# The p-Median Problem with Concave Costs

### Chuan Xu, Abdel Lisser, Janny Leung, Marc Letournel

#### Abstract

In this paper, we propose a capacitated p-median problem with concave costs, in which the global cost incurred for each established facility is a concave function of the quantity q delivered by this facility. We use DICOPT to solve this concave model. And then we transform this model into a linear programming problem and solve it using the commercial solver CPLEX. We also use the metaheuristic Variable Neighbourhood Search (VNS) to solve this problem. Computational results show that our linearization method helps to improve the calculations of the concave model. With VNS, we solve large size instances with up to 1500 facilities within a reasonable CPU time.

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#### Paper Citation

#### in Harvard Style

Xu C., Lisser A., Leung J. and Letournel M. (2014). **The p-Median Problem with Concave Costs** . In *Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-017-8, pages 205-212. DOI: 10.5220/0004832502050212

#### in Bibtex Style

@conference{icores14,

author={Chuan Xu and Abdel Lisser and Janny Leung and Marc Letournel},

title={The p-Median Problem with Concave Costs},

booktitle={Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2014},

pages={205-212},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004832502050212},

isbn={978-989-758-017-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - The p-Median Problem with Concave Costs

SN - 978-989-758-017-8

AU - Xu C.

AU - Lisser A.

AU - Leung J.

AU - Letournel M.

PY - 2014

SP - 205

EP - 212

DO - 10.5220/0004832502050212