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Reliability improvement of rolling stock planning with maintenance requirements for high-speed railway

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  • Niu, Jiaxin
  • Qiao, Ke
  • Zhao, Peng

Abstract

The rolling stock planning problem is a key step in the high-speed railway transit planning process. When trip delays, railway departments may need to incur considerable additional costs for plan adjustments to quickly resume operations. Therefore, we consider the impact of trip delay probabilities during rolling stock planning, aiming to minimise the total travel cost and maximise plan robustness to enhance the reliability of plan execution. A space–time–state network is established to describe the operation of rolling stocks considering accumulated mileage and running time constraints for maintenance, representing the rolling stock planning problem as a mixed-integer nonlinear programming model. Then, an alternating direction method of multipliers (ADMM)-based decomposition mechanism that decomposes the model into a set of rolling stock route selection subproblems is introduced, where each subproblem is efficiently solved by a maintenance-constrained shortest path algorithm related to reliability. A set of different scale real-life cases based on trips managed by a depot in China are used to verify the effectiveness of the proposed model and algorithm. The results show that the ADMM considerably outperforms the traditional Lagrangian relaxation (LR) method. On a set of larger-scale cases, the proposed ADMM with enhancements obtains an optimality gap of 2.42 % on average. This result is substantially better than LR, which provides optimality gaps of 32.55 % on average. Finally, the model in this paper effectively enhances the probability of successful rolling stock route execution in trip delay scenarios, resulting in a rolling stock plan with improved reliability.

Suggested Citation

  • Niu, Jiaxin & Qiao, Ke & Zhao, Peng, 2025. "Reliability improvement of rolling stock planning with maintenance requirements for high-speed railway," Reliability Engineering and System Safety, Elsevier, vol. 259(C).
  • Handle: RePEc:eee:reensy:v:259:y:2025:i:c:s0951832025001759
    DOI: 10.1016/j.ress.2025.110972
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    References listed on IDEAS

    as
    1. 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.
    2. 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).
    3. Bhattacharyya, S.K. & Cheliyan, A.S., 2019. "Optimization of a subsea production system for cost and reliability using its fault tree model," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 213-219.
    4. Silva, L.M.R. & Guedes Soares, C., 2023. "Robust optimization model of an offshore oil production system for cost and pipeline risk of failure," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    5. Valentina Cacchiani & Alberto Caprara & Laura Galli & Leo Kroon & Gábor Maróti & Paolo Toth, 2012. "Railway Rolling Stock Planning: Robustness Against Large Disruptions," Transportation Science, INFORMS, vol. 46(2), pages 217-232, May.
    6. Haahr, Jørgen T. & Wagenaar, Joris C. & Veelenturf, Lucas P. & Kroon, Leo G., 2016. "A comparison of two exact methods for passenger railway rolling stock (re)scheduling," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 91(C), pages 15-32.
    7. 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.
    8. Zhang, Yongxiang & Peng, Qiyuan & Yao, Yu & Zhang, Xin & Zhou, Xuesong, 2019. "Solving cyclic train timetabling problem through model reformulation: Extended time-space network construct and Alternating Direction Method of Multipliers methods," Transportation Research Part B: Methodological, Elsevier, vol. 128(C), pages 344-379.
    9. He, Zhichao & Wang, Yanhui & Sun, Wanhua & Hao, Yucheng & Xia, Weifu, 2025. "A proactive opportunistic maintenance decision model based on reliability in train systems," Reliability Engineering and System Safety, Elsevier, vol. 255(C).
    10. Fu, Yuqiang & Wang, Jun, 2022. "Optimum periodic maintenance policy of repairable multi-component system with component reallocation and system overhaul," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    11. 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.
    12. Lin, Zhiyuan & Kwan, Raymond S.K., 2016. "A branch-and-price approach for solving the train unit scheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 97-120.
    13. Kelly, Dana L. & Smith, Curtis L., 2009. "Bayesian inference in probabilistic risk assessment—The current state of the art," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 628-643.
    14. Rocchetta, Roberto & Crespo, Luis G. & Kenny, Sean P., 2020. "A scenario optimization approach to reliability-based design," Reliability Engineering and System Safety, Elsevier, vol. 196(C).
    15. Gábor Maróti & Leo Kroon, 2005. "Maintenance Routing for Train Units: The Transition Model," Transportation Science, INFORMS, vol. 39(4), pages 518-525, November.
    16. Lin, Boliang & Wu, Jianping & Lin, Ruixi & Wang, Jiaxi & Wang, Hui & Zhang, Xuhui, 2019. "Optimization of high-level preventive maintenance scheduling for high-speed trains," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 261-275.
    17. Valentina Cacchiani & Alberto Caprara & Matteo Fischetti, 2012. "A Lagrangian Heuristic for Robustness, with an Application to Train Timetabling," Transportation Science, INFORMS, vol. 46(1), pages 124-133, February.
    18. Zio, E., 2018. "The future of risk assessment," Reliability Engineering and System Safety, Elsevier, vol. 177(C), pages 176-190.
    19. Michel Gamache & François Soumis & Daniel Villeneuve & Jacques Desrosiers & Éric Gélinas, 1998. "The Preferential Bidding System at Air Canada," Transportation Science, INFORMS, vol. 32(3), pages 246-255, August.
    20. Xu, Xiaoming & Li, Chung-Lun & Xu, Zhou, 2018. "Integrated train timetabling and locomotive assignment," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 573-593.
    21. Fioole, Pieter-Jan & Kroon, Leo & Maroti, Gabor & Schrijver, Alexander, 2006. "A rolling stock circulation model for combining and splitting of passenger trains," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1281-1297, October.
    22. Erwin Abbink & Bianca van den Berg & Leo Kroon & Marc Salomon, 2004. "Allocation of Railway Rolling Stock for Passenger Trains," Transportation Science, INFORMS, vol. 38(1), pages 33-41, February.
    23. Yao, Yu & Zhu, Xiaoning & Dong, Hongyu & Wu, Shengnan & Wu, Hailong & Carol Tong, Lu & Zhou, Xuesong, 2019. "ADMM-based problem decomposition scheme for vehicle routing problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 156-174.
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