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Planar Location and Design of a New Facility with Inner and Outer Competition: An Interval Lexicographical-like Solution Procedure


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  • José Fernández


  • Blas Pelegrín
  • Frank Plastria
  • Boglárka Tóth
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    A chain has to decide the location and design for a single new facility in a region where a set of facilities already exists offering the same type of product. Some of the existing facilities belong to the chain and the others are competitors. Since competition comes from outside the chain, the maximization of the profit is the main objective of the chain’s owner. Customers are supposed to patronize all the facilities, the old and the new, proportionally to the attraction they feel for them. The entrance of the new facility may thus also have a detrimental effect on the market shares of the existing chain-owned facilities, and this cannibalization should be minimized as a secondary objective. This problem is formulated as a biobjective optimization problem, and a variant of the lexicographic method is proposed to generate certain efficient solutions. This requires solving two related optimization problems, both neither convex nor concave, for which a unified interval branch and bound method is developed. Computational experiments on randomly generated problems show the feasibility of the approach, while an application of the model with real data demonstrates its use for economical analysis. Copyright Springer Science+Business Media, LLC 2007

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    Bibliographic Info

    Article provided by Springer in its journal Networks and Spatial Economics.

    Volume (Year): 7 (2007)
    Issue (Month): 1 (March)
    Pages: 19-44

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    Handle: RePEc:kap:netspa:v:7:y:2007:i:1:p:19-44

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    Keywords: Continuous location; Facility design; Competition; Profit optimization; Cannibalization; Biobjective optimization; Efficient set; Lexicographic method; Global optimization; Interval analysis;


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    1. Daniel Serra & Rosa Colomé, 1998. "Consumer choice in competitive location models: Formulations and heuristics," Economics Working Papers 290, Department of Economics and Business, Universitat Pompeu Fabra.
    2. 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.
    3. Plastria, Frank, 1992. "GBSSS: The generalized big square small square method for planar single-facility location," European Journal of Operational Research, Elsevier, vol. 62(2), pages 163-174, October.
    4. Wendell, R. E. & McKelvey, R. D., 1981. "New perspectives in competitive location theory," European Journal of Operational Research, Elsevier, vol. 6(2), pages 174-182, February.
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    Cited by:
    1. Schöbel, Anita & Scholz, Daniel, 2014. "A solution algorithm for non-convex mixed integer optimization problems with only few continuous variables," European Journal of Operational Research, Elsevier, vol. 232(2), pages 266-275.
    2. Küçükaydin, Hande & Aras, Necati & Kuban AltInel, I., 2011. "Competitive facility location problem with attractiveness adjustment of the follower: A bilevel programming model and its solution," European Journal of Operational Research, Elsevier, vol. 208(3), pages 206-220, February.


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