A flexible model and efficient solution strategies for discrete location problems

Authors:
Alfredo Marín;Stefan Nickel;Justo Puerto;Sebastian Velten
Affiliations:
Universidad de Murcia, Departamento de Estadística e Investigación Operativa, 30100 Murcia, Spain;Saarland University, Chair of Operations Research and Logistics, Faculty of Law and Economics, P.O. Box 15 11 50, 66041 Saarbrücken, Germany and Fraunhofer Institute for Industrial Mathematic ...;University of Seville, Faculty of Mathematics, 41012 Seville, Spain;Saarland University, Chair of Operations Research and Logistics, Faculty of Law and Economics, P.O. Box 15 11 50, 66041 Saarbrücken, Germany
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

Flexible discrete location problems are a generalization of most classical discrete locations problems like p-median or p-center problems. They can be modeled by using so-called ordered median functions. 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 other customers. In this paper a covering type of model for the discrete ordered median problem is presented. For the solution of this model two sets of valid inequalities, which reduces the number of binary variables tremendously, and several variable fixing strategies are identified. Based on these concepts a specialized branch & cut procedure is proposed and extensive computational results are reported.