IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v97y2017icp182-213.html
   My bibliography  Save this article

Dynamic passenger demand oriented metro train scheduling with energy-efficiency and waiting time minimization: Mixed-integer linear programming approaches

Author

Listed:
  • Yin, Jiateng
  • Yang, Lixing
  • Tang, Tao
  • Gao, Ziyou
  • Ran, Bin

Abstract

In the daily operation of metro systems, the train scheduling problem aims to find a set of space-time paths for multiple trains that determine their departure and arrival times at metro stations, while train operations are in charge of selecting the best operational speed to satisfy the punctuality and operation costs. Different from the most existing researches that treat these two problems separately, this paper proposes an integrated approach for the train scheduling problem on a bi-direction urban metro line in order to minimize the operational costs (i.e., energy consumption) and passenger waiting time. More specifically, we simultaneously consider (1) the train operational velocity choices that correspond to the energy consumption of trains on each travelling arc, and (2) the dynamic passenger demands at each station for the calculation of total passenger waiting time in the planning horizon. By employing a space-time network representation in the formulations, this complex train scheduling and control problem with dynamic passenger demands is rigorously formulated into two optimization models with linear forms. The first model is an integer programming model that jointly minimizes train traction energy consumption and passenger waiting time. The second model, which is formulated as a mixed-integer programming model, further considers the utilization of regenerative braking energy on the basis of the first model. Due to the computational complexity of these two models, especially for large-scale real-world instances, we develop a Lagrangian relaxation (LR)-based heuristic algorithm that decomposes the primal problem into two sets of subproblems and thus enables to find a good solution in short computational time. Finally, two sets of numerical experiments, involving a relatively small-scale case and a real-world instance based on the operation data of Beijing metro are implemented to verify the effectiveness of the proposed approaches.

