Capacitated network design—polyhedral structure and computation

We study a capacity expansion problem that arises in telecommunication network design. Given a capacitated network and a traffic demand matrix, the objective is to add capacity to the edges, in multiples of various modularities, and route traffic, so that the overall cost is minimized. We study the polyhedral structure of a mixed-integer formulation of the problem and develop a cutting-plane algorithm using facet defining inequalities. The algorithm produces an extended formulation providing both a very good lower bound and a starting point for branch and bound. The overall algorithm appears effective when applied to problem instances using real-life data.