Journal of Combinatorial Optimization

, Volume 19, Issue 1, pp 69–83 | Cite as

A tighter formulation of the p-median problem

  • Sourour ElloumiEmail author


Given a set of clients and a set of potential sites for facilities, the p-median problem consists of opening a set of p sites and assigning each client to the closest open facility to it. It can be viewed as a variation of the uncapacitated facility location problem. We propose a new formulation of this problem by a mixed integer linear problem. We show that this formulation, while it has the same value by LP-relaxation, can be much more efficient than two previous formulations. The computational experiment performed on two sets of benchmark instances has showed that the efficiency of the standard branch-and-cut algorithm has been significantly improved. Finally, we explore the structure of the new formulation in order to derive reduction rules and to accelerate the LP-relaxation resolution.


Facility location p-median Integer programming Formulation 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.CEDRIC-CNAMParisFrance

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