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Ordered Median Location Problems

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Location Science

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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 ℓp-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.

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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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Authors and Affiliations

  1. IMUS, Universidad de Sevilla, Seville, Spain

    Justo Puerto

  2. Dpto. Estadística e Investigación Operativa, Universidad de Cadiz, Cadiz, Spain

    Antonio M. Rodríguez-Chía

Authors
  1. Justo Puerto
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  2. Antonio M. Rodríguez-Chía
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Corresponding author

Correspondence to Antonio M. Rodríguez-Chía .

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Editors and Affiliations

  1. HEC Montréal, Montréal, QC, Canada

    Gilbert Laporte

  2. Institute for Operations Research, Karlsruhe Institute of Technology, Karlsruhe, Germany

    Stefan Nickel

  3. Faculty of Science, University of Lisbon, Lisbon, Portugal

    Francisco Saldanha da Gama

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Puerto, J., Rodríguez-Chía, A.M. (2019). Ordered Median Location Problems. In: Laporte, G., Nickel, S., Saldanha da Gama, F. (eds) Location Science. Springer, Cham. https://doi.org/10.1007/978-3-030-32177-2_10

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