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Isodistant points in competitive network facility location

Author

Listed:
  • Blas Pelegrín

    ()

  • Rafael Suárez-Vega

    ()

  • Saúl Cano

    ()

Abstract

An isodistant point is any point on a network which is located at a predetermined distance from some node. For some competitive facility location problems on a network, it is verified that optimal (or near-optimal) locations are found in the set of nodes and isodistant points (or points in the vicinity of isodistant points). While the nodes are known, the isodistant points have to be determined for each problem. Surprisingly, no algorithm has been proposed to generate the isodistant points on a network. In this paper, we present a variety of such problems and propose an algorithm to find all isodistant points for given threshold distances associated with the nodes. The number of isodistant points is upper bounded by nm, where n and m are the number of nodes and the number of edges, respectively. Computational experiments are presented which show that isodistant points can be generated in short run time and the number of such points is much smaller than nm. Thus, for networks of moderate size, it is possible to find optimal (or near-optimal) solutions through the Integer Linear Programming formulations corresponding to the discrete version of such problems, in which a finite set of points are taken as location candidates. Copyright Sociedad de Estadística e Investigación Operativa 2012

Suggested Citation

  • Blas Pelegrín & Rafael Suárez-Vega & Saúl Cano, 2012. "Isodistant points in competitive network facility location," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 639-660, October.
  • Handle: RePEc:spr:topjnl:v:20:y:2012:i:3:p:639-660
    DOI: 10.1007/s11750-010-0148-6
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    References listed on IDEAS

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    1. ReVelle, C. S. & Eiselt, H. A., 2005. "Location analysis: A synthesis and survey," European Journal of Operational Research, Elsevier, vol. 165(1), pages 1-19, August.
    2. Hakimi, S. Louis, 1983. "On locating new facilities in a competitive environment," European Journal of Operational Research, Elsevier, vol. 12(1), pages 29-35, January.
    3. Osborne, Martin J & Pitchik, Carolyn, 1987. "Equilibrium in Hotelling's Model of Spatial Competition," Econometrica, Econometric Society, vol. 55(4), pages 911-922, July.
    4. Plastria, Frank, 2001. "Static competitive facility location: An overview of optimisation approaches," European Journal of Operational Research, Elsevier, vol. 129(3), pages 461-470, March.
    5. Daniel Serra & Charles Revelle, 1997. "Competitive location and pricing on networks," Economics Working Papers 219, Department of Economics and Business, Universitat Pompeu Fabra.
    6. Peter Peeters & Frank Plastria, 1998. "Discretization results for the Huff and Pareto-Huff competitive location models on networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(2), pages 247-260, December.
    7. Rafael Suárez-Vega & Dolores R. Santos-Peñate & Pablo Dorta-González, 2007. "The follower location problem with attraction thresholds," Papers in Regional Science, Wiley Blackwell, vol. 86(1), pages 123-137, March.
    8. Daniel Serra & Charles Revelle, 1994. "Competitive location in discrete space," Economics Working Papers 96, Department of Economics and Business, Universitat Pompeu Fabra.
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    Citations

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    Cited by:

    1. Mercedes Pelegrín & Blas Pelegrín, 0. "Nash equilibria in location games on a network," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 0, pages 1-17.
    2. repec:spr:orspec:v:39:y:2017:i:3:d:10.1007_s00291-017-0472-4 is not listed on IDEAS
    3. Rafael Suárez-Vega & Dolores Santos-Peñate & Pablo Dorta-González, 2014. "Location and quality selection for new facilities on a network market," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 52(2), pages 537-560, March.

    More about this item

    Keywords

    Facility location; Threshold distances; Spatial competition; 90B80; 90B85;

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