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To stop or not to stop: a time-constrained trip covering location problem on a tree network

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  • M. C. López-de-los-Mozos

    (Universidad de Sevilla)

  • Juan A. Mesa

    (Universidad de Sevilla)

Abstract

Location of new stations/stops in public transportation networks has attracted much interest from both the point of views of theory and applications. In this paper we consider a set of pairs of points in the plane demanding traveling between the elements of each pair, and a tree network embedded in the plane representing the transportation system. An alternative mode of transportation competes with the combined plane-network mode so that the modal choice is made by distance (time) comparisons. The aim of the problem dealt with in this paper is to locate a new station/stop so that the traffic through the network would be maximized. Since stops at new stations increases the time of passengers that already used the combined mode, and may persuade them to change the mode, a constraint on the increase of the overall time is imposed. A quadratic in the number of pairs time algorithm is proposed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:316:y:2022:i:2:d:10.1007_s10479-021-03981-w
    DOI: 10.1007/s10479-021-03981-w
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    References listed on IDEAS

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    1. Dwi Groß & Horst Hamacher & Simone Horn & Anita Schöbel, 2009. "Stop location design in public transportation networks: covering and accessibility objectives," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 335-346, December.
    2. Ennio Cascetta, 2009. "Transportation Systems Analysis," Springer Optimization and Its Applications, Springer, number 978-0-387-75857-2, June.
    3. P. M. Dearing & R. L. Francis & T. J. Lowe, 1976. "Convex Location Problems on Tree Networks," Operations Research, INFORMS, vol. 24(4), pages 628-642, August.
    4. Mark-Christoph Körner & Juan Mesa & Federico Perea & Anita Schöbel & Daniel Scholz, 2014. "A maximum trip covering location problem with an alternative mode of transportation on tree networks and segments," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 227-253, April.
    5. López-de-los-Mozos, M.C. & Mesa, Juan A. & Schöbel, Anita, 2017. "A general approach for the location of transfer points on a network with a trip covering criterion and mixed distances," European Journal of Operational Research, Elsevier, vol. 260(1), pages 108-121.
    6. Gilbert Laporte & Juan Mesa & Francisco Ortega & Ignacio Sevillano, 2005. "Maximizing Trip Coverage in the Location of a Single Rapid Transit Alignment," Annals of Operations Research, Springer, vol. 136(1), pages 49-63, April.
    7. 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.
    8. Emilio Carrizosa & Jonas Harbering & Anita Schöbel, 2016. "Minimizing the passengers’ traveling time in the stop location problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(10), pages 1325-1337, October.
    9. Vukan R. Vuchic & Gordon F. Newell, 1968. "Rapid Transit Interstation Spacings for Minimum Travel Time," Transportation Science, INFORMS, vol. 2(4), pages 303-339, November.
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