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Routing Trains Through Railway Junctions: A New Set-Packing Approach

Author

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  • Richard Lusby

    (Department of Management Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark)

  • Jesper Larsen

    (Department of Management Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark)

  • David Ryan

    (Department of Engineering Science, The University of Auckland, Auckland 1142, New Zealand)

  • Matthias Ehrgott

    (Department of Engineering Science, The University of Auckland, Auckland 1142, New Zealand)

Abstract

The problem of routing trains through railway junctions is an integral part of railway operations. Large junctions are highly interconnected networks of track where multiple railway lines merge, intersect, and split. The number of possible routings makes this a very complicated problem. We show how the problem can be formulated as a set-packing model with a resource-based constraint system. We prove that this formulation is tighter than the conventional node-packing model, and develop a branch-and-price algorithm that exploits the structure of the set-packing model. A discussion of the variable generation phase, as well as a pricing routine in which these variables are represented by tree structures, is also described. Computational experiments on 25 random timetables show this to be an efficient approach.

Suggested Citation

  • Richard Lusby & Jesper Larsen & David Ryan & Matthias Ehrgott, 2011. "Routing Trains Through Railway Junctions: A New Set-Packing Approach," Transportation Science, INFORMS, vol. 45(2), pages 228-245, May.
    • Handle: RePEc:inm:ortrsc:v:45:y:2011:i:2:p:228-245
    DOI: 10.1287/trsc.1100.0362
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    References listed on IDEAS

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    Cited by:

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    4. Sels, P. & Vansteenwegen, P. & Dewilde, T. & Cattrysse, D. & Waquet, B. & Joubert, A., 2014. "The train platforming problem: The infrastructure management company perspective," Transportation Research Part B: Methodological, Elsevier, vol. 61(C), pages 55-72.
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    8. Zhang, Yongxiang & D'Ariano, Andrea & He, Bisheng & Peng, Qiyuan, 2019. "Microscopic optimization model and algorithm for integrating train timetabling and track maintenance task scheduling," Transportation Research Part B: Methodological, Elsevier, vol. 127(C), pages 237-278.
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    11. Sparing, Daniel & Goverde, Rob M.P., 2017. "A cycle time optimization model for generating stable periodic railway timetables," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 198-223.
    12. Dewilde, Thijs & Sels, Peter & Cattrysse, Dirk & Vansteenwegen, Pieter, 2014. "Improving the robustness in railway station areas," European Journal of Operational Research, Elsevier, vol. 235(1), pages 276-286.

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