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Integrated optimization of train stopping plan and seat allocation scheme for railway systems under equilibrium travel choice and elastic demand

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  • Xu, Guangming
  • Liu, Yihan
  • Gao, Yihan
  • Liu, Wei

Abstract

This paper examines the integrated optimization of train stopping plan and seat allocation scheme in railway systems, where equilibrium passenger travel choice under elastic demand is considered. The integrated optimization problem is formulated as a non-concave and non-linear mixed-integer mathematical model, where the objective is to maximize the system net benefit considering ticket revenue, consumer surplus, and cost associated with train stoppings. The integrated optimization model can be reformulated into a mixed-integer linear programming (MILP) model based on a series of linearization, relaxation, and outer-approximation techniques, which can then be solved by commercial MILP solvers (e.g., GUROBI). We also compare the integrated optimization approach with that when the train stopping plan and seat allocation are optimized separately and identify the potential benefits. Numerical studies have been conducted on a small-scale example, the Zhengzhou-Xi’an and Shanghai-Beijing high-speed railway corridors to illustrate the proposed model and solution approach.

Suggested Citation

  • Xu, Guangming & Liu, Yihan & Gao, Yihan & Liu, Wei, 2023. "Integrated optimization of train stopping plan and seat allocation scheme for railway systems under equilibrium travel choice and elastic demand," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:transe:v:177:y:2023:i:c:s1366554523002193
    DOI: 10.1016/j.tre.2023.103231
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    as
    1. Li, Zhujun & Shalaby, Amer & Roorda, Matthew J. & Mao, Baohua, 2021. "Urban rail service design for collaborative passenger and freight transport," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 147(C).
    2. A. Ciancimino & G. Inzerillo & S. Lucidi & L. Palagi, 1999. "A Mathematical Programming Approach for the Solution of the Railway Yield Management Problem," Transportation Science, INFORMS, vol. 33(2), pages 168-181, May.
    3. Zhang, Fangni & Yang, Zhiwei & Jiao, Jingjuan & Liu, Wei & Wu, Wenjie, 2020. "The effects of high-speed rail development on regional equity in China," Transportation Research Part A: Policy and Practice, Elsevier, vol. 141(C), pages 180-202.
    4. Alexander Armstrong & Joern Meissner, 2010. "Railway Revenue Management: Overview and Models (Operations Research)," Working Papers MRG/0019, Department of Management Science, Lancaster University, revised Jul 2010.
    5. Schmid, Basil & Molloy, Joseph & Peer, Stefanie & Jokubauskaite, Simona & Aschauer, Florian & Hössinger, Reinhard & Gerike, Regine & Jara-Diaz, Sergio R. & Axhausen, Kay W., 2021. "The value of travel time savings and the value of leisure in Zurich: Estimation, decomposition and policy implications," Transportation Research Part A: Policy and Practice, Elsevier, vol. 150(C), pages 186-215.
    6. Cacchiani, Valentina & Qi, Jianguo & Yang, Lixing, 2020. "Robust optimization models for integrated train stop planning and timetabling with passenger demand uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 136(C), pages 1-29.
    7. Tian, Qiong & Liu, Peng & Ong, Ghim Ping & Huang, Hai-Jun, 2021. "Morning commuting pattern and crowding pricing in a many-to-one public transit system with heterogeneous users," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    8. Hetrakul, Pratt & Cirillo, Cinzia, 2014. "A latent class choice based model system for railway optimal pricing and seat allocation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 61(C), pages 68-83.
    9. 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.
    10. Goossens, Jan-Willem & van Hoesel, Stan & Kroon, Leo, 2006. "On solving multi-type railway line planning problems," European Journal of Operational Research, Elsevier, vol. 168(2), pages 403-424, January.
    11. Xu, Guangming & Liu, Wei & Wu, Runfa & Yang, Hai, 2021. "A double time-scale passenger assignment model for high-speed railway networks with continuum capacity approximation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 150(C).
    12. Chang, Yu-Hern & Yeh, Chung-Hsing & Shen, Ching-Cheng, 2000. "A multiobjective model for passenger train services planning: application to Taiwan's high-speed rail line," Transportation Research Part B: Methodological, Elsevier, vol. 34(2), pages 91-106, February.
