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Network Optimization in Transportation Scheduling

2. Overview. Railroad Blocking ProblemsMotivated by CSX TransportationAirline Fleet Scheduling ProblemsFunded by United AirlinesLocomotive Scheduling ProblemsFunded by CSX Transportation. 3. Based on joint research with Jian Liu. RAILROAD BLOCKING PROBLEM. 4. Railroad Blocking Problem

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Network Optimization in Transportation Scheduling

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    1. 1 Network Optimization in Transportation Scheduling Ravindra K. Ahuja Supply Chain and Logistics Engineering (SCALE) Center Industrial & Systems Engineering University of Florida Gainesville, FL 32611 ahuja@ufl.edu; www.ise.ufl.edu/ahuja

    2. 2

    3. 3 Based on joint research with Jian Liu RAILROAD BLOCKING PROBLEM

    4. 4 Railroad Blocking Problem

    5. 5 Airline Schedule Design Problem

    6. 6 Airline Schedule Design Problem (contd.)

    7. 7 Railroad Blocking Problem

    8. 8 Blocking Problem

    9. 9 Size of the Problem

    10. 10 Difficulty of the Problem

    11. 11 Prior Research Bodin et al. [1980] Assad [1983] Van Dyke [1986, 1988] Newton, Barnhart and Vance [1998] Barnhart, Jin and Vance [2000] None of the above or any OR approach is used in practice.

    12. 12 Our Approaches Integer Programming Based Methods Slow and unpredictable Network Optimization Methods Construction methods Improvement methods

    13. 13 Basic Approach Start with a feasible solution of the blocking problem. Optimize the blocking solution at only one node (leaving the solution at other nodes unchanged) and reroute shipments. Repeat as long as there are improvements.

    14. 14 An Illustration

    15. 15 Basic Approach (contd.) Out of about 3,000 arcs emanating from a node, select 50 arcs and redirect up to 50,000 shipments to minimize the cost of flow.

    16. 16 Basic Approach (contd.)

    17. 17 Computational Results Considering that about 10 million cars travel annually, the resulting savings are huge. We expect the savings to be over $50 million.

    18. 18 Benefits of Network Based Methods Reasonable running times 10-20 minutes Scaleable with the increase in problem size Accuracy We believe that our solutions are within 2% - 3% of the optimal solution. Flexible Can incorporate a variety of practical constraints.

    19. 19 Future Work Working with railroads to identify and incorporate several practical considerations. Develop a decision support system for solving the blocking problem.

    20. 20 Additional Applications Airline Network Design Trucking Network Design Package Delivery Network Design

    21. 21 Based on joint research with Liu Jian James B. Orlin Dushyant Sharma Research supported by United Airlines AIRLINE FLEET SCHEDULING

    22. 22 Fleet Assignment Model (FAM) Assign planes of different types to different flight legs so as to minimize the total cost of assignment.?

    23. 23 Input to Flight Assignment Model

    24. 24 Output of Flight Assignment Model

    25. 25 Through Flights

    26. 26 Additional Through Flights

    27. 27 Current Solution Technique

    28. 28 The Combined Through Fleet Assignment Model (ctFAM)

    29. 29 Our Approach for ctFAM

    30. 30 Single A-B Swaps (Before the swap)

    31. 31 Single A-B Swaps (After the swap)

    32. 32 Finding Improving A-B Swaps

    33. 33 Finding Improving Changes (contd.) Define the cost of each arc as the cost of switching plane types. A negative cost cycle gives a profitable A-B swap.

    34. 34 Multi A-B Swaps

    35. 35 Identifying Profitable AB-Swaps

    36. 36 Neighborhood Search for the ctFAM Start with a feasible solution x. Select two fleet types A and B. Construct AB-Improvement Graph GAB(x). Find negative-cost (constrained) cycle in GAB(x) and update x. Repeat as long as there are negative cost cycles in GAB(x) for some fleet types A and B.

    37. 37 Computational Results on ctFAM

    38. 38 ctFAM with Time Windows

    39. 39 ctFAM with Time windows (contd.)

    40. 40 Computational Results

    41. 41 Neighborhood Search in Airline Scheduling

    42. 42 Locomotive Scheduling Problems Based on joint research with Jian Liu, University of Florida, Gainesville James B. Orlin, MIT, Cambridge Dushyant Sharma, MIT, Cambridge Larry Shughart, CSX Transportation, Jacksonville Funded by CSX Transportation

    43. 43 Locomotive Schedule Planning Problem

    44. 44 Some Features

    45. 45 Decision Variables

    46. 46 Hard Constraints

    47. 47 Problem Size

    48. 48 Two-Stage Optimization

    49. 49 Problem Decomposition

    50. 50 Computational Results

    51. 51 Computational Results (contd.)

    52. 52 Summary of Computational Results

    53. 53 Next Research Phase

    54. 54 Summary

    55. 55 Research Papers

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