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Simultaneous Assignment of Locomotives and Cars to Passenger Trains

Author

Listed:
  • Jean-François Cordeau

    (École des Hautes Études Commerciales and GERAD, Montréal, Canada)

  • François Soumis

    (École Polytechnique de Montréal and GERAD, Montréal, Canada)

  • Jacques Desrosiers

    (École des Hautes Études Commerciales and GERAD, Montréal, Canada)

Abstract

The problem of assigning locomotives and cars to trains is a complex task for most railways. In this paper, we propose a multicommodity network flow-based model for assigning locomotives and cars to trains in the context of passenger transportation. The model has a convenient structure that facilitates the introduction of maintenance constraints, car switching penalties, and substitution possibilities. The large integer programming formulation is solved by a branch-and-bound method that relaxes some of the integrality constraints. At each node of the tree, a mixed-integer problem is solved by a Benders decomposition approach in which the LP relaxations of multicommodity network flow problems are optimized either by the simplex algorithm or by Dantzig-Wolfe decomposition. Some computational refinements, such as the generation of Pareto-optimal cuts, are proposed to improve the performance of the algorithm. Computational experiments performed on two sets of data from a railroad show that the approach can be used to produce optimal solutions to complex problems.

Suggested Citation

  • Jean-François Cordeau & François Soumis & Jacques Desrosiers, 2001. "Simultaneous Assignment of Locomotives and Cars to Passenger Trains," Operations Research, INFORMS, vol. 49(4), pages 531-548, August.
    • Handle: RePEc:inm:oropre:v:49:y:2001:i:4:p:531-548
    DOI: 10.1287/opre.49.4.531.11226
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    References listed on IDEAS

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    1. T. L. Magnanti & R. T. Wong, 1981. "Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria," Operations Research, INFORMS, vol. 29(3), pages 464-484, June.
    2. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    3. Jean-François Cordeau & François Soumis & Jacques Desrosiers, 2000. "A Benders Decomposition Approach for the Locomotive and Car Assignment Problem," Transportation Science, INFORMS, vol. 34(2), pages 133-149, May.
    4. Jean-François Cordeau & Paolo Toth & Daniele Vigo, 1998. "A Survey of Optimization Models for Train Routing and Scheduling," Transportation Science, INFORMS, vol. 32(4), pages 380-404, November.
    5. Dale McDaniel & Mike Devine, 1977. "A Modified Benders' Partitioning Algorithm for Mixed Integer Programming," Management Science, INFORMS, vol. 24(3), pages 312-319, November.
    6. K. V. Ramani & B. K. Mandal, 1992. "Operational Planning of Passenger Trains in Indian Railways," Interfaces, INFORMS, vol. 22(5), pages 39-51, October.
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