IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i23p4818-d1290512.html
   My bibliography  Save this article

Pricing Analysis for Railway Multi-Ride Tickets: An Optimization Approach for Uncertain Demand within an Agreed Time Limit

Author

Listed:
  • Yu Wang

    (Institute of Computing Technology, China Academy of Railway Sciences Corporation Limited, Beijing 100081, China
    School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100091, China)

  • Jiafa Zhu

    (Institute of Transportation & Economics, China Academy of Railway Sciences Corporation Limited, Beijing 100081, China)

Abstract

A multi-ride ticket with a certain period of validity and maximum number of uses has been introduced into railway transport. The key to pricing the railway multi-ride ticket is determining the uncertain demand within an agreed time limit. Unfortunately, limited studies have focused on this pricing issue. Therefore, we focused on railway multi-ride ticket pricing optimization in two different scenarios: a single train with multiple stops and multiple trains with multiple stops. First, the expected coefficient and incentive coefficient were introduced to describe the decision-making process for multi-ride tickets and simulate the change in passengers’ travel behavior after purchasing multi-ride tickets. Then, passenger demand functions based on a normal distribution were developed to establish the pricing models with maximized revenue. Finally, we adopted improved particle swarm optimization (PSO) to solve the models. Two numerical cases were used to verify the models separately for two application scenarios. The results revealed that the multi-ride ticket pricing problem is not a simple summation of pricing for one-time travel of passengers. In the situation of a single train with multiple stops, the expected coefficient is positively related to the total income, whereas the incentive coefficient has limited influence on the optimal price and total revenue. Furthermore, a multi-ride ticket should allow the passenger to take trains eight times at most in 8 days at the price of CNY 4922 (abbreviated as 4922 (8, 8)) rather than 3785 (8, 6). Railway enterprises should cautiously limit the scope of trains available for multi-ride tickets in the case of multiple trains with multiple stops.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4818-:d:1290512
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/23/4818/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/23/4818/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Balakrishnan, Anantaram & Banciu, Mihai & Glowacka, Karolina & Mirchandani, Prakash, 2013. "Hierarchical approach for survivable network design," European Journal of Operational Research, Elsevier, vol. 225(2), pages 223-235.
    2. 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.
    3. 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.
    4. 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.
    5. Chatwin, Richard E., 2000. "Optimal dynamic pricing of perishable products with stochastic demand and a finite set of prices," European Journal of Operational Research, Elsevier, vol. 125(1), pages 149-174, August.
    6. Daniel Adelman, 2007. "Dynamic Bid Prices in Revenue Management," Operations Research, INFORMS, vol. 55(4), pages 647-661, August.
    7. Youyi Feng & Baichun Xiao, 2000. "A Continuous-Time Yield Management Model with Multiple Prices and Reversible Price Changes," Management Science, INFORMS, vol. 46(5), pages 644-657, May.
    8. Lin, Kyle Y. & Sibdari, Soheil Y., 2009. "Dynamic price competition with discrete customer choices," European Journal of Operational Research, Elsevier, vol. 197(3), pages 969-980, September.
    9. 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).
    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. 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.
    2. Sibdari, Soheil & Pyke, David F., 2010. "A competitive dynamic pricing model when demand is interdependent over time," European Journal of Operational Research, Elsevier, vol. 207(1), pages 330-338, November.
    3. Ming Yin & Zheng Wan & Kap Hwan Kim & Shi Yuan Zheng, 2019. "An optimal variable pricing model for container line revenue management systems," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 21(2), pages 173-191, June.
    4. Sibdari, Soheil & Pyke, David F., 2014. "Dynamic pricing with uncertain production cost: An alternating-move approach," European Journal of Operational Research, Elsevier, vol. 236(1), pages 218-228.
    5. Dong Li & Zhan Pang & Lixian Qian, 2023. "Bid price controls for car rental network revenue management," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 261-282, January.
    6. Pak, K. & Piersma, N., 2002. "airline revenue management," ERIM Report Series Research in Management ERS-2002-12-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.
    7. Pak, K. & Piersma, N., 2002. "Airline revenue management: an overview of OR techniques 1982-2001," Econometric Institute Research Papers EI 2002-03, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    8. Alfredo Torrico & Alejandro Toriello, 2022. "Dynamic Relaxations for Online Bipartite Matching," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 1871-1884, July.
    9. Zhang Wensi & Li Jinlin & Ran Lun, 2014. "Price Increasing Timing of Competitive Perishable Products," Journal of Systems Science and Information, De Gruyter, vol. 2(1), pages 29-37, February.
    10. 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.
    11. Shelby Brumelle & Darius Walczak, 2003. "Dynamic Airline Revenue Management with Multiple Semi-Markov Demand," Operations Research, INFORMS, vol. 51(1), pages 137-148, February.
    12. Lin, Kyle Y., 2006. "Dynamic pricing with real-time demand learning," European Journal of Operational Research, Elsevier, vol. 174(1), pages 522-538, October.
    13. Lin, Kyle Y. & Sibdari, Soheil Y., 2009. "Dynamic price competition with discrete customer choices," European Journal of Operational Research, Elsevier, vol. 197(3), pages 969-980, September.
    14. Guillermo Gallego & Ming Hu, 2014. "Dynamic Pricing of Perishable Assets Under Competition," Management Science, INFORMS, vol. 60(5), pages 1241-1259, May.
    15. Wang, Tingsong & Meng, Qiang & Tian, Xuecheng, 2024. "Dynamic container slot allocation for a liner shipping service," Transportation Research Part B: Methodological, Elsevier, vol. 179(C).
    16. Laumer, Simon & Barz, Christiane, 2023. "Reductions of non-separable approximate linear programs for network revenue management," European Journal of Operational Research, Elsevier, vol. 309(1), pages 252-270.
    17. Sumit Kunnumkal & Kalyan Talluri, 2016. "On a Piecewise-Linear Approximation for Network Revenue Management," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 72-91, February.
    18. 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.
    19. 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.
    20. Cao, Ping & Li, Jianbin & Yan, Hong, 2012. "Optimal dynamic pricing of inventories with stochastic demand and discounted criterion," European Journal of Operational Research, Elsevier, vol. 217(3), pages 580-588.

    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:23:p:4818-:d:1290512. 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.