Compact MILP formulations for the p-center problem

Zacharie Alès (1, 2) , Sourour Elloumi (1, 2)

1 CEDRIC - OC - CEDRIC. Optimisation Combinatoire
2 OC - Optimisation et commande

The p-center problem consists in selecting p centers among M to cover N clients, such that the maximal distance between a client and its closest selected center is minimized. For this problem we propose two new and compact integer formulations. Our first formulation is an improvement of a previous formulation. It significantly decreases the number of constraints while preserving the optimal value of the linear relaxation. Our second formulation contains less variables and constraints but it has a weaker linear relaxation bound. We besides introduce an algorithm which enables us to compute strong bounds and significantly reduce the size of our formulations. Finally, the efficiency of the algorithm and the proposed formulations are compared in terms of quality of the linear relaxation and computation time over instances from OR-Library.

Mots clés: p-center; discrete location; equivalent formulations; integer programming

Domaines: Recherche opérationnelle [math.OC]

Zacharie Alès, Sourour Elloumi. Compact MILP formulations for the p-center problem. Jon Lee; Giovanni Rinaldi; A. Ridha Mahjoub. Combinatorial Optimization, 10856, Springer, pp.14-25, 2018, Lecture Notes in Computer Science, 978-3-319-96151-4. ⟨10.1007/978-3-319-96151-4_2⟩. ⟨hal-01811455⟩