Solving Train Schedule Design Problems using Decomposition and Network Flows

Transcription

1 Solving Train Schedule Design Problems using Decomposition and Network Flows Ravindra K. Ahuja, President

2 Collaborators Development Partnership with BNSF Architects & Designers: Pooja Dewan, BNSF Railway Krishna C. Jha, Innovative Scheduling Arvind Kumar, Innovative Scheduling Ravindra K. Ahuja, Innovative Scheduling 2

3 Overview of the Presentation Train Scheduling Optimizer: An Overview Case Studies: Optimizing Train Schedules Innovative Train Scheduling Optimizer (ITSO) Decision Support System 3

4 Flow of Blocks on Trains

5 Train Schedule Design Problem Blocks Trains Shipments Shipment-Block Assignments Crew Locomotive Train Scheduling Optimizer Block-to-Train Assignments Trip Plan Balanced Crew Assignment Balanced Locomotive Assignment 5

6 Decision Variables Decision: Train origins, destinations, and routes Train days of operation and train times Train block-to-train assignment by day of the week Trip plans for all cars Locomotive assignment Crew assignment Constraints Yard capacity constraints Line capacity constraints Train capacity constraints Business rules 6

7 Contribution: Integration of Railroad Resources Constrained by Network Capacity Crew Railcar ITSO Locomotive Constrained by Operating Rules We consider these three resources by maintaining three time-space networks. 7

8 Railcar Flow Network Train 1 car car car car Ground Nodes Time Train 2 car car Train 3 car car car car car car car car car car car car Train 1 car car Train 2 car car Train 5 car car car car car We construct the weekly time-space train network and flow railcars through this network. 8

9 Locomotive Flow Network Train 1 Train 2 Train 4 Train 5 Train 3 Train 6 We construct the weekly space-time train network and locomotives cycle through this network. 9

10 Crew Scheduling at US Railroads Each train requires a crew and changes crew at several locations as it travels from its origin to its destination

11 Crew Flow Network Home Terminal Time Away Terminal We construct the weekly space-time crew network and crews cycle through this network. We create a separate network for each crew district Train Arcs Deadhead Arcs Rest Arcs 11

12 Constraints Yard Constraints Number of trains originating at any node in each given time window is limited. Number of trains terminating at any node in each given time window is limited. Number of trains passing through each node in each given time window is limited. Track Constraints Speed of a train on a track depends upon the type of train. Number of trains passing through any corridor in any given time window is limited. Satisfy headway constraints 12

13 Constraints (contd.) Train Capacity Constraints The number of cars on any train is limited The length of any train is limited The weight-carrying capacity of any train is limited No more than specified number of blocks per train Number of stops of a train is limited Locomotive Constraints Honor locomotive minimum connection times between trains Provide number of locomotive based on train tonnages Crew Constraints Honor crew minimum connection times between trains Honor crew union rules related to work and rest 13

14 Objective Function Terms Car miles Car days Block swaps Train miles Loco cost Train starts Crew cost 14

15 Our Contribution Problem size for a weekly problem: Number of railcars: 100,000 2,000 Number of locomotives: 2,000 4,000 Number of crew districts: Number of crews: 4,000-6,000 We have developed a computer program to solve this problem within 1-2 hours on a laptop. Uses a variety of operations research techniques: Construction heuristics Network flows & Linear programming Neighborhood search Very large-scale neighborhood (VLSN) search 15

16 A Two-Stage Decomposition Process Train Route Optimization Train Details Optimization Train schedule without time Train routes Block-train assignment Locomotive assignment Crew assignment Train schedule with time Train routes Block-train assignment Locomotive assignment Crew assignment 16

17 Train Route Optimization Determine train schedule without train times and day of operation. Construction Enumerate all potential train routes Determine the goodness of each route Select the best route Improvement Improve routes using neighborhood search Improve routes using VLSN search Repeat until all blocks are routed 17

18 Train Details Optimization Train Time Optimization Train Operating Days Optimization Block-to-Train Optimization Decide train arrival and departure times at each stop node on the route Decide operating days of trains Decide block-to-train assignments by day of week We use neighborhood search approach to optimize each set of decision variables. Assess the impact of each alternative with respect to the three resources: railcars, crews, and locomotives. 18

19 Three Time-Space Networks Railcar Network Crew Network Locomotive Network 19

20 Current Enhancements We are now adding meet-pass planning to the software where any change in the solution is evaluated with respect to track considerations. The train schedule will also create a meet-pass plan with respect to track infrastructure. We are also including yard operations in the software. The solution will incorporate yard capacities at the detail level and produce detailed yard reports. 20