Suggested Citation

  • Yin, Jiateng & Yang, Lixing & Tang, Tao & Gao, Ziyou & Ran, Bin, 2017. "Dynamic passenger demand oriented metro train scheduling with energy-efficiency and waiting time minimization: Mixed-integer linear programming approaches," Transportation Research Part B: Methodological, Elsevier, vol. 97(C), pages 182-213.
    • Handle: RePEc:eee:transb:v:97:y:2017:i:c:p:182-213
    DOI: 10.1016/j.trb.2017.01.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261516305082
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2017.01.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Liu, Jiangtao & Zhou, Xuesong, 2016. "Capacitated transit service network design with boundedly rational agents," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 225-250.
    2. 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.
    3. Jeffery L. Kennington & Charles D. Nicholson, 2010. "The Uncapacitated Time-Space Fixed-Charge Network Flow Problem: An Empirical Investigation of Procedures for Arc Capacity Assignment," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 326-337, May.
    4. Bektas, Tolga & Laporte, Gilbert, 2011. "The Pollution-Routing Problem," Transportation Research Part B: Methodological, Elsevier, vol. 45(8), pages 1232-1250, September.
    5. Shi, Ning & Song, Haiqing & Powell, Warren B., 2014. "The dynamic fleet management problem with uncertain demand and customer chosen service level," International Journal of Production Economics, Elsevier, vol. 148(C), pages 110-121.
    6. Corman, Francesco & D'Ariano, Andrea & Pacciarelli, Dario & Pranzo, Marco, 2010. "A tabu search algorithm for rerouting trains during rail operations," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 175-192, January.
    7. Niu, Huimin & Zhou, Xuesong & Gao, Ruhu, 2015. "Train scheduling for minimizing passenger waiting time with time-dependent demand and skip-stop patterns: Nonlinear integer programming models with linear constraints," Transportation Research Part B: Methodological, Elsevier, vol. 76(C), pages 117-135.
    8. Li, Xiaopeng & Ma, Jiaqi & Cui, Jianxun & Ghiasi, Amir & Zhou, Fang, 2016. "Design framework of large-scale one-way electric vehicle sharing systems: A continuum approximation model," Transportation Research Part B: Methodological, Elsevier, vol. 88(C), pages 21-45.
    9. Cacchiani, Valentina & Toth, Paolo, 2012. "Nominal and robust train timetabling problems," European Journal of Operational Research, Elsevier, vol. 219(3), pages 727-737.
    10. Cacchiani, Valentina & Furini, Fabio & Kidd, Martin Philip, 2016. "Approaches to a real-world Train Timetabling Problem in a railway node," Omega, Elsevier, vol. 58(C), pages 97-110.
    11. Weijun Xie & Yanfeng Ouyang & Sze Chun Wong, 2016. "Reliable Location-Routing Design Under Probabilistic Facility Disruptions," Transportation Science, INFORMS, vol. 50(3), pages 1128-1138, August.
    12. Lu, Chung-Cheng & Liu, Jiangtao & Qu, Yunchao & Peeta, Srinivas & Rouphail, Nagui M. & Zhou, Xuesong, 2016. "Eco-system optimal time-dependent flow assignment in a congested network," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 217-239.
    13. Yang, Lixing & Zhou, Xuesong, 2014. "Constraint reformulation and a Lagrangian relaxation-based solution algorithm for a least expected time path problem," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 22-44.
    14. Xu, Xiaoming & Li, Keping & Yang, Lixing, 2015. "Scheduling heterogeneous train traffic on double tracks with efficient dispatching rules," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 364-384.
    15. Yin, Jiateng & Tang, Tao & Yang, Lixing & Gao, Ziyou & Ran, Bin, 2016. "Energy-efficient metro train rescheduling with uncertain time-variant passenger demands: An approximate dynamic programming approach," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 178-210.
    16. 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.
    17. Yang, Lixing & Zhou, Xuesong, 2017. "Optimizing on-time arrival probability and percentile travel time for elementary path finding in time-dependent transportation networks: Linear mixed integer programming reformulations," Transportation Research Part B: Methodological, Elsevier, vol. 96(C), pages 68-91.
    18. D'Ariano, Andrea & Pacciarelli, Dario & Pranzo, Marco, 2007. "A branch and bound algorithm for scheduling trains in a railway network," European Journal of Operational Research, Elsevier, vol. 183(2), pages 643-657, December.
    19. Barrena, Eva & Canca, David & Coelho, Leandro C. & Laporte, Gilbert, 2014. "Single-line rail rapid transit timetabling under dynamic passenger demand," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 134-150.
