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Isodistant points in competitive network facility location

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  • 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. H. A. Eiselt & Gilbert Laporte & Jacques-François Thisse, 1993. "Competitive Location Models: A Framework and Bibliography," Transportation Science, INFORMS, vol. 27(1), pages 44-54, February.
    3. David L. Huff, 1966. "A Programmed Solution for Approximating an Optimum Retail Location," Land Economics, University of Wisconsin Press, vol. 42(3), pages 293-303.
    4. 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.
    5. Osborne, Martin J & Pitchik, Carolyn, 1987. "Equilibrium in Hotelling's Model of Spatial Competition," Econometrica, Econometric Society, vol. 55(4), pages 911-922, July.
    6. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    7. Daniel Serra & Charles Revelle, 1997. "Competitive location and pricing on networks," Economics Working Papers 219, Department of Economics and Business, Universitat Pompeu Fabra.
    8. 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.
    9. 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.
    10. 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.
    11. Daniel Serra & Charles Revelle, 1994. "Competitive location in discrete space," Economics Working Papers 96, Department of Economics and Business, Universitat Pompeu Fabra.
    12. LEDERER, Philip J. & THISSE, Jacques-François, 1990. "Competitive location on networks under delivered pricing," LIDAM Reprints CORE 893, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Blas Pelegrín & Pascual Fernández & María Dolores García, 2018. "Computation of Multi-facility Location Nash Equilibria on a Network Under Quantity Competition," Networks and Spatial Economics, Springer, vol. 18(4), pages 999-1017, December.
    2. Mercedes Pelegrín & Blas Pelegrín, 2017. "Nash equilibria in location games on a network," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(3), pages 775-791, July.
    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.

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