Annals of Operations Research

, Volume 267, Issue 1–2, pp 179–201 | Cite as

A bi-objective approach to discrete cost-bottleneck location problems

  • Sune Lauth GadegaardEmail author
  • Andreas Klose
  • Lars Relund Nielsen
Multiple Objective Optimization


This paper considers a family of bi-objective discrete facility location problems with a cost objective and a bottleneck objective. A special case is, for instance, a bi-objective version of the (vertex) p-centdian problem. We show that bi-objective facility location problems of this type can be solved efficiently by means of an \(\varepsilon \)-constraint method that solves at most \((n-1)\cdot m\) minisum problems, where n is the number of customer points and m the number of potential facility sites. Additionally, we compare the approach to a lexicographic \(\varepsilon \)-constrained method that only returns efficient solutions and to a two-phase method relying on the perpendicular search method. We report extensive computational results obtained from several classes of facility location problems. The proposed algorithm compares very favorably to both the lexicographic \(\varepsilon \)-constrained method and to the two phase method.


Discrete facility location Bi-objective optimization \(\varepsilon \)-Constrained method Lexicographic optimization 



The authors would like to thank Professor Kim Allan Andersen for insightful comments and suggestions. This work was supported by a grant from Købmand Ferdinand Sallings Mindefond.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Sune Lauth Gadegaard
    • 1
    Email author
  • Andreas Klose
    • 2
  • Lars Relund Nielsen
    • 1
  1. 1.Department of Economics and Business Economics, School of Business and Social SciencesAarhus UniversityAarhus VDenmark
  2. 2.Department of Mathematics, Science and TechnologyAarhus UniversityAarhus CDenmark

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