IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v56y2022i6p1432-1451.html

The Cheapest Ticket Problem in Public Transport

Author

Listed:
  • Anita Schöbel

    (Department of Mathematics, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany; Fraunhofer Institute for Industrial Mathematics, 67663 Kaiserslautern, Germany)

  • Reena Urban

    (Department of Mathematics, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany)

Abstract

Route choice models in public transport have been discussed for a long time. The main reason why a passenger chooses a specific path is usually based on its length or travel time. However, also the ticket price that passengers have to pay may influence their decision because passengers prefer cheaper paths over more expensive ones. In this paper, we deal with the cheapest ticket problem , which asks for a cheapest ticket to travel between a pair of stations. The complexity and the algorithmic approach to solve this problem depend crucially on the underlying fare structure ; for example, it is easy if the ticket price is proportional to the distance traveled (as in distance tariff fare structures), but may become NP-complete in zone tariff fare structures. We hence discuss the cheapest ticket problem for different variations of distance- and zone-based fare structures. We start by modeling the respective fare structure mathematically, then identify its main properties, and finally provide a polynomial algorithm, or prove NP-completeness of the cheapest ticket problem. We also provide general results on the combination of two fare structures, which is often observed in practice.

Suggested Citation

  • Anita Schöbel & Reena Urban, 2022. "The Cheapest Ticket Problem in Public Transport," Transportation Science, INFORMS, vol. 56(6), pages 1432-1451, November.
    • Handle: RePEc:inm:ortrsc:v:56:y:2022:i:6:p:1432-1451
    DOI: 10.1287/trsc.2022.1138
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/trsc.2022.1138
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.2022.1138?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
    ---><---

    References listed on IDEAS

    as
    1. Ralf Borndörfer & Heide Hoppmann & Marika Karbstein, 2017. "Passenger routing for periodic timetable optimization," Public Transport, Springer, vol. 9(1), pages 115-135, July.
    2. Refael Hassin, 1992. "Approximation Schemes for the Restricted Shortest Path Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 36-42, February.
    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. Bowen Cui & Jianwei Zhang, 2025. "Exact and Approximation Algorithms for Task Offloading with Service Caching and Dependency in Mobile Edge Computing," Future Internet, MDPI, vol. 17(6), pages 1-20, June.
    2. Hartleb, Johann & Schmidt, Marie, 2022. "Railway timetabling with integrated passenger distribution," European Journal of Operational Research, Elsevier, vol. 298(3), pages 953-966.
    3. Esaignani Selvarajah & Rui Zhang, 2014. "Supply chain scheduling to minimize holding costs with outsourcing," Annals of Operations Research, Springer, vol. 217(1), pages 479-490, June.
    4. Randeep Bhatia & Sudipto Guha & Samir Khuller & Yoram J. Sussmann, 1998. "Facility Location with Dynamic Distance Functions," Journal of Combinatorial Optimization, Springer, vol. 2(3), pages 199-217, September.
    5. Geng, Zhichao & Yuan, Jinjiang, 2023. "Single-machine scheduling of multiple projects with controllable processing times," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1074-1090.
    6. Hartleb, J. & Schmidt, M.E. & Friedrich, M. & Huisman, D., 2019. "A good or a bad timetable: Do different evaluation functions agree?," ERIM Report Series Research in Management ERS-2019-002-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. Boaz Golany & Moshe Kress & Michal Penn & Uriel G. Rothblum, 2012. "Network Optimization Models for Resource Allocation in Developing Military Countermeasures," Operations Research, INFORMS, vol. 60(1), pages 48-63, February.
    8. Xie, J. & Wong, S.C. & Zhan, S. & Lo, S.M. & Chen, Anthony, 2020. "Train schedule optimization based on schedule-based stochastic passenger assignment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 136(C).
    9. Xie, Chi & Travis Waller, S., 2012. "Parametric search and problem decomposition for approximating Pareto-optimal paths," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1043-1067.
    10. Faramroze G. Engineer & George L. Nemhauser & Martin W. P. Savelsbergh, 2011. "Dynamic Programming-Based Column Generation on Time-Expanded Networks: Application to the Dial-a-Flight Problem," INFORMS Journal on Computing, INFORMS, vol. 23(1), pages 105-119, February.
    11. Buu-Chau Truong & Kim-Hung Pho & Van-Buol Nguyen & Bui Anh Tuan & Wing-Keung Wong, 2019. "Graph Theory And Environmental Algorithmic Solutions To Assign Vehicles Application To Garbage Collection In Vietnam," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(3), pages 1-35, September.
    12. Michael Holzhauser & Sven O. Krumke, 2018. "A generalized approximation framework for fractional network flow and packing problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 19-50, February.
    13. Junyan Su & Qiulin Lin & Minghua Chen, 2025. "Optimizing carbon footprint in long-haul heavy-duty E-Truck transportation," Nature Communications, Nature, vol. 16(1), pages 1-16, December.
    14. Polinder, Gert-Jaap & Schmidt, Marie & Huisman, Dennis, 2021. "Timetabling for strategic passenger railway planning," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 111-135.
    15. Luigi Di Puglia Pugliese & Francesca Guerriero, 2013. "A Reference Point Approach for the Resource Constrained Shortest Path Problems," Transportation Science, INFORMS, vol. 47(2), pages 247-265, May.
    16. Hartleb, J. & Schmidt, M.E., 2019. "Railway timetabling with integrated passenger distribution," ERIM Report Series Research in Management ERS-2019-012-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.
    17. Chen, Xujin & Hu, Jie & Hu, Xiaodong, 2009. "A polynomial solvable minimum risk spanning tree problem with interval data," European Journal of Operational Research, Elsevier, vol. 198(1), pages 43-46, October.
    18. Jenkins , Alan, 2005. "Performance Appraisal Research: A Critical Review of Work on “The Social Context and Politics of Appraisal”," ESSEC Working Papers DR 05004, ESSEC Research Center, ESSEC Business School.
    19. Junran Lichen & Jianping Li & Ko-Wei Lih & Xingxing Yu, 0. "Approximation algorithms for constructing required subgraphs using stock pieces of fixed length," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-22.
    20. João Paiva Fonseca & Tobias Zündorf & Evelien van der Hurk & Yongqiu Zhu & Allan Larsen, 2022. "A matheuristic for passenger service optimization through timetabling with free passenger route choice," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(4), pages 1087-1129, December.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:inm:ortrsc:v:56:y:2022:i:6:p:1432-1451. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.