Computational Optimization and Applications

, Volume 73, Issue 2, pp 603–645 | Cite as

Ordered p-median problems with neighbourhoods

  • Víctor BlancoEmail author


In this paper, we introduce a new variant of the p-median facility location problem in which it is assumed that the exact location of the potential facilities is unknown. Instead, each of the facilities must be located in a region around their initially assigned location (the neighborhood). In this problem, two main decisions have to be made simultaneously: the determination of the potential facilities that must be open to serve the customers’ demand and the location of the open facilities in their neighborhoods, at global minimum cost. We present several mixed integer non-linear programming formulations for a wide family of objective functions which are common in Location Analysis: ordered median functions. We also develop two math-heuristic approaches for solving the problem. We report the results of extensive computational experiments.


Facility location Mixed integer second order cone programming Neighborhoods Ordered median 

Mathematics Subject Classification

90B85 90C22 90C30 47A30 



The author was partially supported by Project MTM2016-74983-C2-1-R (MINECO, Spain), the research group SEJ-534 (Junta de Andalucía) and the research project PP2016-PIP06 (Universidad de Granada). The author would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.IEMath-GRUniversidad de GranadaGranadaSpain
  2. 2.Department of Quantitative Methods for Economics and BusinessUniversidad de GranadaGranadaSpain

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