Metric Inequalities and the Network Loading Problem

Given a simple graph G(V,E) and a set of traffic demands between the nodes of G, the Network Loading Problem consists of installing minimum cost integer capacities on the edges of G allowing routing of the traffic demands. In this paper we study the Capacity Formulation of the Network Loading Problem, introducing the new class of the Tight Metric Inequalities, that completely characterize the convex hull of the integer feasible solutions of the problem. We present separation algorithms for Tight Metric Inequalities and a cutting plane algorithm, reporting on computational experience.