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Intelligent Modelingfor Decision Making
Katta G. Murty
Industrial and Operations Engineering
University of Michigan
Ann Arbor, Michigan 48109-2117 USA
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Operations Research (OR) Deals WithMaking Optimal Decisions
Main strategy: Construct math model for decisionproblem
List all relevant decision variables, bounds andconstraints on them (from the way the systemoperates), objective function(s) to optimize
Solve model using efficient algorithm to findoptimal solutions
Make necessary changes and implementsolution
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Math Modeling
OR theory developed efficient algorithms to solve several singleobjective decision models
But practitioners find no model in OR theory fits their problem well
Real world problems usually multi-objective and lack nice structureof models discussed in theory, there is a big gap between theoryand practice.
The gap between practice and theory and its bridge
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Math Modeling (continued)
To get good results, essential to modelintelligently using heuristic modifications,approximations, relaxations, hierarchicaldecomposition
Will illustrate this using work done atHong Kong Container Port, and a busrental company in Seoul
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“Achieving Elastic CapacityThrough Data-intensiveDecision Support System (DSS)”Professor Katta G. MurtyIndustrial and Operations EngineeringUniversity of Michigan, Ann ArborHong Kong University of Science & TechnologyWork done at Hong Kong Container Port
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Hng KongInternational TerminalsHong KongInternational Terminals
The largest privately ownedterminal in the world’s busiestcontainer port
Operating under extremelylimited space and the highestyard density yet achieving one ofhighest productivity amongstports
Key Facilities
Quay Crane: 41
Yard Crane: 116
Internal Trucks: > 400
Yard Stacking Capacity: >80,000 boxes (= 111football stadiums)
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The Container Storage Yard
Storage yard(SY). Containersin stacks 4 - 6high. RTGCs(Rubber TiredGantry Cranes),stack andretrievecontainers. SYdivided intorectangularblocks.
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Storage Block
RTGC has7 rows inblockbetweenits legs. 6forcontainerstorage,7th fortruckpassing.
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QCs on Dock
QCs unloadcontainers,place themon ITs. ITstake themto SY forstorageuntilconsigneepicks them.ITs bringexportcontainersfrom SY toQCs to loadinto vessel.
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The flow of outboundcontainers
SY=Storage Yard
Underneath each location or operation, we list theequipment that handles the containers there
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Arrival, Storage and Retrieval ofImport Containers
Flow of inbound containers
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Top View of a Block B1 BeingServed by an RTGC
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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 ServiceQuality Metrics
HIT
TruckTruck
TurnaroundTurnaround
TimeTime
VesselVessel
TurnaroundTurnaround
TimeTime
QuayQuay
CraneCrane
RateRate
ReshuffleReshuffle
raterate
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Objectives of the Study
Minimize congestion on terminal roadsystem
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 arrivingcontainers, 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 tominimize quay crane, truck waiting time, numberof trucks used, and number of trucks in yard
Decision Problem Solved
HIT
HIT
![j0234755[1]](data/images/img21.gif)
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D3:Develop procedure to estimate truckrequirement profile and optimum truck driverhiring scheme
No. of Trucks Required
Decision Problem Solved
HourHour
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D4:Optimize yard crane deployment to blocks to minimizecrane time spent on the terminal road network
Decision Problem Solved
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D5:Allocate appointment times to external trucksto minimize turnaround time, and theirnumber in yard during peak time and levelworkload
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 ExportContainers
to go for Storage
.
.
.
Data on Blocks
B1: 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 Berths
Berth 1: 180 ImportContainers to go forStorage
.
.
.
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 FlowModel for Routing Trucks
fij= total no. container turns flowingon 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
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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 forFill Ratio Equalization
9 blocks, each with 600 spaces
ai = No. Containers in Block i, at period end ifno new containers sent there
xi = Decision Variables, no. new containerssent to Block i during the period
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LP Model to Determine Container QuotaNumbers for Blocks
.
