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A maximum trip covering location problem with an alternative mode of transportation on tree networks and segments

Author

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  • Mark-Christoph Körner
  • Juan Mesa
  • Federico Perea
  • Anita Schöbel
  • Daniel Scholz

Abstract

In this paper the following facility location problem in a mixed planar-network space is considered: We assume that traveling along a given network is faster than traveling within the plane according to the Euclidean distance. A pair of points (A i ,A j ) is called covered if the time to access the network from A i plus the time for traveling along the network plus the time for reaching A j is lower than, or equal to, a given acceptance level related to the travel time without using the network. The objective is to find facilities (i.e. entry and exit points) on the network that maximize the number of covered pairs. We present a reformulation of the problem using convex covering sets and use this formulation to derive a finite dominating set and an algorithm for locating two facilities on a tree network. Moreover, we adapt a geometric branch and bound approach to the discrete nature of the problem and suggest a procedure for locating more than two facilities on a single line, which is evaluated numerically. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:topjnl:v:22:y:2014:i:1:p:227-253
    DOI: 10.1007/s11750-012-0251-y
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    References listed on IDEAS

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    6. Laporte, Gilbert & Mesa, Juan A. & Perea, Federico, 2010. "A game theoretic framework for the robust railway transit network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 447-459, May.
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    Cited by:

    1. Tanaka, Ken-ichi & Furuta, Takehiro & Toriumi, Shigeki, 2019. "Railway flow interception location model: Model development and case study of Tokyo metropolitan railway network," Operations Research Perspectives, Elsevier, vol. 6(C).
    2. 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.
    3. 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.
    4. 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.
    5. Perea, Federico & Mesa, Juan A. & Laporte, Gilbert, 2014. "Adding a new station and a road link to a road–rail network in the presence of modal competition," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 1-16.

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    Keywords

    Location; Covering problem; Transportation; 90B85; 90B80;
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