    20. Li, Pengfei & Mirchandani, Pitu & Zhou, Xuesong, 2015. "Solving simultaneous route guidance and traffic signal optimization problem using space-phase-time hypernetwork," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 103-130.
    21. Zhou, Xuesong & Zhong, Ming, 2007. "Single-track train timetabling with guaranteed optimality: Branch-and-bound algorithms with enhanced lower bounds," Transportation Research Part B: Methodological, Elsevier, vol. 41(3), pages 320-341, March.
    22. Mu, Shi & Dessouky, Maged, 2013. "Efficient dispatching rules on double tracks with heterogeneous train traffic," Transportation Research Part B: Methodological, Elsevier, vol. 51(C), pages 45-64.
    23. Rachel C. W. Wong & Tony W. Y. Yuen & Kwok Wah Fung & Janny M. Y. Leung, 2008. "Optimizing Timetable Synchronization for Rail Mass Transit," Transportation Science, INFORMS, vol. 42(1), pages 57-69, February.
    24. Cordone, Roberto & Redaelli, Francesco, 2011. "Optimizing the demand captured by a railway system with a regular timetable," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 430-446, February.
    25. Dorfman, M. J. & Medanic, J., 2004. "Scheduling trains on a railway network using a discrete event model of railway traffic," Transportation Research Part B: Methodological, Elsevier, vol. 38(1), pages 81-98, January.
    26. Dauzère-Pérès, Stéphane & De Almeida, David & Guyon, Olivier & Benhizia, Faten, 2015. "A Lagrangian heuristic framework for a real-life integrated planning problem of railway transportation resources," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 138-150.
    27. Albrecht, Amie & Howlett, Phil & Pudney, Peter & Vu, Xuan & Zhou, Peng, 2016. "The key principles of optimal train control—Part 1: Formulation of the model, strategies of optimal type, evolutionary lines, location of optimal switching points," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 482-508.
    28. Leo G. Kroon & Leon W. P. Peeters & Joris C. Wagenaar & Rob A. Zuidwijk, 2014. "Flexible Connections in PESP Models for Cyclic Passenger Railway Timetabling," Transportation Science, INFORMS, vol. 48(1), pages 136-154, February.
    29. Yang, Lixing & Zhang, Yan & Li, Shukai & Gao, Yuan, 2016. "A two-stage stochastic optimization model for the transfer activity choice in metro networks," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 271-297.
    30. Meng, Lingyun & Zhou, Xuesong, 2014. "Simultaneous train rerouting and rescheduling on an N-track network: A model reformulation with network-based cumulative flow variables," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 208-234.
    31. Christopher Kennedy, 2002. "A comparison of the sustainability of public and private transportation systems: Study of the Greater Toronto Area," Transportation, Springer, vol. 29(4), pages 459-493, November.
    32. Zhou, Xuesong & Zhong, Ming, 2005. "Bicriteria train scheduling for high-speed passenger railroad planning applications," European Journal of Operational Research, Elsevier, vol. 167(3), pages 752-771, December.
    33. Liu, Rongfang (Rachel) & Golovitcher, Iakov M., 2003. "Energy-efficient operation of rail vehicles," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(10), pages 917-932, December.
    34. Yang, Lixing & Qi, Jianguo & Li, Shukai & Gao, Yuan, 2016. "Collaborative optimization for train scheduling and train stop planning on high-speed railways," Omega, Elsevier, vol. 64(C), pages 57-76.
    35. Li, Xiang & Lo, Hong K., 2014. "An energy-efficient scheduling and speed control approach for metro rail operations," Transportation Research Part B: Methodological, Elsevier, vol. 64(C), pages 73-89.
    36. Ye, Hongbo & Liu, Ronghui, 2016. "A multiphase optimal control method for multi-train control and scheduling on railway lines," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 377-393.
    37. Tong, Lu & Zhou, Xuesong & Miller, Harvey J., 2015. "Transportation network design for maximizing space–time accessibility," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 555-576.
    38. Yang, Lixing & Zhou, Xuesong & Gao, Ziyou, 2014. "Credibility-based rescheduling model in a double-track railway network: a fuzzy reliable optimization approach," Omega, Elsevier, vol. 48(C), pages 75-93.
    39. Mahmoudi, Monirehalsadat & Zhou, Xuesong, 2016. "Finding optimal solutions for vehicle routing problem with pickup and delivery services with time windows: A dynamic programming approach based on state–space–time network representations," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 19-42.
    40. Higgins, A. & Kozan, E. & Ferreira, L., 1996. "Optimal scheduling of trains on a single line track," Transportation Research Part B: Methodological, Elsevier, vol. 30(2), pages 147-161, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yin, Jiateng & Tang, Tao & Yang, Lixing & Gao, Ziyou & Ran, Bin, 2016. "Energy-efficient metro train rescheduling with uncertain time-variant passenger demands: An approximate dynamic programming approach," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 178-210.
