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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

Abstract

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

Suggested Citation

  • José Fernández & Blas Pelegrín & Frank Plastria & Boglárka Tóth, 2007. "Planar Location and Design of a New Facility with Inner and Outer Competition: An Interval Lexicographical-like Solution Procedure," Networks and Spatial Economics, Springer, vol. 7(1), pages 19-44, March.
    • Handle: RePEc:kap:netspa:v:7:y:2007:i:1:p:19-44
    DOI: 10.1007/s11067-006-9005-4
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Drezner, Zvi & Eiselt, H.A., 2024. "Competitive location models: A review," European Journal of Operational Research, Elsevier, vol. 316(1), pages 5-18.
    2. Blas Pelegrín & Pascual Fernández & María Dolores García Pérez, 2016. "Profit maximization and reduction of the cannibalization effect in chain expansion," Annals of Operations Research, Springer, vol. 246(1), pages 57-75, November.
    3. 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.
    4. Tammy Drezner, 2011. "Cannibalization in a Competitive Environment," International Regional Science Review, , vol. 34(3), pages 306-322, July.
    5. Suárez-Vega, Rafael & Gutiérrez-Acuña, José Luis & Rodríguez-Díaz, Manuel, 2019. "Using a productivity function based method to design a new shopping centre," Journal of Retailing and Consumer Services, Elsevier, vol. 51(C), pages 176-185.
    6. Pelegrín, Blas & Fernández, Pascual & Dolores García Pérez, María & Cano Hernández, Saúl, 2012. "On the location of new facilities for chain expansion under delivered pricing," Omega, Elsevier, vol. 40(2), pages 149-158, April.
    7. 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.
    8. Blanquero, Rafael & Carrizosa, Emilio & Schöbel, Anita & Scholz, Daniel, 2011. "A global optimization procedure for the location of a median line in the three-dimensional space," European Journal of Operational Research, Elsevier, vol. 215(1), pages 14-20, November.
    9. H Küçükaydın & N Aras & İ K Altınel, 2011. "A discrete competitive facility location model with variable attractiveness," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(9), pages 1726-1741, September.

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