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Decomposing the Train-Scheduling Problem into Integer-Optimal Polytopes

Author

Listed:
  • Masoud Barah

    (Department of Industrial and Systems Engineering, University of Tennessee, Knoxville, Tennessee 37996)

  • Abbas Seifi

    (Department of Industrial Engineering and Management Systems, Amirkabir University of Technology, Tehran 15875, Iran)

  • James Ostrowski

    (Department of Industrial and Systems Engineering, University of Tennessee, Knoxville, Tennessee 37996)

Abstract

This paper presents conditions for which the linear relaxation for the train-scheduling problem is integer optimal. These conditions are then used to identify how to partition a general problem’s feasible region into integer-optimal polytopes. Such an approach yields an extended formulation that contains far fewer binary variables. Our computational experiments show that this approach results in significant computational savings. Moreover, this approach scales well when the train-scheduling problem is modeled using smaller time increments, allowing for higher fidelity models to be solved without significantly increasing the required computational time.

Suggested Citation

  • Masoud Barah & Abbas Seifi & James Ostrowski, 2019. "Decomposing the Train-Scheduling Problem into Integer-Optimal Polytopes," Transportation Science, INFORMS, vol. 53(3), pages 763-772, May.
    • Handle: RePEc:inm:ortrsc:v:53:y:2019:i:3:p:763-772
    DOI: 10.1287/trsc.2018.0848
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    References listed on IDEAS

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    1. Harrod, Steven & Schlechte, Thomas, 2013. "A direct comparison of physical block occupancy versus timed block occupancy in train timetabling formulations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 54(C), pages 50-66.
    2. Zhou, Xuesong & Zhong, Ming, 2007. "Single-track train timetabling with guaranteed optimality: Branch-and-bound algorithms with enhanced lower bounds," Transportation Research Part B: Methodological, Elsevier, vol. 41(3), pages 320-341, March.
    3. G. Caimi & F. Chudak & M. Fuchsberger & M. Laumanns & R. Zenklusen, 2011. "A New Resource-Constrained Multicommodity Flow Model for Conflict-Free Train Routing and Scheduling," Transportation Science, INFORMS, vol. 45(2), pages 212-227, May.
    4. Alberto Caprara & Matteo Fischetti & Paolo Toth, 2002. "Modeling and Solving the Train Timetabling Problem," Operations Research, INFORMS, vol. 50(5), pages 851-861, October.
    5. Cacchiani, Valentina & Toth, Paolo, 2012. "Nominal and robust train timetabling problems," European Journal of Operational Research, Elsevier, vol. 219(3), pages 727-737.
    6. U. Brännlund & P. O. Lindberg & A. Nõu & J.-E. Nilsson, 1998. "Railway Timetabling Using Lagrangian Relaxation," Transportation Science, INFORMS, vol. 32(4), pages 358-369, November.
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