IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i6p1290-d1090441.html
   My bibliography  Save this article

Joint Optimization of Time-Dependent Line Planning and Differential Pricing with Passenger Train Choice in High-Speed Railway Networks

Author

Listed:
  • Wenliang Zhou

    (School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China)

  • Xiang Li

    (School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China)

  • Xin Shi

    (School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China)

Abstract

Line planning problems and differential pricing problems are complementary processes in the railway system, but these two problems were generally considered separate processes in most of the existing literature. This paper studies a time-dependent line planning problem and differential pricing problem with passenger train choice in high-speed railway networks under elastic origin-destination-period demand. After clearly and flexibly describing the organization cost of operators, the price cost, and the time cost of passengers in a physical infrastructure-based directed graph, a non-linear joint optimization model is designed with a diversity of optimization goals of maximizing the total revenue of railway operators minus the total travel cost of passengers. An algorithm based on a simulated annealing framework is designed to solve the joint optimization model, and six neighborhood search strategies are designed by combining the features of the studied problem and designed model closely to improve the efficiency of the solution search. The results based on both a toy railway network and a real-world railway network show that the optimized time-dependent line plan and differential price plan are beneficial to increasing the total revenue of railway operators and improving the travel service of railway passengers.

Suggested Citation

  • Wenliang Zhou & Xiang Li & Xin Shi, 2023. "Joint Optimization of Time-Dependent Line Planning and Differential Pricing with Passenger Train Choice in High-Speed Railway Networks," Mathematics, MDPI, vol. 11(6), pages 1-28, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1290-:d:1090441
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/6/1290/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/6/1290/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jin Qin & Wenxuan Qu & Xuanke Wu & Yijia Zeng, 2019. "Differential Pricing Strategies of High Speed Railway Based on Prospect Theory: An Empirical Study from China," Sustainability, MDPI, vol. 11(14), pages 1-17, July.
    2. Szeto, W.Y. & Jiang, Y., 2014. "Transit route and frequency design: Bi-level modeling and hybrid artificial bee colony algorithm approach," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 235-263.
    3. 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.
    4. Gilbert Laporte & Juan A. Mesa, 2015. "The Design of Rapid Transit Networks," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 581-594, Springer.
    5. 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.
    6. Ralf Borndörfer & Martin Grötschel & Marc E. Pfetsch, 2007. "A Column-Generation Approach to Line Planning in Public Transport," Transportation Science, INFORMS, vol. 41(1), pages 123-132, February.
    7. Canca, David & Andrade-Pineda, José Luis & De los Santos, Alicia & Calle, Marcos, 2018. "The Railway Rapid Transit frequency setting problem with speed-dependent operation costs," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 494-519.
    8. Canca, David & De-Los-Santos, Alicia & Laporte, Gilbert & Mesa, Juan A., 2019. "Integrated Railway Rapid Transit Network Design and Line Planning problem with maximum profit," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 127(C), pages 1-30.
    9. Jan-Willem Goossens & Stan van Hoesel & Leo Kroon, 2004. "A Branch-and-Cut Approach for Solving Railway Line-Planning Problems," Transportation Science, INFORMS, vol. 38(3), pages 379-393, August.
    10. Jin Qin & Xiqiong Li & Kang Yang & Guangming Xu, 2022. "Joint Optimization of Ticket Pricing Strategy and Train Stop Plan for High-Speed Railway: A Case Study," Mathematics, MDPI, vol. 10(10), pages 1-17, May.
    11. Claessens, M. T. & van Dijk, N. M. & Zwaneveld, P. J., 1998. "Cost optimal allocation of rail passenger lines," European Journal of Operational Research, Elsevier, vol. 110(3), pages 474-489, November.
    12. 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).
    13. Canca, David & Barrena, Eva & De-Los-Santos, Alicia & Andrade-Pineda, José Luis, 2016. "Setting lines frequency and capacity in dense railway rapid transit networks with simultaneous passenger assignment," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 251-267.
    14. Guihaire, Valérie & Hao, Jin-Kao, 2008. "Transit network design and scheduling: A global review," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(10), pages 1251-1273, December.
    15. Goerigk, Marc & Schmidt, Marie, 2017. "Line planning with user-optimal route choice," European Journal of Operational Research, Elsevier, vol. 259(2), pages 424-436.
    16. Szeto, W.Y. & Wu, Yongzhong, 2011. "A simultaneous bus route design and frequency setting problem for Tin Shui Wai, Hong Kong," European Journal of Operational Research, Elsevier, vol. 209(2), pages 141-155, March.
    17. Huanyin Su & Shuting Peng & Lianbo Deng & Weixiang Xu & Qiongfang Zeng & Luca D'Acierno, 2021. "Optimal Differential Pricing for Intercity High-Speed Railway Services with Time-Dependent Demand and Passenger Choice Behaviors under Capacity Constraints," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-13, November.
