IDEAS home Printed from https://ideas.repec.org/a/eee/transe/v157y2022ics1366554521003379.html
   My bibliography  Save this article

Optimal pricing and seat allocation schemes in passenger railway systems

Author

Listed:
  • Xu, Guangming
  • Zhong, Linhuan
  • Hu, Xinlei
  • Liu, Wei

Abstract

This paper examines optimal pricing and seat allocation schemes in passenger railway systems, where ticket pricing and seat allocation (or capacity allocation) are both Origin-Destination specific. We consider that the demand is sensitive to the ticket price, and a non-concave and non-linear mixed integer optimization model is then formulated for the ticket pricing and seat allocation problem to maximize the railway ticket revenue. To find the optimal solution of the ticket revenue maximization problem effectively, the proposed non-concave and non-linear model is reformulated such that the objective function and constraints are linear with respect to the decision variables or the logarithms of the decision variables. The linearized model is then further relaxed as a mixed-integer programing problem (MILP). Based on the above linearization and relaxation techniques, a globally optimal solution can be obtained by iteratively solving the relaxed MILP and adopting the range reduction scheme. Two numerical examples are presented for illustration.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:transe:v:157:y:2022:i:c:s1366554521003379
    DOI: 10.1016/j.tre.2021.102580
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1366554521003379
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.tre.2021.102580?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. 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. Wang, David Z.W. & Liu, Haoxiang & Szeto, W.Y., 2015. "A novel discrete network design problem formulation and its global optimization solution algorithm," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 79(C), pages 213-230.
    3. Janakiram Subramanian & Shaler Stidham & Conrad J. Lautenbacher, 1999. "Airline Yield Management with Overbooking, Cancellations, and No-Shows," Transportation Science, INFORMS, vol. 33(2), pages 147-167, May.
    4. 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.
    5. 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.
    6. Peter P. Belobaba, 1987. "Survey Paper---Airline Yield Management An Overview of Seat Inventory Control," Transportation Science, INFORMS, vol. 21(2), pages 63-73, May.
    7. 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.
    8. Chew, Ek Peng & Lee, Chulung & Liu, Rujing, 2009. "Joint inventory allocation and pricing decisions for perishable products," International Journal of Production Economics, Elsevier, vol. 120(1), pages 139-150, July.
    9. 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.
    10. 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.
    11. Lawrence R. Weatherford, 1997. "Using Prices More Realistically as Decision Variables in Perishable-Asset Revenue Management Problems," Journal of Combinatorial Optimization, Springer, vol. 1(3), pages 277-304, October.
    12. 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).
    13. Jeffrey I. McGill & Garrett J. van Ryzin, 1999. "Revenue Management: Research Overview and Prospects," Transportation Science, INFORMS, vol. 33(2), pages 233-256, May.
    14. Liu, Haoxiang & Szeto, W.Y. & Long, Jiancheng, 2019. "Bike network design problem with a path-size logit-based equilibrium constraint: Formulation, global optimization, and matheuristic," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 127(C), pages 284-307.
    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. Chaoxu Tong & Huseyin Topaloglu, 2014. "On the Approximate Linear Programming Approach for Network Revenue Management Problems," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 121-134, February.
    17. Alavi Fard, Farzad & Sy, Malick & Ivanov, Dmitry, 2019. "Optimal overbooking strategies in the airlines using dynamic programming approach in continuous time," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 128(C), pages 384-399.
    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. Ferran Sancho, 2009. "Calibration Of Ces Functions For Real-World Multisectoral Modeling," Economic Systems Research, Taylor & Francis Journals, vol. 21(1), pages 45-58.
    20. Yang, Zhiwei & Li, Can & Jiao, Jingjuan & Liu, Wei & Zhang, Fangni, 2020. "On the joint impact of high-speed rail and megalopolis policy on regional economic growth in China," Transport Policy, Elsevier, vol. 99(C), pages 20-30.
    21. 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.
    22. Zhan, Shuguang & Wong, S.C. & Lo, S.M., 2020. "Social equity-based timetabling and ticket pricing for high-speed railways," Transportation Research Part A: Policy and Practice, Elsevier, vol. 137(C), pages 165-186.
    23. Gunnar Flötteröd & Michel Bierlaire & Kai Nagel, 2011. "Bayesian Demand Calibration for Dynamic Traffic Simulations," Transportation Science, INFORMS, vol. 45(4), pages 541-561, November.
    24. 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.
    25. Wuyang Yuan & Lei Nie & Xin Wu & Huiling Fu, 2018. "A dynamic bid price approach for the seat inventory control problem in railway networks with consideration of passenger transfer," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-23, August.
    26. 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.
    27. 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.
    28. Li, Zhi-Chun & Lam, William H.K. & Wong, S.C. & Sumalee, A., 2012. "Design of a rail transit line for profit maximization in a linear transportation corridor," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(1), pages 50-70.
    29. An, Kun & Lo, Hong K., 2015. "Robust transit network design with stochastic demand considering development density," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 737-754.
    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. Li, Changle & Ma, Jiao & Luan, Tom H. & Zhou, Xun & Xiong, Lei, 2018. "An incentive-based optimizing strategy of service frequency for an urban rail transit system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 106-122.
    32. Osorio, Carolina, 2019. "High-dimensional offline origin-destination (OD) demand calibration for stochastic traffic simulators of large-scale road networks," Transportation Research Part B: Methodological, Elsevier, vol. 124(C), pages 18-43.
    33. Qiu, Xuan & Lee, Chung-Yee, 2019. "Quantity discount pricing for rail transport in a dry port system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 563-580.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Haque, Md Tabish & Hamid, Faiz, 2023. "Social distancing and revenue management—A post-pandemic adaptation for railways," Omega, Elsevier, vol. 114(C).
    2. Xueyi Guan & Jin Qin & Chenghui Mao & Wenliang Zhou, 2023. "A Literature Review of Railway Pricing Based on Revenue Management," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    3. 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).
    4. 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.
    5. Yu Wang & Jiafa Zhu, 2023. "Pricing Analysis for Railway Multi-Ride Tickets: An Optimization Approach for Uncertain Demand within an Agreed Time Limit," Mathematics, MDPI, vol. 11(23), pages 1-21, November.
    6. 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.
    7. Li, Jianbin & Liu, Lang & Luo, Xiaomeng & Zhu, Stuart X., 2023. "Interactive bundle pricing strategy for online pharmacies," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).

