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Solution of the Train Platforming Problem

Author

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  • Alberto Caprara

    (DEIS, University of Bologna, 40136 Bologna, Italy)

  • Laura Galli

    (DEIS, University of Bologna, 40136 Bologna, Italy)

  • Paolo Toth

    (DEIS, University of Bologna, 40136 Bologna, Italy)

Abstract

In this paper we study a general formulation of the train platforming problem, which contains as special cases all the versions previously considered in the literature as well as a case study from Rete Ferroviaria Italiana, the Italian Infrastructure Manager. In particular, motivated by our case study, we consider a general quadratic objective function, and propose a new way to linearize it by using a small number of new variables along with a set of constraints that can be separated efficiently by solving an appropriate linear program. The resulting integer linear programming formulation has a continuous relaxation that leads to strong bounds on the optimal value. For the instances in our case study, the solution approach based on this relaxation produces solutions that are much better than those produced by a simple heuristic method currently in use, and that often turn out to be (nearly) optimal.

Suggested Citation

  • Alberto Caprara & Laura Galli & Paolo Toth, 2011. "Solution of the Train Platforming Problem," Transportation Science, INFORMS, vol. 45(2), pages 246-257, May.
    • Handle: RePEc:inm:ortrsc:v:45:y:2011:i:2:p:246-257
    DOI: 10.1287/trsc.1100.0366
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    References listed on IDEAS

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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. Roca-Riu, Mireia & Fernández, Elena & Estrada, Miquel, 2015. "Parking slot assignment for urban distribution: Models and formulations," Omega, Elsevier, vol. 57(PB), pages 157-175.
    3. Guo, Peng & Weidinger, Felix & Boysen, Nils, 2019. "Parallel machine scheduling with job synchronization to enable efficient material flows in hub terminals," Omega, Elsevier, vol. 89(C), pages 110-121.
    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.
    5. Alberto Caprara & Laura Galli & Sebastian Stiller & Paolo Toth, 2014. "Delay-Robust Event Scheduling," Operations Research, INFORMS, vol. 62(2), pages 274-283, April.
    6. Zhang, Qin & Lusby, Richard Martin & Shang, Pan & Zhu, Xiaoning, 2022. "A heuristic approach to integrate train timetabling, platforming, and railway network maintenance scheduling decisions," Transportation Research Part B: Methodological, Elsevier, vol. 158(C), pages 210-238.
    7. 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.
    8. Dollevoet, T.A.B. & Huisman, D. & Schöbel, A. & Schmidt, M.E., 2012. "Delay Management including Capacities of Stations," Econometric Institute Research Papers EI 2012-22, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    9. Lu, Gongyuan & Nie, Yu(Marco) & Liu, Xiaobo & Li, Denghui, 2019. "Trajectory-based traffic management inside an autonomous vehicle zone," Transportation Research Part B: Methodological, Elsevier, vol. 120(C), pages 76-98.
    10. San Segundo, Pablo & Furini, Fabio & León, Rafael, 2022. "A new branch-and-filter exact algorithm for binary constraint satisfaction problems," European Journal of Operational Research, Elsevier, vol. 299(2), pages 448-467.
    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. Nils Boysen & Simon Emde & Konrad Stephan & Markus Weiß, 2015. "Synchronization in hub terminals with the circular arrangement problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(6), pages 454-469, September.
    13. Rupp, Johannes & Boysen, Nils & Briskorn, Dirk, 2022. "Optimizing consolidation processes in hubs: The hub-arrival-departure problem," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1051-1066.
    14. Lu, Gongyuan & Ning, Jia & Liu, Xiaobo & Nie, Yu (Marco), 2022. "Train platforming and rescheduling with flexible interlocking mechanisms: An aggregate approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 159(C).
    15. Weiya Chen & Weiting Yang & Guangdong Zhang, 2022. "Track Utilization Optimization Method for Arrival Yard of Marshalling Station Considering Arrival and Break-Up Coordination Operation," Mathematics, MDPI, vol. 10(18), pages 1-12, September.
    16. Twan Dollevoet & Dennis Huisman & Leo Kroon & Marie Schmidt & Anita Schöbel, 2015. "Delay Management Including Capacities of Stations," Transportation Science, INFORMS, vol. 49(2), pages 185-203, May.
    17. Rajnish Kumar & Goutam Sen & Samarjit Kar & Manoj Kumar Tiwari, 2018. "Station Dispatching Problem for a Large Terminal: A Constraint Programming Approach," Interfaces, INFORMS, vol. 48(6), pages 510-528, November.
    18. Sels, P. & Dewilde, T. & Cattrysse, D. & Vansteenwegen, P., 2016. "Reducing the passenger travel time in practice by the automated construction of a robust railway timetable," Transportation Research Part B: Methodological, Elsevier, vol. 84(C), pages 124-156.
    19. Vansteenwegen, Pieter & Dewilde, Thijs & Burggraeve, Sofie & Cattrysse, Dirk, 2016. "An iterative approach for reducing the impact of infrastructure maintenance on the performance of railway systems," European Journal of Operational Research, Elsevier, vol. 252(1), pages 39-53.
    20. Leonardo Lamorgese & Carlo Mannino & Mauro Piacentini, 2016. "Optimal Train Dispatching by Benders’-Like Reformulation," Transportation Science, INFORMS, vol. 50(3), pages 910-925, August.
    21. Leonardo Lamorgese & Carlo Mannino, 2015. "An Exact Decomposition Approach for the Real-Time Train Dispatching Problem," Operations Research, INFORMS, vol. 63(1), pages 48-64, February.
    22. Yinggui Zhang & Ruihua Hu & Qiongfang Zeng & Yuhang Wang & Ya Liu & Shan Huang, 2023. "Optimal Train Platforming with Shunting Operations for Multidirectional Passenger Stations: A Case Study of Guangzhou Station," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
    23. Jingliu Xu & Zhimei Wang & Shangjun Yao & Jiarong Xue, 2022. "Train Operations Organization in High-Speed Railway Station Considering Variable Configuration," Sustainability, MDPI, vol. 14(4), pages 1-17, February.

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