Intelligent Modeling for Decision Making Katta G. Murty Industrial and Operations Engineering University of Michigan Ann Arbor, Michigan 48109-2117 USA murty@umich.edu

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

The gap between practice and theory and its bridge 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

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

“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  

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)

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.

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

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.

The flow of outbound containers SY=Storage Yard Underneath each location or operation, we list the equipment that handles the containers there

Arrival, Storage and Retrieval of Import Containers Flow of inbound containers

Top View of a Block B1 Being Served by an RTGC

Land Scarcity for Terminal Development in Hong Kong

The Highest Land Utilization Terminal in the World 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 HK handles more throughput with less land

Key Service Quality Metrics Truck Turnaround Time Quay Crane Rate HIT Reshuffle rate Vessel Turnaround Time

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

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

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

Decision Problem Solved D3: Develop procedure to estimate truck requirement profile and optimum truck driver hiring scheme No. of Trucks Required Hour

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

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

D1: Data for flow model to route trucks 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 Export Block 1 Block 2 Berth 1 HIT HIT Import Import HIT Block 3 Block 4 HIT HIT Block 5 Block 6 Berth 2 Gate Complex Container Yard Berth Data on Blocks B1: 40 Export Containers to Berth 1 10 Export Containers to Berth 4 20 Import Containers to Gate . Data: 400 Export Containers to go for Storage . Data on Berths Berth 1: 180 Import Containers to go for Storage .

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)}

Variation in Workload Over Time

Three Separate Policies Equalize fill ratios in blocks Truck dispatching policy Storage space assignment in a block

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

LP Model to Determine Container Quota Numbers for Blocks . Linear Programming formulation is: Subject to

Numerical Example Average stored containers/block = (2570+1040)/9 = 400 i ai xi No. Remaining Total 2570 1040 100 7 300 740 120 3 280 460 150 2 250 210 300 6 100 110 325 8 75 35 350 5 50 375 4 25 400 1 425 9 ---

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

D2: Result from a Simulation Run n = number Trucks/Quay Crane h = number Containers to process in hatch = 30

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

D3: Truck Requirement Profile h = number of containers unloaded, loaded in a hatch (h) = average time minutes = 8.28 + 1.79 h (h) = standard deviation = 1.31 + 0.019 h Time allotted = (h) + (h)

Benefits from Work on D3 Estimate hourly truck requirements for planning OR Techniques: Estimation, simulation, linear regression Decision frequency: Daily; takes few minutes

D4: Crane Movement Between Blocks Crane minutes to move From Block To block B6 B7 B8 B9 B1 20 25 35 30 B2 10 15 B3 B4 B5 Solved as transportation model, about once per two hours, typically size < 15x 15, takes few seconds

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

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

Summary of Techniques Used Problem Techniques Size Frequency Comp. Time D1 Route trucks, allocate storage LP, combinatorial optimization, integer programming Quota for 95 blocks Every 4 hours Few seconds Truck dispatch Heuristic rule Each truck Real time D2 Truck/Crane allocation Queuing, estimation and simulation - One-time D3 Procedure to estimate truck requirements Estimation, simulation and linear regression Estimate truck requirement profile Planning 15 vessel schedules Once a day Few minutes D4 Crane movement Estimation and network flows <= 15 x 15 Once about 2 hours D5 Booking system Estimation, queuing and simulation

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%

More Benefits Customers Staff Social “Catch Up Port” in Asia Shipping lines’ savings amount to US$65 million per year Enhance overall customer satisfaction and loyalty Reduce workload with increased productivity Boost to staff morale Avoid the construction of new berths which results in less pollution and adverse effects to the society

Business Benefits to HPH and Customers Financial 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

References 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.