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Competitive Multifacility Location on Networks: the (r∣Xp)‐Medianoid Problem

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  • Rafael Suárez‐Vega
  • Dolores R. Santos‐Peñate
  • Pablo Dorta‐González

Abstract

. We investigate the (r∣Xp)‐medianoid problem for networks. This is a competitive location problem that consists of determining the locations of r facilities belonging to a firm in order to maximize its market share in a space where a competitor is already operating with p facilities. We consider six scenarios resulting from the combination of three customer choice rules (binary, partially binary, and proportional) with two types of services (essential and unessential). Known discretization results about the existence of a solution for the set of nodes are extended. Some examples and computational experience using heuristic algorithms are presented.

Suggested Citation

  • Rafael Suárez‐Vega & Dolores R. Santos‐Peñate & Pablo Dorta‐González, 2004. "Competitive Multifacility Location on Networks: the (r∣Xp)‐Medianoid Problem," Journal of Regional Science, Wiley Blackwell, vol. 44(3), pages 569-588, August.
    • Handle: RePEc:bla:jregsc:v:44:y:2004:i:3:p:569-588
    DOI: 10.1111/j.0022-4146.2004.00349.x
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    1. Daniel Serra & Rosa Colomé, 2001. "articles: Consumer choice and optimal locations models: Formulations and heuristics," Papers in Regional Science, Springer;Regional Science Association International, vol. 80(4), pages 439-464.
    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. Alfred A. Kuehn & Michael J. Hamburger, 1963. "A Heuristic Program for Locating Warehouses," Management Science, INFORMS, vol. 9(4), pages 643-666, July.
    4. Michael B. Teitz & Polly Bart, 1968. "Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph," Operations Research, INFORMS, vol. 16(5), pages 955-961, October.
    5. 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.
    6. T L Friesz & T Miller & R L Tobin, 1988. "Algorithms for Spatially Competitive Network Facility-Location," Environment and Planning B, , vol. 15(2), pages 191-203, June.
    7. 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.
    8. Eiselt, H. A. & Laporte, G., 1989. "Competitive spatial models," European Journal of Operational Research, Elsevier, vol. 39(3), pages 231-242, April.
    9. Bauer, A. & Domschke, Wolfgang & Pesch, E., 1993. "Competitive location on a network," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 36425, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    10. Oded Berman & Dmitry Krass, 2002. "Locating Multiple Competitive Facilities: Spatial Interaction Models with Variable Expenditures," Annals of Operations Research, Springer, vol. 111(1), pages 197-225, March.
    11. Bauer, Andreas & Domschke, Wolfgang & Pesch, Erwin, 1993. "Competitive location on a network," European Journal of Operational Research, Elsevier, vol. 66(3), pages 372-391, May.
    12. 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.
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    3. Méndez-Vogel, Gonzalo & Marianov, Vladimir & Lüer-Villagra, Armin & Eiselt, H.A., 2023. "Store location with multipurpose shopping trips and a new random utility customers’ choice model," European Journal of Operational Research, Elsevier, vol. 305(2), pages 708-721.

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