21 Incremental Train Scheduling This feature incrementally changes a given train plan. User can specify which aspect of the train plan can be changed: New train origin stations New train destination stations Train time optimization Train frequency optimization Train block-train assignment User can also control the extent of change allowed. 21

22 Overview of the Presentation Train Scheduling Optimizer: An Overview Case Studies: Optimizing Train Schedules Innovative Train Scheduling Decision Support System 22

23 Case Study Overview We are conducting studies for two Class I railroads to improve their current train schedules and estimate the cost savings of our train plans. We do not wish to disclose the identity of these railroads. These results are still being evaluated by our railroad partners, thus the results may change. However, we believe that these savings estimates are realizable. 23

24 Case Study 1: Incremental Optimization Objective: Reduce the number of crew starts by at least 100 per week. Constraints: Do not add any new train. Do not change train frequencies or train timings. Degrees of Freedom: May eliminate some trains completely. Optimally re-assign the blocks riding on deleted trains to other trains. 24

25 Case Study 1 Results Statistics Train Symbols Total Train Starts Total Train Miles Total Crew Starts Total Crew Fleet Size Total Car Miles Total Car Hours % Improvement 5.31% 4.81% 2.19% 2.23% 1.63% 0.00% -0.10% Conclusions: Trains starts reduced by 4.8% resulting in 2.2% decrease in crew starts. A reduction in over 100 crew starts was achieved even with the tight constraints imposed. These results have been evaluated by our railroad partner and they find the incremental train schedule implementable. 25

26 Case Study 2: Incremental Optimization Objective: Reduce the number of crew starts by at least 200 per week. Constraints: Do not change train timings. Degrees of Freedom: May eliminate some trains completely. Model may add some trains (less than we delete) Change frequencies of few trains. Optimally re-assign the blocks riding on deleted trains to other trains. 26

27 Case Study 2 Results Statistics Train Symbols Total Train Starts Total Train Miles Total Crew Starts Total Crew Fleet Size Total Car Miles Total Car Hrs % Improvement 6.19% 7.31% 4.21% 4.52% 1.37% 0.07% 0.12% Conclusions: Trains starts reduced by 7.31% resulting in 4.52% decrease in crew starts. A reduction in over 200 crew starts was achieved. These results are being evaluated by our railroad partner. 27

28 Case Study 3: Clean-Slate Optimization Objective: Determine a zero-base or clean-slate train schedule and obtain the maximum possible cost savings in car-hire, crew and locomotive costs. Constraints: Use network capacities as used in the railroad s current plan Degrees of Freedom: May delete or/and some trains. May change train frequencies. May change train timings. May change block-train assignments. 28

29 Case Study 3 Results Train Cost Savings Average Train Starts Average Train Miles Average # Trains Work Events Crew Cost Savings Average Crew Wage Average Deadhead Crews Average # Away Nights Average # HAHT Crew Penalty Hours Total number of Crew Starts 1.49% 1.02% 1.15% 1.23% 0.23% 3.50% 14.52% 1.14% Locomotive Cost Savings Ownership Cost Active Pulling Cost Deadheading Cost Light Travel Cost Total Locomotive Requirement Car Cost Savings Average Block Swaps Total Cars Hours Total Car Miles 4.05% 1.10% 3.55% 9.46% 4.05% -1.91% 0.24% 0.01% 29

30 Summary Determining a railroad s train schedule is a very complex optimization problem. Optimization-based methods promise significant improvements over a railroad s manually generated train schedule. The savings obtained by the train scheduling optimizer are very impressive. Though these savings estimate are yet to be fully verified by our railroad partners, we believe that these are quite realistic and attainable. 30

31 Overview of the Presentation Train Scheduling Optimizer: An Overview Case Studies: Optimizing Train Schedules Innovative Train Scheduling Optimizer (ITSO) Decision Support System 31

32 ITSO: A Web-Based Decision Support System We have built a web-based decision support system for train scheduling that can be used for clean-slate and incremental train scheduling. Features of this system: Ability to create and manage multiple scenario. Each scenario can store multiple train schedules. Ability to analyze any solution in any scenario and drill-down to the desired level of details. Ability to compare two solutions in the same scenario in great detail. Ability to calibrate constraints and costs to perform extensive what-if analysis. Ability to enable users to manually modify the model generated solutions. 32

33 Next Steps Our train scheduling software is available for consulting activities. We will be happy to work with you to reduce your train operating costs and create significant value for you. 33

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