    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. 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).
    2. 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).
    3. Haque, Md Tabish & Hamid, Faiz, 2023. "Social distancing and revenue management—A post-pandemic adaptation for railways," Omega, Elsevier, vol. 114(C).
    4. Xiang Zhao & Xinghua Shan & Jinfei Wu, 2023. "The Impact of Seat Resource Fragmentation on Railway Network Revenue Management," Networks and Spatial Economics, Springer, vol. 23(1), pages 135-177, March.
    5. 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.
    6. Wuyang Yuan & Lei Nie & Xin Wu & Huiling Fu, 2018. "A dynamic bid price approach for the seat inventory control problem in railway networks with consideration of passenger transfer," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-23, August.
    7. Jin Qin & Yijia Zeng & Xia Yang & Yuxin He & Xuanke Wu & Wenxuan Qu, 2019. "Time-Dependent Pricing for High-Speed Railway in China Based on Revenue Management," Sustainability, MDPI, vol. 11(16), pages 1-18, August.
    8. Yu Wang & Xinghua Shan & Hongye Wang & Junfeng Zhang & Xiaoyan Lv & Jinfei Wu, 2022. "Ticket Allocation Optimization of Fuxing Train Based on Overcrowding Control: An Empirical Study from China," Sustainability, MDPI, vol. 14(12), pages 1-12, June.
    9. Nayan, Ashish & Wang, David Z.W., 2017. "Optimal bus transit route packaging in a privatized contracting regime," Transportation Research Part A: Policy and Practice, Elsevier, vol. 97(C), pages 146-157.
    10. Liu, Haoxiang & Szeto, W.Y. & Long, Jiancheng, 2019. "Bike network design problem with a path-size logit-based equilibrium constraint: Formulation, global optimization, and matheuristic," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 127(C), pages 284-307.
    11. Haque, Md Tabish & Hamid, Faiz, 2022. "An optimization model to assign seats in long distance trains to minimize SARS-CoV-2 diffusion," Transportation Research Part A: Policy and Practice, Elsevier, vol. 162(C), pages 104-120.
    12. Wang, Yu & Liu, Haoxiang & Fan, Yinchao & Ding, Jianxun & Long, Jiancheng, 2022. "Large-scale multimodal transportation network models and algorithms-Part II: Network capacity and network design problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 167(C).
    13. Tian, Qingyun & Wang, David Z.W. & Lin, Yun Hui, 2021. "Service operation design in a transit network with congested common lines," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 81-102.
    14. Syed Asif Raza & Rafi Ashrafi & Ali Akgunduz, 2020. "A bibliometric analysis of revenue management in airline industry," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 19(6), pages 436-465, December.
    15. Xueyi Guan & Jin Qin & Chenghui Mao & Wenliang Zhou, 2023. "A Literature Review of Railway Pricing Based on Revenue Management," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    16. Ma, Jie & Tse, Ying Kei & Wang, Xiaojun & Zhang, Minhao, 2019. "Examining customer perception and behaviour through social media research – An empirical study of the United Airlines overbooking crisis," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 127(C), pages 192-205.
    17. Zhang, Fang & Lu, Jian & Hu, Xiaojian & Meng, Qiang, 2023. "Integrated deployment of dedicated lane and roadside unit considering uncertain road capacity under the mixed-autonomy traffic environment," Transportation Research Part B: Methodological, Elsevier, vol. 174(C).
    18. Jeffrey I. McGill & Garrett J. van Ryzin, 1999. "Revenue Management: Research Overview and Prospects," Transportation Science, INFORMS, vol. 33(2), pages 233-256, May.
    19. Hiramatsu, Tomoru, 2023. "Inter-metropolitan regional migration galvanized by high-speed rail: A simulation analysis of the Linear Chuo Shinkansen line in Japan," Socio-Economic Planning Sciences, Elsevier, vol. 85(C).
    20. Tan, Zhijia & Yang, Hai & Tan, Wei & Li, Zhichun, 2016. "Pareto-improving transportation network design and ownership regimes," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 292-309.

    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:transe:v:157:y:2022:i:c:s1366554521003379. 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/600244/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.