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Mixed-Integer Programming for Railway Capacity Analysis and Cyclic, Combined Train Timetabling and Platforming

Author

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  • Matthew E. H. Petering

    (Department of Industrial and Manufacturing Engineering, University of Wisconsin–Milwaukee, Milwaukee, Wisconsin 53201)

  • Mojtaba Heydar

    (School of Electrical Engineering and Computer Science, University of Newcastle, Callaghan, NSW 2308, Australia)

  • Dietrich R. Bergmann

    (Railway Systems Engineering, Ann Arbor, Michigan 48113)

Abstract

We present the literature’s first mixed-integer linear programming model of a cyclic, combined train timetabling and platforming problem. The model’s objectives are to minimize (1) the cycle length and (2) the total journey time of all trains dispatched during one cycle. The model falls outside the framework of the well-known periodic event scheduling problem and explicitly considers the minimization of cycle length using linear constraints and a linear objective function. We define the model, propose methods for obtaining bounds on the optimal objective value, and describe preprocessing techniques for reducing the number of variables and constraints. Numerous life-size problem instances are solved to optimality using IBM ILOG CPLEX. Results show the model’s effectiveness in pursuing objectives 1 and 2, the benefits of deciding the cyclic train order versus assuming a given order, and the model’s ability to calculate railway capacity without bias.

Suggested Citation

  • Matthew E. H. Petering & Mojtaba Heydar & Dietrich R. Bergmann, 2016. "Mixed-Integer Programming for Railway Capacity Analysis and Cyclic, Combined Train Timetabling and Platforming," Transportation Science, INFORMS, vol. 50(3), pages 892-909, August.
    • Handle: RePEc:inm:ortrsc:v:50:y:2016:i:3:p:892-909
    DOI: 10.1287/trsc.2015.0652
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    References listed on IDEAS

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    Cited by:

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    3. Zhou, Wenliang & Tian, Junli & Xue, Lijuan & Jiang, Min & Deng, Lianbo & Qin, Jin, 2017. "Multi-periodic train timetabling using a period-type-based Lagrangian relaxation decomposition," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 144-173.
    4. Lu Yang & Leishan Zhou & Hanxiao Zhou & Chang Han & Wenqiang Zhao, 2023. "A Lagrangian Method for Calculation of Passing Capacity on a Railway Hub Station," Mathematics, MDPI, vol. 11(6), pages 1-20, March.
    5. Xu, Xiaoming & Li, Chung-Lun & Xu, Zhou, 2021. "Train timetabling with stop-skipping, passenger flow, and platform choice considerations," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 52-74.
    6. Zeyu Wang & Leishan Zhou & Bin Guo & Xing Chen & Hanxiao Zhou, 2021. "An Efficient Hybrid Approach for Scheduling the Train Timetable for the Longer Distance High-Speed Railway," Sustainability, MDPI, vol. 13(5), pages 1-22, February.

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