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A Branch-and-Price algorithm for railway rolling stock rescheduling

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  • Lusby, Richard M.
  • Haahr, Jørgen Thorlund
  • Larsen, Jesper
  • Pisinger, David

Abstract

How to best reschedule their fleet of rolling stock units during a disruption is an optimization problem regularly faced by railway operators. Despite the problem’s high complexity, it is still usually solved manually. In this paper we propose a path based mathematical formulation and solve it using a Branch-and-Price algorithm. We demonstrate that, unlike flow based approaches, our formulation is more easily extended to handle certain families of constraints, such as train unit maintenance restrictions. The proposed algorithm is benchmarked on several real-life instances provided by the suburban railway operator in Copenhagen, DSB S-tog. When used in combination with a lower bound method taken from the literature we show that near-optimal solutions to this rescheduling problem can be found within a few seconds. Furthermore, we show that the proposed methodology can be used, with minor modification, on a tactical planning level, where it produces near-optimal rolling stock schedules in minutes of CPU time.

Suggested Citation

  • Lusby, Richard M. & Haahr, Jørgen Thorlund & Larsen, Jesper & Pisinger, David, 2017. "A Branch-and-Price algorithm for railway rolling stock rescheduling," Transportation Research Part B: Methodological, Elsevier, vol. 99(C), pages 228-250.
    • Handle: RePEc:eee:transb:v:99:y:2017:i:c:p:228-250
    DOI: 10.1016/j.trb.2017.03.003
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    1. Hoogervorst, R. & Dollevoet, T.A.B. & Maróti, G. & Huisman, D., 2018. "Reducing Passenger Delays by Rolling Stock Rescheduling," Econometric Institute Research Papers EI2018-29, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Zhao, Yanlu & Alfandari, Laurent, 2020. "Design of diversified package tours for the digital travel industry : A branch-cut-and-price approach," European Journal of Operational Research, Elsevier, vol. 285(3), pages 825-843.
    3. Ralf Borndörfer & Thomas Eßer & Patrick Frankenberger & Andreas Huck & Christoph Jobmann & Boris Krostitz & Karsten Kuchenbecker & Kai Mohrhagen & Philipp Nagl & Michael Peterson & Markus Reuther & Th, 2021. "Deutsche Bahn Schedules Train Rotations Using Hypergraph Optimization," Interfaces, INFORMS, vol. 51(1), pages 42-62, February.
    4. Hoogervorst, R. & Dollevoet, T.A.B. & Maróti, G. & Huisman, D., 2019. "A Variable Neighborhood Search Heuristic for Rolling Stock Rescheduling," Econometric Institute Research Papers EI2019-34, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Niu, Huimin & Zhou, Xuesong & Tian, Xiaopeng, 2018. "Coordinating assignment and routing decisions in transit vehicle schedules: A variable-splitting Lagrangian decomposition approach for solution symmetry breaking," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 70-101.
    6. Wang, Yihui & Zhao, Kangqi & D’Ariano, Andrea & Niu, Ru & Li, Shukai & Luan, Xiaojie, 2021. "Real-time integrated train rescheduling and rolling stock circulation planning for a metro line under disruptions," Transportation Research Part B: Methodological, Elsevier, vol. 152(C), pages 87-117.
    7. Feng, Tao & Lusby, Richard M. & Zhang, Yongxiang & Tao, Siyu & Zhang, Bojian & Peng, Qiyuan, 2024. "A branch-and-price algorithm for integrating urban rail crew scheduling and rostering problems," Transportation Research Part B: Methodological, Elsevier, vol. 183(C).
    8. Chai, Simin & Yin, Jiateng & D’Ariano, Andrea & Liu, Ronghui & Yang, Lixing & Tang, Tao, 2024. "A branch-and-cut algorithm for scheduling train platoons in urban rail networks," Transportation Research Part B: Methodological, Elsevier, vol. 181(C).
    9. Yang, Lin & Gao, Yuan & D’Ariano, Andrea & Xu, Suxiu, 2024. "Integrated optimization of train timetable and train unit circulation for a Y-type urban rail transit system with flexible train composition mode," Omega, Elsevier, vol. 122(C).
    10. Zhong, Qingwei & Lusby, Richard M. & Larsen, Jesper & Zhang, Yongxiang & Peng, Qiyuan, 2019. "Rolling stock scheduling with maintenance requirements at the Chinese High-Speed Railway," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 24-44.
    11. Mark M. Dekker & Rolf N. Lieshout & Robin C. Ball & Paul C. Bouman & Stefan C. Dekker & Henk A. Dijkstra & Rob M. P. Goverde & Dennis Huisman & Debabrata Panja & Alfons A. M. Schaafsma & Marjan Akker, 2022. "A next step in disruption management: combining operations research and complexity science," Public Transport, Springer, vol. 14(1), pages 5-26, March.
    12. Lin, Boliang & Zhao, Yinan, 2021. "Synchronized optimization of EMU train assignment and second-level preventive maintenance scheduling," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    13. Patricia Bickert & Cristian Grozea & Ronny Hans & Matthias Koch & Christina Riehn & Armin Wolf, 2021. "Optimising Rolling Stock Planning including Maintenance with Constraint Programming and Quantum Annealing," Papers 2109.07212, arXiv.org, revised Sep 2023.
    14. Kuo, Yong-Hong & Leung, Janny M.Y. & Yan, Yimo, 2023. "Public transport for smart cities: Recent innovations and future challenges," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1001-1026.

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