Submitted to Operations Research manuscript (Please, provide the mansucript number!) Solving large p-median problems with a radius formulation Sergio Garc´ ıa Departmento de Estad´ ıstica, Universidad Carlos III de Madrid, Spain, sergio.garcia@uc3m.es Martine Labb´ e Depart´ ement d’Informatique, Universit´ e Libre de Bruxelles, Belgium, mlabbe@ulb.ac.be Alfredo Mar´ ın Departamento de Estad´ ıstica e Investigaci´ on Operativa, Universidad de Murcia, Spain, amarin@um.es By means of a model based on a set covering formulation, it is shown how the p-median problem can be solved with just a small subset of constraints and variables, which is embedded in a branch-and-bound framework based on dynamic reliability branching. This method is more than competitive in terms of computational times and size of the instances which have been optimally solved. In particular, problems of size larger than the largest ones considered in the literature up to now are solved exactly in this paper. Key words : Discrete Location, p-median, column-and-row generation 1. Introduction Significant research efforts have been devoted to discrete location problems because of both their importance for practice and their theoretical interest. These models are not only used to optimally locate facilities, but they also appear as subproblems of a wider spectrum of logistic problems and, under a different appearance, they can be identified in several scientific fields where equivalent problems are studied. Indeed, the p-Median Problem, together with the Simple Plant Location Problem, could be considered the two best studied problems in Discrete Location. Given a set of n customers (nodes, vertices ) and non-negative costs c ij ,1 ≤ i, j ≤ n, the p- Median Problem consists in choosing a subset of p elements (medians ) where to establish facilities and allocate the non-median nodes to these medians in such a way that the total allocation cost be minimum. Although the p-Median Problem is NP-hard (Kariv and Hakimi (1979)), several successful approaches have been used to solve instances with up to a few thousands nodes (Briant 1