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A parallelized Lagrangean relaxation approach for the discrete ordered median problem

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Abstract

We study a flexible discrete location model which has as particular cases the \(p\)-median problem, the \(p\)-center problem and the \(k\)-centrum problem, among many others, called the discrete ordered median problem. A previous formulation is adapted and a Lagrangean relaxation is carried out on this formulation in order to produce lower and upper bounds on the optimal value of the problem. The relaxed problem can be split into several subproblems whose resolution is simultaneously tackled by means of a parallelized algorithm. The results are compared to other methods proposed in the literature for this problem.

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Acknowledgments

This work has been funded by grants from the Spanish Ministry of Science and Innovation (MTM2012-36163-C06-04, TIN2008-01117, ECO2011-24927 and TIN2012-37483-C03-03), Junta de Andalucía (P10-TIC-6002, P11-TIC-7176 and P12-TIC-301), Program CEI from MICINN (PYR-2012-15 CEI BioTIC GENIL, CEB09-0010) and Fundación Séneca (08716/PI/08), in part financed by the European Regional Development Fund (ERDF). Juana López Redondo is a fellow of the Spanish “Ramón y Cajal” contract program, co-financed by the European Social Fund.

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Authors and Affiliations

  1. Departamento de Informática, Universidad de Almería, ceiA3, Almería, Spain

    Juana L. Redondo & Pilar M. Ortigosa

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

    Alfredo Marín

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  1. Juana L. Redondo
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  2. Alfredo Marín
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  3. Pilar M. Ortigosa
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Correspondence to Pilar M. Ortigosa.

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Redondo, J.L., Marín, A. & Ortigosa, P.M. A parallelized Lagrangean relaxation approach for the discrete ordered median problem. Ann Oper Res 246, 253–272 (2016). https://doi.org/10.1007/s10479-014-1744-x

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  • DOI: https://doi.org/10.1007/s10479-014-1744-x

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