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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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    1. Peter J. Zwaneveld & Leo G. Kroon & H. Edwin Romeijn & Marc Salomon & Stéphane Dauzère-Pérès & Stan P. M. Van Hoesel & Harrie W. Ambergen, 1996. "Routing Trains Through Railway Stations: Model Formulation and Algorithms," Transportation Science, INFORMS, vol. 30(3), pages 181-194, August.
    2. 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.
    3. Christian Liebchen, 2008. "The First Optimized Railway Timetable in Practice," Transportation Science, INFORMS, vol. 42(4), pages 420-435, November.
    4. Dennis Huisman & Leo G. Kroon & Ramon M. Lentink & Michiel J. C. M. Vromans, 2005. "Operations Research in passenger railway transportation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(4), pages 467-497, November.
    5. 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.
    6. Chakroborty, Partha & Vikram, Durgesh, 2008. "Optimum assignment of trains to platforms under partial schedule compliance," Transportation Research Part B: Methodological, Elsevier, vol. 42(2), pages 169-184, February.
    7. Abril, M. & Barber, F. & Ingolotti, L. & Salido, M.A. & Tormos, P. & Lova, A., 2008. "An assessment of railway capacity," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 44(5), pages 774-806, September.
    8. Carey, Malachy & Crawford, Ivan, 2007. "Scheduling trains on a network of busy complex stations," Transportation Research Part B: Methodological, Elsevier, vol. 41(2), pages 159-178, February.
    9. Ghoseiri, Keivan & Szidarovszky, Ferenc & Asgharpour, Mohammad Jawad, 2004. "A multi-objective train scheduling model and solution," Transportation Research Part B: Methodological, Elsevier, vol. 38(10), pages 927-952, December.
    10. 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.
    11. Carey, Malachy, 1994. "A model and strategy for train pathing with choice of lines, platforms, and routes," Transportation Research Part B: Methodological, Elsevier, vol. 28(5), pages 333-353, October.
    12. Alain Billionnet, 2003. "Using Integer Programming to Solve the Train-Platforming Problem," Transportation Science, INFORMS, vol. 37(2), pages 213-222, May.
    13. Harrod, Steven, 2009. "Capacity factors of a mixed speed railway network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 45(5), pages 830-841, September.
    14. 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.
    15. Morten N. Nielsen & Bjorn Hove & Jens Clausen, 2006. "Constructing periodic timetables using MIP - a case study from DSB S-train," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 1(3), pages 213-227.
    16. Lee, Yusin & Chen, Chuen-Yih, 2009. "A heuristic for the train pathing and timetabling problem," Transportation Research Part B: Methodological, Elsevier, vol. 43(8-9), pages 837-851, September.
    17. Burdett, R.L. & Kozan, E., 2006. "Techniques for absolute capacity determination in railways," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 616-632, September.
    18. Chung, Ji-Won & Oh, Seog-Moon & Choi, In-Chan, 2009. "A hybrid genetic algorithm for train sequencing in the Korean railway," Omega, Elsevier, vol. 37(3), pages 555-565, June.
    19. Alberto Caprara & Laura Galli & Paolo Toth, 2011. "Solution of the Train Platforming Problem," Transportation Science, INFORMS, vol. 45(2), pages 246-257, May.
    20. 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.
    21. Carey, Malachy & Carville, Sinead, 2003. "Scheduling and platforming trains at busy complex stations," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(3), pages 195-224, March.
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    Cited by:

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    2. 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.
    3. Ruxin Wang & Lei Nie & Yuyan Tan, 2020. "Evaluating Line Capacity with an Analytical UIC Code 406 Compression Method and Blocking Time Stairway," Energies, MDPI, vol. 13(7), pages 1-16, April.
    4. 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.
    5. 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.
    6. 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.

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