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An extended covering model for flexible discrete and equity location problems

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Abstract

To model flexible objectives for discrete location problems, ordered median functions can be applied. These functions multiply a weight to the cost of fulfilling the demand of a customer which depends on the position of that cost relative to the costs of fulfilling the demand of the other customers. In this paper a reformulated and more compact version of a covering model for the discrete ordered median problem (DOMP) is considered. It is shown that by using this reformulation better solution times can be obtained. This is especially true for some objectives that are often employed in location theory. In addition, the covering model is extended so that ordered median functions with negative weights are feasible as well. This type of modeling weights has not been treated in the literature on the DOMP before. We show that several discrete location problems with equity objectives are particular cases of this model. As a result, a mixed-integer linear model for this type of problems is obtained for the first time.

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Authors and Affiliations

  1. Departamento de Estadística e Investigación Operativa, Universidad de Murcia, Murcia, Spain

    Alfredo Marín

  2. Lehrstuhl für Operations Research und Logistik, Universität des Saarlandes, Saarbrücken, Germany

    Stefan Nickel

  3. Abteilung Optimierung, Fraunhofer Institut für Techno- und Wirtschaftsmathematik (ITWM), Kaiserslautern, Germany

    Sebastian Velten

Authors
  1. Alfredo Marín
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  2. Stefan Nickel
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  3. Sebastian Velten
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Correspondence to Alfredo Marín.

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Marín, A., Nickel, S. & Velten, S. An extended covering model for flexible discrete and equity location problems. Math Meth Oper Res 71, 125–163 (2010). https://doi.org/10.1007/s00186-009-0288-3

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  • DOI: https://doi.org/10.1007/s00186-009-0288-3

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