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Resolving instability in railway timetabling problems

Author

Listed:
  • Nikola Bešinović

    (Delft University of Technology)

  • Egidio Quaglietta

    (Delft University of Technology
    Control, Command and Signalling, Network Rail)

  • Rob M. P. Goverde

    (Delft University of Technology)

Abstract

A significant growth of the railway transportation demand is forecasted in the next decades which needs an increase of network capacity. Where possible, infrastructure upgrading can provide extra capacity; although in some cases, this is not enough to satisfy the entire transportation demand even if optimised timetabling is performed. We propose a heuristic model to develop a stable timetable which maximises the satisfaction of transportation demand in situations where network capacity is limited. In case the demand cannot be fully satisfied, the model relaxes the given line plan and timetable design parameters. The aim is to keep as many train services as possible and reduce the level of service minimally. We develop a mixed integer linear programming (MILP) model for minimising the cycle time to find an optimised stable timetable for the given line plan. The heuristic iteratively solves the MILP model and applies relaxation measures. We tested the model on the Dutch network. The results showed that the model can generate stable timetables by removing train services from the critical circuit, and also, higher transportation demand can be satisfied by additionally relaxing timetable design parameters.

Suggested Citation

  • Nikola Bešinović & Egidio Quaglietta & Rob M. P. Goverde, 2019. "Resolving instability in railway timetabling problems," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(5), pages 833-861, December.
    • Handle: RePEc:spr:eurjtl:v:8:y:2019:i:5:d:10.1007_s13676-019-00148-3
    DOI: 10.1007/s13676-019-00148-3
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    References listed on IDEAS

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    1. Leo G. Kroon & Leon W. P. Peeters, 2003. "A Variable Trip Time Model for Cyclic Railway Timetabling," Transportation Science, INFORMS, vol. 37(2), pages 198-212, May.
    2. Bešinović, Nikola & Goverde, Rob M.P. & Quaglietta, Egidio & Roberti, Roberto, 2016. "An integrated micro–macro approach to robust railway timetabling," Transportation Research Part B: Methodological, Elsevier, vol. 87(C), pages 14-32.
    3. Karl Nachtigall & Jens Opitz, 2008. "A Modulo Network Simplex Method for Solving Periodic Timetable Optimisation Problems," Operations Research Proceedings, in: Jörg Kalcsics & Stefan Nickel (ed.), Operations Research Proceedings 2007, pages 461-466, Springer.
    4. Goverde, Rob M.P., 2007. "Railway timetable stability analysis using max-plus system theory," Transportation Research Part B: Methodological, Elsevier, vol. 41(2), pages 179-201, February.
    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. 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.
    7. Christian Liebchen, 2008. "The First Optimized Railway Timetable in Practice," Transportation Science, INFORMS, vol. 42(4), pages 420-435, November.
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    Cited by:

    1. Liping Ge & Stefan Voß & Lin Xie, 2022. "Robustness and disturbances in public transport," Public Transport, Springer, vol. 14(1), pages 191-261, March.
    2. Luisa I. Martínez-Merino & Diego Ponce & Justo Puerto, 2023. "Constraint relaxation for the discrete ordered median problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 538-561, October.

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