers, to minimize congestion and reshuffling

Gate Container Yard

HIT

Berth

HIT

HIT

HIT

HIT

HIT

Decision Problem Solved

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D2: Optimize trucks allocation/quay crane to minimize quay crane, truck waiting time, number of trucks used, and number of trucks in yard

Decision Problem Solved

HITHIT

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D3: Develop procedure to estimate truck requirement profile and optimum truck driver hiring scheme

No

. of

Tru

cks

Req

uir

ed

Decision Problem Solved

HourHour

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D4: Optimize yard crane deployment to blocks to minimize

crane time spent on the terminal road network

Decision Problem Solved

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D5: Allocate appointment times to external trucks to minimize turnaround time, and their number in yard during peak time and level workload

Decision Problem Solved /Under Study

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Expected Number of Containers in Planning Period at Each Node, to Go to Various Destination Nodes

HIT

Gate Complex Container Yard

HIT

Berth

Data: 400 Export Containers

to go for Storage...

Data on BlocksB1: 40 Export Containers to Berth 1 10 Export Containers to Berth 4

20 Import Containers to Gate...

HIT

HIT

HIT

HIT

HIT

Block 1 Block 2

Block 3 Block 4

Block 5 Block 6

Data on BerthsBerth 1: 180 Import Containers to go for

Storage...

HIT

Berth 1

Berth 2

ExportExport

ImportImport

ExportExport

ImportImport

D1: Data for flow model to route trucksD1: Data for flow model to route trucks

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Decision Variables in Multi-Commodity Flow Model for Routing Trucks

fij = total no. container turns

flowing on arc (i, j) in planning period

= max {fij: over all arcs (i, j)}

= min {fij: over all arcs (i, j)}

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Variation in Workload Over Time

No. Effective Movesover a Typical Day

0

50

100

150

200

250

300

350

400

450

Time (hr-quarter)

Num

ber

of M

oves

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27

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Three Separate Policies

Equalize fill ratios in blocks

Truck dispatching policy

Storage space assignment in a block

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Numerical Example for Fill Ratio Equalization

9 blocks, each with 600 spaces

ai = No. Containers in Block i, at period end if no new containers

sent there

xi = Decision Variables, no. new containers sent to Block i during

the period

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LP Model to Determine Container Quota Numbers for Blocks

.

Linear Programming formulation is:

Subject to i ii uu )(Min

iuuxa iiii all ,400)(

1040 ix

iuux iii all ,0 , ,

i ii xa |400|Min

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Numerical Example

i ai xiNo.

Remaining

Total 2570 1040

1007

1203

1502

3006

3258

3505

3754

4001

4259

300 740

280 460

250 210

100 110

75 35

50 0

25

0

0

0 0

0

---

Average stored containers/block = (2570+1040)/9 = 400Average stored containers/block = (2570+1040)/9 = 400

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Innovations in Work on D1

First paper to study congestion inside container terminals Controlling congestion by equalization fill ratios and truck

dispatching LP model for fill ratio equalization, its combinatorial solution First paper to relate container stacking to bin packing Hardware Developed: for real time monitoring and

communication OR Techniques: LP, IP, Combinatorial Optimization Decision Frequency: Container quota numbers for 95 blocks

each four hours; take few seconds

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D2: Result from a Simulation Run

n = number Trucks/Quay Craneh = number Containers to process in hatch = 30

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Innovations in Work on D2

Recognize importance of reducing number of trucks to reduce congestion

Internal trucks pooling system, adopted worldwide

OR Techniques: Estimation, Queuing theory, simulation

Decision Frequency: One-time decision

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D3: Truck Requirement Profile

h = number of containers unloaded, loaded in a hatchh = number of containers unloaded, loaded in a hatch

(h) = average time (h) = average time minutes = 8.28 + 1.79 hminutes = 8.28 + 1.79 h

(h) = standard deviation = 1.31 + 0.019 h (h) = standard deviation = 1.31 + 0.019 h

Time allotted = Time allotted = (h) + (h) + (h)(h)

