Computational study of large-scale p-median problems

Given a directed graph G(V,A), the p-Median problem consists of determining p nodes (the median nodes) minimizing the total distance from the other nodes of the graph. We present a Branch-and- Cut-and-Price algorithm yielding provably good solutions for instances with |V| ≤ 3795. Key ingredients of the algorithm are a delayed column-and-row generation technique, exploiting the special structure of the formulation, to solve the LP-relaxation, and cutting planes to strengthen the formulation and limit the size of the enumeration tree.