Exact procedures for solving the discrete ordered median problem |
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Authors: | Natashia Boland Patricia Domínguez-Marín Stefan Nickel Justo Puerto |
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Affiliation: | 1. Department of Mathematics & Statistics, University of Melbourne, Parkville VIC 3010, Australia;2. SAP AG, Walldorf;3. Chair of Operations Research and Logistics, Saarland University, D-66041 Saarbrücken;4. Dept. Estadística e I.O. Facultad de Matemáticas, Universidad de Sevilla. C/ Tarfia s/n, 41012 Sevilla, Spain |
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Abstract: | The discrete ordered median problem (DOMP) integrates classical discrete location problems, such as the N-median, N-center and Uncapacitated Facility Location problems. It was introduced by Nickel (In: Fleischmann B, Lasch R, Derigs U, Domschke W, Rieder U, editors. Operations Research Proceedings 2000, Berlin: Springer, 2001. p. 71–76), who formulated it as both a nonlinear and a linear integer program. We propose an alternative integer linear programming formulation for the DOMP, discuss relationships between both integer linear programming formulations, and show how properties of optimal solutions can be used to strengthen these formulations. Moreover, we present a specific branch and bound procedure to solve the DOMP more efficiently. We test the integer linear programming formulations and this branch and bound method computationally on randomly generated test problems. |
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Keywords: | Discrete location Integer programming |
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