Networks and Spatial Economics

, Volume 7, Issue 1, pp 19–44 | Cite as

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

  • José Fernández
  • Blas Pelegrín
  • Frank Plastria
  • Boglárka Tóth


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.


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


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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • José Fernández
    • 1
    • 2
  • Blas Pelegrín
    • 2
  • Frank Plastria
    • 3
  • Boglárka Tóth
    • 2
  1. 1.Facultad de MatemáticasUniversidad de MurciaMurciaSpain
  2. 2.Department of Statistics and Operations ResearchUniversity of MurciaMurciaSpain
  3. 3.MOSI-Department of Mathematics, Operations Research and Information Systems for ManagementVrije Universiteit BrusselBrusselsBelgium

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