    2. Zhou, Leishan & Tong, Lu (Carol) & Chen, Junhua & Tang, Jinjin & Zhou, Xuesong, 2017. "Joint optimization of high-speed train timetables and speed profiles: A unified modeling approach using space-time-speed grid networks," Transportation Research Part B: Methodological, Elsevier, vol. 97(C), pages 157-181.
    3. Liu, Renming & Li, Shukai & Yang, Lixing, 2020. "Collaborative optimization for metro train scheduling and train connections combined with passenger flow control strategy," Omega, Elsevier, vol. 90(C).
    4. 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.
    5. Xiaoming Xu & Keping Li & Lixing Yang & Ziyou Gao, 2019. "An efficient train scheduling algorithm on a single-track railway system," Journal of Scheduling, Springer, vol. 22(1), pages 85-105, February.
    6. Zhou, Wenliang & Teng, Hualiang, 2016. "Simultaneous passenger train routing and timetabling using an efficient train-based Lagrangian relaxation decomposition," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 409-439.
    7. Jiateng Yin & Lixing Yang & Xuesong Zhou & Tao Tang & Ziyou Gao, 2019. "Balancing a one‐way corridor capacity and safety‐oriented reliability: A stochastic optimization approach for metro train timetabling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(4), pages 297-320, June.
    8. Li, Wenjie & Yang, Lixing & Wang, Li & Zhou, Xuesong & Liu, Ronghui & Gao, Ziyou, 2017. "Eco-reliable path finding in time-variant and stochastic networks," Energy, Elsevier, vol. 121(C), pages 372-387.
    9. Xu, Xiaoming & Li, Keping & Yang, Lixing, 2015. "Scheduling heterogeneous train traffic on double tracks with efficient dispatching rules," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 364-384.
    10. Kang, Liujiang & Meng, Qiang, 2017. "Two-phase decomposition method for the last train departure time choice in subway networks," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 568-582.
    11. Tian, Xiaopeng & Niu, Huimin, 2020. "Optimization of demand-oriented train timetables under overtaking operations: A surrogate-dual-variable column generation for eliminating indivisibility," Transportation Research Part B: Methodological, Elsevier, vol. 142(C), pages 143-173.
    12. Mo, Pengli & D’Ariano, Andrea & Yang, Lixing & Veelenturf, Lucas P. & Gao, Ziyou, 2021. "An exact method for the integrated optimization of subway lines operation strategies with asymmetric passenger demand and operating costs," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 283-321.
    13. Julia Lange & Frank Werner, 2018. "Approaches to modeling train scheduling problems as job-shop problems with blocking constraints," Journal of Scheduling, Springer, vol. 21(2), pages 191-207, April.
    14. Yin, Jiateng & D’Ariano, Andrea & Wang, Yihui & Yang, Lixing & Tang, Tao, 2021. "Timetable coordination in a rail transit network with time-dependent passenger demand," European Journal of Operational Research, Elsevier, vol. 295(1), pages 183-202.
    15. Meng, Lingyun & Zhou, Xuesong, 2019. "An integrated train service plan optimization model with variable demand: A team-based scheduling approach with dual cost information in a layered network," Transportation Research Part B: Methodological, Elsevier, vol. 125(C), pages 1-28.
    16. Zhang, Chuntian & Gao, Yuan & Yang, Lixing & Gao, Ziyou & Qi, Jianguo, 2020. "Joint optimization of train scheduling and maintenance planning in a railway network: A heuristic algorithm using Lagrangian relaxation," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 64-92.
    17. Zhang, Yongxiang & D'Ariano, Andrea & He, Bisheng & Peng, Qiyuan, 2019. "Microscopic optimization model and algorithm for integrating train timetabling and track maintenance task scheduling," Transportation Research Part B: Methodological, Elsevier, vol. 127(C), pages 237-278.
    18. E. Ursavas & Stuart X. Zhu, 2018. "Integrated Passenger and Freight Train Planning on Shared-Use Corridors," Service Science, INFORMS, vol. 52(6), pages 1376-1390, December.
    19. Shi, Jungang & Yang, Lixing & Yang, Jing & Gao, Ziyou, 2018. "Service-oriented train timetabling with collaborative passenger flow control on an oversaturated metro line: An integer linear optimization approach," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 26-59.
    20. Yu-Jun Zheng, 2018. "Emergency Train Scheduling on Chinese High-Speed Railways," Transportation Science, INFORMS, vol. 52(5), pages 1077-1091, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:97:y:2017:i:c:p:182-213. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.