Linear Programming formulation is:
Subject to
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Numerical Example
i
ai
xi
No.Remaining
Total
2570
1040
100
7
120
3
150
2
300
6
325
8
350
5
375
4
400
1
425
9
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 truckdispatching
LP model for fill ratio equalization, its combinatorial solution
First paper to relate container stacking to bin packing
Hardware Developed: for real time monitoring andcommunication
OR Techniques: LP, IP, Combinatorial Optimization
Decision Frequency: Container quota numbers for 95 blockseach four hours; take few seconds
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D2: Result from a Simulation Run
n = number Trucks/Quay Crane
h = number Containers to process in hatch = 30
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Innovations in Work on D2
Recognize importance of reducing number of trucks toreduce 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 minutes = 8.28 + 1.79 h(h) = average time minutes = 8.28 + 1.79 h
(h) = standard deviation = 1.31 + 0.019 h(h) = standard deviation = 1.31 + 0.019 h
Time allotted = (h) + (h)Time allotted = (h) + (h)
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Benefits from Work on D3
Estimate hourly truck requirements for planning
OR Techniques: Estimation, simulation, linearregression
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< 15x 15, takes few secondsSolved as transportation model, about once per two hours, typically size< 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 Trucksto Pickup During Peak Hours
Optimal quota number for external trucks to pick up ineach 30 minute interval determined by simulation
Appointment time booking system is automatedtelephone-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 reducenumber of external trucks in peak hours & their turnaround time
Hardware Developed: Automated telephone-based bookingsystem
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
D1
Route trucks,allocate storage
LP, combinatorialoptimization,integerprogramming
Quota for95 blocks
Every 4 hours
Few seconds
D1
Truck dispatch
Heuristic rule
Each truck
Real time
Real time
D2
Truck/Craneallocation
Queuing,estimation andsimulation
-
One-time
-
D3
Procedure toestimate truckrequirements
Estimation,simulation andlinear regression
-
One-time
-
D3
Estimate truckrequirement profile
Planning
15 vesselschedules
Once a day
Few minutes
D4
Crane movement
Estimation andnetwork flows
<= 15 x 15
Once about 2hours
Few seconds
D5
Booking system
Estimation,queuing andsimulation
-
One-time
-
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Improvement in Key Quality Service Metrics
HIT
External Truck TurnaroundTime ↓30%External Truck TurnaroundTime ↓30%
Internal Truck Turnaround TimeInternal Truck Turnaround Time
↓16%↓16%
Vessel Turnaround Time ↓30%Vessel Turnaround Time ↓30%
Vessel Operating Rate ↑47%Vessel Operating Rate ↑47%
Quay Crane Rate ↑45%Quay Crane Rate ↑45%
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More Benefits
Reduce workloadwith increasedproductivityReduce workloadwith increasedproductivity
Boost to moraleBoost to staffmorale
Staff
Customers
“Catch Up Port” in“Catch Up Port” inAsia
Shipping lines’savings amount toUS$65 million peryearShipping lines’savings amount toUS$65 million peryear
Enhance overallcustomersatisfaction andloyaltyEnhance overallcustomersatisfaction andloyalty
Social
Avoid theconstruction ofnew berths which in lesspollution andadverse effects tothe societyAvoid theconstruction ofnew berths whichresults in lesspollution andadverse effects tothe 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 million
Total 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 ElasticCapacity Using a Data-Intensive Decision SupportSystem'', 2004 Edelman Contest Finalist Paper, toappear in Interfaces, January-February 2005.
2. Katta G. Murty, Jiyin Liu, Yat-Wah Wan, Richard Linn,``A decision support system for operations in a containerterminal'', to appear in Decision Support Systems, 2005;available online at www.sciencedirect.com
3. Katta G. Murty, Woo-Je Kim, ``Intelligent DMSS forChartered Bus Allocation in Seoul, South Korea'',November 2004.