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Cost optimal periodic train scheduling

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  • Thomas Lindner
  • Uwe Zimmermann

Abstract

For real world railroad networks, we consider minimizing operational cost of train schedules which depend on choosing different train types of diverse speed and cost. We develop a mixed integer linear programming model for this train scheduling problem. For practical problem sizes, it seems to be impossible to directly solve the model within a reasonable amount of time. However, suitable decomposition leads to much better performance. In the first part of the decomposition, only the train type related constraints stay active. In the second part, using an optimal solution of this relaxation, we select and fix train types and try to generate a train schedule satisfying the remaining constraints. This decomposition idea provides the cornerstone for an algorithm integrating cutting planes and branch-and-bound. We present computational results for railroad networks from Germany and the Netherlands. Copyright Springer-Verlag 2005

Suggested Citation

  • Thomas Lindner & Uwe Zimmermann, 2005. "Cost optimal periodic train scheduling," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 281-295, November.
    • Handle: RePEc:spr:mathme:v:62:y:2005:i:2:p:281-295
    DOI: 10.1007/s00186-005-0001-0
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    References listed on IDEAS

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    1. 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.
    2. Odijk, Michiel A., 1996. "A constraint generation algorithm for the construction of periodic railway timetables," Transportation Research Part B: Methodological, Elsevier, vol. 30(6), pages 455-464, December.
    3. Claessens, M. T. & van Dijk, N. M. & Zwaneveld, P. J., 1998. "Cost optimal allocation of rail passenger lines," European Journal of Operational Research, Elsevier, vol. 110(3), pages 474-489, November.
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    Cited by:

    1. 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.
    2. Cacchiani, Valentina & Toth, Paolo, 2012. "Nominal and robust train timetabling problems," European Journal of Operational Research, Elsevier, vol. 219(3), pages 727-737.
    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. Bach, Lukas & Gendreau, Michel & Wøhlk, Sanne, 2015. "Freight railway operator timetabling and engine scheduling," European Journal of Operational Research, Elsevier, vol. 241(2), pages 309-319.
    5. Cacchiani, Valentina & Furini, Fabio & Kidd, Martin Philip, 2016. "Approaches to a real-world Train Timetabling Problem in a railway node," Omega, Elsevier, vol. 58(C), pages 97-110.
    6. Wenliang Zhou & Junli Tian & Jin Qin & Lianbo Deng & TangJian Wei, 2015. "Optimization of Multiperiod Mixed Train Schedule on High-Speed Railway," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-14, April.
    7. 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.

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