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Ordered Median Location Problems

  • Justo Puerto
  • Antonio M. Rodríguez-ChíaEmail author
Chapter
  • 46 Downloads

Abstract

This chapter analyzes the ordered median location problem in three different frameworks: continuous, discrete and networks; where some classical but also new results have been collected. For each solution space we study general properties that lead to solution algorithms. In the continuous case, we present two solution approaches for the planar case with polyhedral norms (the most intuitive case) and a novel approach applicable for the general case based on a hierarchy of semidefinite programs that can approximate up to any degree of accuracy the solution of any ordered median problem in finite dimension spaces with polyhedral or p-norms. We also cover the problem on networks deriving finite dominating sets for some particular classes of λ parameters and showing the impossibility of finding a FDS with polynomial cardinality for general lambdas in the multifacility case. Finally, we present a covering based formulation for the capacitated discrete ordered median problem with binary assignment which is rather promising in terms of gap and CPU time for solving this family of problems.

Keywords

Ordered median function Finite dominating set Mixed integer linear programming 

Notes

Acknowledgements

The authors were partially supported by projects MTM2016-74983-C2-01/02-R (Ministry of Economy and Competitiveness∖FEDER, Spain).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.IMUSUniversidad de SevillaSevilleSpain
  2. 2.Dpto. Estadística e Investigación OperativaUniversidad de CadizCadizSpain

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