# Intelligent Modeling for Decision Making

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```					Intelligent Modeling for Decision Making
Katta G. Murty Industrial 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

2

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

3

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 Engineering University of Michigan, Ann Arbor Hong Kong University of Science & Technology
Work done at Hong Kong Container Port

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Hong Kong International 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 Facilities

Quay Crane: 41 Yard Crane: 116 Internal Trucks: > 400 Yard 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
Arrival at terminal and storage Customer Terminal Gate External External Tractor Tractor  Documentation  Inspection  Storage space assignment Storage Yard Yard Crane Retrieval and loading into vessel Quayside Internal Tractor Quay Crane Vessel

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Arrival, Storage and Retrieval of Import Containers
Retrieval, pickup by customer Customer Terminal Gate External External Tractor Tractor Unloading, storage Storage Quayside Yard Internal Quay Yard Tractor Crane Crane Vessel

Flow of inbound containers

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Top View of a Block B1 Being Served by an RTGC
B3

Storage lanes

B1

B2

Truck lane

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Land Scarcity for Terminal Development in Hong Kong

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The Highest Land Utilization Terminal in the World

CTB Hamburg
Land Area / Number of Berth Throughput (2003)

HIT Hong Kong

Pier T Long Beach

39.5 acre 2.3m TEU

25.1 acre 6.4m TEU

72.0 acre 1.2m TEU

HK handles more throughput with less land
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Key Service Quality Metrics
Truck Turnaround Time Quay Crane Rate

HIT

Reshuffle rate

Vessel
Turnaround Time
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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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Decision Problem Solved
D1: Route trucks and allocate storage spaces to arriving containers, to minimize congestion and reshuffling
HIT

HIT HIT

HIT

HIT

HIT

Gate

Container Yard

Berth

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

HIT HIT

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Decision Problem Solved
D3: Develop procedure to estimate truck requirement profile and optimum truck driver hiring scheme
140 130

No. of Trucks Required

120

110

100

90

80

70 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Hour

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Hour

Decision Problem Solved
D4: Optimize yard crane deployment to blocks to minimize crane time spent on the terminal road network

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Decision Problem Solved /Under Study
D5: Allocate appointment times to external trucks to minimize turnaround time, and their number in yard during peak time and level workload

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Expected Number of Containers in Planning Period at Each Node, to Go to Various Destination Nodes
D1: Data for flow model to route trucks
HIT HIT
HIT

Export

Block 1
HIT

Block 2
HIT

Export
Berth 1

Import
Block 3
HIT

Block 4
HIT

Impor t
HIT

Block 5

Block 6

Berth 2

Gate Complex
Data: 400 Export Containers to go for Storage . . .

Container Yard
Data on Blocks B1: 40 Export Containers to Berth 1 10 Export Containers to Berth 4 20 Import Containers to Gate . . .

Berth
Data on Berths Berth 1: 180 Import Containers to go for Storage . . .

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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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Number of Moves

00

100

150

200

250

300

350

400

450

50

0

_0 _3 _2 _1 _0 _3 _2 _1 _0 _3 _2 _1 _0 _3 _2 _1 _0 _3 _2 _1

00 01 02 03 03 04 05 06 06 07 08 09 09 10 11 12 12 13 14 15 15 16 17 18 18 19 20 21 21 22 23 _0 _3 _2 _1 _0 _3 _2 _1 _0 _3 _2 _1

No. Effective Moves over a Typical Day

Time (hr-quarter)

25

26

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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


.Min

i | ai  xi  400 |
Min (ui  ui ) i
  ui )  400,



Linear Programming formulation is:

Subject to

 ai  xi  (ui

all i

x

i

 1040

xi , ui , ui  0, all i
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Numerical Example
Average stored containers/block = (2570+1040)/9 = 400

i
7 3 2

ai
100 120 150 300 325 350 375 400 425

xi
300 280 250 100 75 50 25 0 0

No. Remaining 740 460 210 110 35 0 0 0 0

6 8 5
4 1 9

Total

2570

1040

--31

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 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 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) = average time minutes = 8.28 + 1.79 h




(h) = standard deviation = 1.31 + 0.019 h
Time allotted = (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
Crane minutes to move
From Block B6 B1 B2 B3 20 25 30 To block B7 25 10 25 B8 35 20 10 B9 30 15 20

B4
B5

35
30

15
20

25
10

10
25

Solved as transportation model, about once per two hours, typically size < 15x 15, takes few seconds
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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 Route trucks, allocate storage Truck dispatch Truck/Crane allocation Procedure to estimate truck requirements Estimate truck requirement profile Crane movement

Techniques

Size Quota for 95 blocks Each truck -

Frequency

Comp. Time

D1

LP, combinatorial optimization, integer programming
Heuristic rule Queuing, estimation and simulation Estimation, simulation and linear regression Planning Estimation and network flows Estimation, queuing and simulation

Every 4 hours

Few seconds

D1 D2

Real time One-time

Real time -

D3

15 vessel schedules <= 15 x 15

One-time

-

D3 D4

Once a day Once about 2 hours One-time

Few minutes Few seconds - 40

D5

Booking system

-

Improvement in Key Quality Service Metrics

Internal Truck Turnaround Time ↓16%

HIT

External Truck Turnaround Time ↓30%
Quay Crane Rate ↑45%

Vessel Turnaround Time ↓30%
Vessel Operating Rate ↑47%

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More Benefits

Customers
 “Catch Up Port” in

Staff

Social
 Avoid the

Asia  Shipping lines’ savings amount to US\$65 million per year  Enhance overall customer satisfaction and loyalty

with increased productivity  Boost to staff morale

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

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Business Benefits to HPH and Customers
Financial Benefits Summary
Savings US\$54 million Key Improvement Areas Improvement of internal tractor utilization
 

US\$100 million US\$65 million

Handling cost reduction Avoidance of building new facilities

Vessel turnaround time improvement

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 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.

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