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The Continuous Stop Location Problem In Public Transportation Networks

Author

Listed:
  • ANITA SCHöBEL

    (Institut für Numerische und Angewandte Mathematik, Lotzestrasse 16–18, D 37083 Göttingen, Germany)

  • HORST W. HAMACHER

    (Technische Universität Kaiserslautern, Postfach 3049, D 67653 Kaiserslautern, Germany)

  • ANNEGRET LIEBERS

    (Siemens AG, Mobility Division, Infrastructure Logistics, Bücklestr. t5, D 78467 Konstanz, Germany)

  • DOROTHEA WAGNER

    (Institut für Theoretische Informatik, Postfach 6980, D 76128 Karlsruhe, Germany)

Abstract

In this paper we consider the location of stops along the edges of an already existing public transportation network. This can be the introduction of bus stops along some given bus routes, or of railway stations along the tracks in a railway network.The positive effect of new stops is given by the better access of the potential customers to public transportation, while the travel time increases due to the additional stopping activities of the trains. The latter leads to a negative effect for the customers. The goal is tocoverall given demand points with a minimal amount of additional traveling time, where covering may be defined with respect to an arbitrary norm or gauge. This problem is NP-hard, even in the special case of Euclidean distances. In this paper, we derive a finite candidate set leading to a discrete set covering problem. Moreover, we identify network structures in which the coefficient matrix of the resulting set covering problem is totally unimodular, such that the problem can be solved efficiently in this case. Extensions of the problem are also discussed.

Suggested Citation

  • Anita Schöbel & Horst W. Hamacher & Annegret Liebers & Dorothea Wagner, 2009. "The Continuous Stop Location Problem In Public Transportation Networks," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(01), pages 13-30.
    • Handle: RePEc:wsi:apjorx:v:26:y:2009:i:01:n:s0217595909002080
    DOI: 10.1142/S0217595909002080
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    Citations

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    Cited by:

    1. Konrad Steiner & Stefan Irnich, 2018. "Schedule-Based Integrated Intercity Bus Line Planning via Branch-and-Cut," Transportation Science, INFORMS, vol. 52(4), pages 882-897, August.
    2. Ran Wei, 2016. "Coverage Location Models," International Regional Science Review, , vol. 39(1), pages 48-76, January.
    3. Manout, Ouassim & Bonnel, Patrick & Bouzouina, Louafi, 2018. "Transit accessibility: A new definition of transit connectors," Transportation Research Part A: Policy and Practice, Elsevier, vol. 113(C), pages 88-100.
    4. S. Haddadi, 2017. "Benders decomposition for set covering problems," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 60-80, January.
    5. M. C. López-de-los-Mozos & Juan A. Mesa, 2022. "To stop or not to stop: a time-constrained trip covering location problem on a tree network," Annals of Operations Research, Springer, vol. 316(2), pages 1039-1061, September.
    6. Hugo M. Repolho & António P. Antunes & Richard L. Church, 2013. "Optimal Location of Railway Stations: The Lisbon-Porto High-Speed Rail Line," Transportation Science, INFORMS, vol. 47(3), pages 330-343, August.
    7. Batta, Rajan & Lejeune, Miguel & Prasad, Srinivas, 2014. "Public facility location using dispersion, population, and equity criteria," European Journal of Operational Research, Elsevier, vol. 234(3), pages 819-829.
    8. Nazanin Abbasnezhad & Javad Mehri-Takmeh & Javad Vakili, 2020. "The domination over time and its discretisation," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 30(1), pages 5-24.

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