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Benefits from Work on D3

Estimate hourly truck requirements for planning

OR Techniques: Estimation, simulation, linear regression

Decision frequency: Daily; takes few minutes

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D4: Crane Movement Between Blocks

Solved as transportation model, about once per two hours, typically size Solved as transportation model, about once per two hours, typically size < 15x 15, takes few seconds< 15x 15, takes few seconds

Crane minutes to move

From Block To block

B6 B7 B8 B9

B1 20 25 35 30

B2 25 10 20 15

B3 30 25 10 20

B4 35 15 25 10

B5 30 20 10 25

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D5: Appointment Times for External Trucks to Pickup During Peak Hours

Optimal quota number for external trucks to pick up in each 30 minute interval determined by simulation

Appointment time booking system is automated telephone-based system

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Benefits from Work on D5

Quota for half hour determined by simulation

Innovation: First terminal to introduce “booking” to reduce number of external trucks in peak hours & their turnaround time

Hardware Developed: Automated telephone-based booking system

OR Techniques Used: Estimating probability distributions, queuing theory, and simulation

Decision Frequency: One-time decision

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Summary of Techniques Used

Problem Techniques Size Frequency Comp. Time

D1Route trucks, allocate storage

LP, combinatorial optimization, integer programming

Quota for 95 blocks

Every 4 hours Few seconds

D1 Truck dispatch Heuristic rule Each truck Real time Real time

D2Truck/Crane allocation

Queuing, estimation and simulation

- One-time -

D3Procedure to estimate truck requirements

Estimation, simulation and linear regression

- One-time -

D3Estimate truck requirement profile

Planning15 vessel schedules

Once a day Few minutes

D4 Crane movementEstimation and network flows

<= 15 x 15Once about 2

hoursFew seconds

D5 Booking systemEstimation, queuing and simulation

- One-time -

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Improvement in Key Quality Service Metrics

HIT

External Truck Turnaround Time External Truck Turnaround Time

↓30%↓30%

Internal Truck Turnaround TimeInternal Truck Turnaround Time

↓↓16%16%

Vessel Turnaround Time Vessel Turnaround Time ↓30%↓30%

Vessel Operating Rate ↑47%Vessel Operating Rate ↑47%

Quay Crane Rate ↑45%Quay Crane Rate ↑45%

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More Benefits

Reduce workload Reduce workload with increased with increased productivityproductivity

Boost to Boost to staff moralemorale

StaffCustomers

““Catch Up Port” in Catch Up Port” in Asia

Shipping lines’ Shipping lines’ savings amount to savings amount to US$65 million per US$65 million per yearyear

Enhance overall Enhance overall customer customer satisfaction and satisfaction and loyaltyloyalty

Social

Avoid the Avoid the construction of construction of new berths which new berths which results in less in less pollution and pollution and adverse effects to adverse effects to the societythe society

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Business Benefits to HPH and Customers

Financial Benefits SummaryFinancial Benefits Summary

Savings Key Improvement Areas

US$54 million Improvement of internal tractor utilization

US$100 million Handling cost reduction Avoidance of building new facilities

US$65 million Vessel turnaround time improvement

Total Annual Saving US$219 millionTotal Annual Saving US$219 million

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References

1. Katta G. Murty, Yat-Wah Wan, Jiyin Liu, Mitchell M. Tseng, Edmond Leung, Kam-Keung Lai, Herman W. C. Chiu, ``Hong Kong International Terminals Gains Elastic Capacity Using a Data-Intensive Decision Support System'', 2004 Edelman Contest Finalist Paper, to appear in Interfaces, January-February 2005.

2. Katta G. Murty, Jiyin Liu, Yat-Wah Wan, Richard Linn, ``A decision support system for operations in a container terminal'', to appear in Decision Support Systems, 2005; available online at www.sciencedirect.com

3. Katta G. Murty, Woo-Je Kim, ``Intelligent DMSS for Chartered Bus Allocation in Seoul, South Korea'', November 2004.