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Optimisation of seat reservations on trains to minimise transfer distances

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  • Karsten Weicker

    (HTWK Leipzig University of Applied Sciences)

Abstract

This paper introduces a novel optimisation problem motivated by the real-world application of transferring between trains. The driving idea is to minimise the walking distances of all transferring passengers by optimising the assignment of passengers to railcarriages in the seat reservation process. The focus of this work is on formalising and modelling the problem, which has not been studied before. It aims to provide a framework for future considerations. We present three versions of the problem with increasing difficulty: one-train-one-station, one-train-many-stations, and a general problem with multiple trains and stations. Since the simplest version of the problem is a pure assignment problem in the form of minimum-cost bipartite matching, our problem modelling and algorithmic solution approach remain closely related to maxflow problems as they represent a proven method for assignment problems. However, even the one-train-many-stations problem cannot be solved by transforming it into a standard maximum-flow problem. The main result shown is the NP-hardness of the general problem.

Suggested Citation

  • Karsten Weicker, 2023. "Optimisation of seat reservations on trains to minimise transfer distances," Operational Research, Springer, vol. 23(3), pages 1-31, September.
    • Handle: RePEc:spr:operea:v:23:y:2023:i:3:d:10.1007_s12351-023-00786-6
    DOI: 10.1007/s12351-023-00786-6
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    References listed on IDEAS

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    1. Chu, James C. & Korsesthakarn, Kanticha & Hsu, Yu-Ting & Wu, Hua-Yen, 2019. "Models and a solution algorithm for planning transfer synchronization of bus timetables," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 247-266.
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    3. Paola Cappanera & Antonio Frangioni, 2003. "Symmetric and Asymmetric Parallelization of a Cost-Decomposition Algorithm for Multicommodity Flow Problems," INFORMS Journal on Computing, INFORMS, vol. 15(4), pages 369-384, November.
    4. Clausen, Tommy & Hjorth, Allan Nordlunde & Nielsen, Morten & Pisinger, David, 2010. "The off-line group seat reservation problem," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1244-1253, December.
    5. Zhou, Yu & Wang, Yun & Yang, Hai & Yan, Xuedong, 2019. "Last train scheduling for maximizing passenger destination reachability in urban rail transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 79-95.
    6. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
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