    18. Klein, Robert & Koch, Sebastian & Steinhardt, Claudius & Strauss, Arne K., 2020. "A review of revenue management: Recent generalizations and advances in industry applications," European Journal of Operational Research, Elsevier, vol. 284(2), pages 397-412.
    19. Huanyin Su & Wencong Tao & Xinlei Hu, 2019. "A Line Planning Approach for High-Speed Rail Networks with Time-Dependent Demand and Capacity Constraints," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-18, March.
    20. Guan, J.F. & Yang, Hai & Wirasinghe, S.C., 2006. "Simultaneous optimization of transit line configuration and passenger line assignment," Transportation Research Part B: Methodological, Elsevier, vol. 40(10), pages 885-902, December.
    21. Laporte, G. & Mesa, J.A. & Ortega, F.A. & Perea, F., 2011. "Planning rapid transit networks," Socio-Economic Planning Sciences, Elsevier, vol. 45(3), pages 95-104, September.
    22. Bharill, Rohit & Rangaraj, Narayan, 2008. "Revenue management in railway operations: A study of the Rajdhani Express, Indian Railways," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(9), pages 1195-1207, November.
    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. Schiewe, Alexander & Schiewe, Philine & Schmidt, Marie, 2019. "The line planning routing game," European Journal of Operational Research, Elsevier, vol. 274(2), pages 560-573.
    2. Masing, Berenike & Lindner, Niels & Borndörfer, Ralf, 2022. "The price of symmetric line plans in the Parametric City," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 419-443.
    3. Feng, Tao & Lusby, Richard M. & Zhang, Yongxiang & Peng, Qiyuan, 2024. "Integrating train service route design with passenger flow allocation for an urban rail transit line," European Journal of Operational Research, Elsevier, vol. 313(1), pages 146-170.
    4. Abdulkerim Benli & İbrahim Akgün, 2023. "A Multi-Objective Mathematical Programming Model for Transit Network Design and Frequency Setting Problem," Mathematics, MDPI, vol. 11(21), pages 1-23, October.
    5. Wenliang Zhou & Yujun Huang & Naijie Chai & Bo Li & Xiang Li, 2022. "A Line Planning Optimization Model for High-Speed Railway Network Merging Newly-Built Railway Lines," Mathematics, MDPI, vol. 10(17), pages 1-34, September.
    6. Jinfei Wu & Xinghua Shan & Jingxia Sun & Shengyuan Weng & Shuo Zhao, 2023. "Daily Line Planning Optimization for High-Speed Railway Lines," Sustainability, MDPI, vol. 15(4), pages 1-20, February.
    7. Hamid, Faiz & Agarwal, Yogesh K., 2024. "Train stop scheduling problem: An exact approach using valid inequalities and polar duality," European Journal of Operational Research, Elsevier, vol. 313(1), pages 207-224.
    8. Goerigk, Marc & Schmidt, Marie, 2017. "Line planning with user-optimal route choice," European Journal of Operational Research, Elsevier, vol. 259(2), pages 424-436.
    9. Evert Vermeir & Javier Durán-Micco & Pieter Vansteenwegen, 2022. "The grid based approach, a fast local evaluation technique for line planning," 4OR, Springer, vol. 20(4), pages 603-635, December.
    10. Canca, David & Andrade-Pineda, José Luis & De los Santos, Alicia & Calle, Marcos, 2018. "The Railway Rapid Transit frequency setting problem with speed-dependent operation costs," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 494-519.
    11. Simon Bull & Jesper Larsen & Richard M. Lusby & Natalia J. Rezanova, 2019. "Optimising the travel time of a line plan," 4OR, Springer, vol. 17(3), pages 225-259, September.
    12. Javier Durán-Micco & Pieter Vansteenwegen, 2022. "A survey on the transit network design and frequency setting problem," Public Transport, Springer, vol. 14(1), pages 155-190, March.
    13. Fu, Huiling & Nie, Lei & Meng, Lingyun & Sperry, Benjamin R. & He, Zhenhuan, 2015. "A hierarchical line planning approach for a large-scale high speed rail network: The China case," Transportation Research Part A: Policy and Practice, Elsevier, vol. 75(C), pages 61-83.
    14. Zhang, Yongxiang & Peng, Qiyuan & Lu, Gongyuan & Zhong, Qingwei & Yan, Xu & Zhou, Xuesong, 2022. "Integrated line planning and train timetabling through price-based cross-resolution feedback mechanism," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 240-277.
    15. Gattermann, P. & Schiewe, A. & Schmidt, M.E., 2014. "The line planning routing game," ERIM Report Series Research in Management ERS-2014-017-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    16. David Canca & Belén Navarro-Carmona & Gabriel Villa & Alejandro Zarzo, 2023. "A Multilayer Network Approach for the Bimodal Bus–Pedestrian Line Planning Problem," Mathematics, MDPI, vol. 11(19), pages 1-36, October.
    17. Canca, David & Barrena, Eva & De-Los-Santos, Alicia & Andrade-Pineda, José Luis, 2016. "Setting lines frequency and capacity in dense railway rapid transit networks with simultaneous passenger assignment," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 251-267.
    18. Mathias Michaelis & Anita Schöbel, 2009. "Integrating line planning, timetabling, and vehicle scheduling: a customer-oriented heuristic," Public Transport, Springer, vol. 1(3), pages 211-232, August.
    19. Canca, David & De-Los-Santos, Alicia & Laporte, Gilbert & Mesa, Juan A., 2019. "Integrated Railway Rapid Transit Network Design and Line Planning problem with maximum profit," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 127(C), pages 1-30.
    20. Yan, Fei & Goverde, Rob M.P., 2019. "Combined line planning and train timetabling for strongly heterogeneous railway lines with direct connections," Transportation Research Part B: Methodological, Elsevier, vol. 127(C), pages 20-46.

    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:gam:jmathe:v:11:y:2023:i:6:p:1290-:d:1090441. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.