Minimum cost capacity installation for multicommodity network flows

Consider a directed graph G = (V;A), and a set of tra c demands to be shipped between pairs of nodes in V. Capacity has to be installed on the edges of this graph (in integer multiples of a base unit) so that tra c can be routed . In this paper we consider the problem of minimum cost installation of capacity on the arcs to ensure that the required demands can be shipped simultaneously between node pairs. We study two di erent approaches for solving problems of this type. The rst one is based on the idea of metric inequalities (see Onaga and Kakusho 1971]), and uses a formulation with only jAj variables. The second uses an aggregated multicommodity ow formulation and has jVj jAj variables. We rst describe two classes of strong valid inequalities and use them to obtain a complete polyhedral description of the associated polyhedron for the complete graph on 3 nodes. Next we explain our solution methods for both of the approaches in detail and present computational results. Our computatio...

• Type: Journal
• Year: 1998
• Where: MP
• Authors: Daniel Bienstock, Sunil Chopra, Oktay Günlük, Chih-Yang Tsai
• Keywords: Directed Graph, MP 1998, Multicommodity Ow Formulation, Strong Valid Inequalities