    13. Xin Zhang & Lei Nie & Xin Wu & Yu Ke, 2020. "How to Optimize Train Stops under Diverse Passenger Demand: a New Line Planning Method for Large-Scale High-Speed Rail Networks," Networks and Spatial Economics, Springer, vol. 20(4), pages 963-988, December.
    14. Batarce, Marco & Muñoz, Juan Carlos & Ortúzar, Juan de Dios, 2016. "Valuing crowding in public transport: Implications for cost-benefit analysis," Transportation Research Part A: Policy and Practice, Elsevier, vol. 91(C), pages 358-378.
    15. Wang, Xinchang & Wang, Hua & Zhang, Xiaoning, 2016. "Stochastic seat allocation models for passenger rail transportation under customer choice," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 96(C), pages 95-112.
    16. Jiang, Feng & Cacchiani, Valentina & Toth, Paolo, 2017. "Train timetabling by skip-stop planning in highly congested lines," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 149-174.
    17. Hong K. Lo, 2001. "A Cell-Based Traffic Control Formulation: Strategies and Benefits of Dynamic Timing Plans," Transportation Science, INFORMS, vol. 35(2), pages 148-164, May.
    18. Zhou, Yu & Yang, Hai & Wang, Yun & Yan, Xuedong, 2021. "Integrated line configuration and frequency determination with passenger path assignment in urban rail transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 145(C), pages 134-151.
    19. Liu, Haoxiang & Wang, David Z.W., 2015. "Global optimization method for network design problem with stochastic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 72(C), pages 20-39.
    20. Lan, Yingjie & Ball, Michael O. & Karaesmen, Itir Z. & Zhang, Jean X. & Liu, Gloria X., 2015. "Analysis of seat allocation and overbooking decisions with hybrid information," European Journal of Operational Research, Elsevier, vol. 240(2), pages 493-504.
    21. Qi, Jianguo & Yang, Lixing & Di, Zhen & Li, Shukai & Yang, Kai & Gao, Yuan, 2018. "Integrated optimization for train operation zone and stop plan with passenger distributions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 151-173.
    22. You, Peng-Sheng, 2008. "An efficient computational approach for railway booking problems," European Journal of Operational Research, Elsevier, vol. 185(2), pages 811-824, March.
    23. Jian, Sisi & Liu, Wei & Wang, Xiaolei & Yang, Hai & Waller, S. Travis, 2020. "On integrating carsharing and parking sharing services," Transportation Research Part B: Methodological, Elsevier, vol. 142(C), pages 19-44.
    24. Chen, Xinyuan & Zhang, Wei & Guo, Xiaomeng & Liu, Zhiyuan & Wang, Shuaian, 2021. "An improved learning-and-optimization train fare design method for addressing commuting congestion at CBD stations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 153(C).
    25. Jiao, Jingjuan & Wang, Jiaoe & Zhang, Fangni & Jin, Fengjun & Liu, Wei, 2020. "Roles of accessibility, connectivity and spatial interdependence in realizing the economic impact of high-speed rail: Evidence from China," Transport Policy, Elsevier, vol. 91(C), pages 1-15.
    26. Xichun Chen & Junli Wang, 2016. "Collaborative Optimization of Stop Schedule Plan and Ticket Allotment for the Intercity Train," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-7, January.
    27. Shi, Jungang & Yang, Jing & Yang, Lixing & Tao, Lefeng & Qiang, Shengjie & Di, Zhen & Guo, Junhua, 2023. "Safety-oriented train timetabling and stop planning with time-varying and elastic demand on overcrowded commuter metro lines," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 175(C).
    28. Lo, Hong K., 1999. "A novel traffic signal control formulation," Transportation Research Part A: Policy and Practice, Elsevier, vol. 33(6), pages 433-448, August.
    29. 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.
    30. Wang, David Z.W. & Lo, Hong K., 2010. "Global optimum of the linearized network design problem with equilibrium flows," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 482-492, May.
    31. Shi, Feng & Zhou, Zhao & Yao, Jia & Huang, Helai, 2012. "Incorporating transfer reliability into equilibrium analysis of railway passenger flow," European Journal of Operational Research, Elsevier, vol. 220(2), pages 378-385.
    32. Xu, Guangming & Zhong, Linhuan & Hu, Xinlei & Liu, Wei, 2022. "Optimal pricing and seat allocation schemes in passenger railway systems," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 157(C).
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