Optimal solution of the discrete cost multicommodity network design problem

We investigate a multicommodity network design problem where a discrete set of technologies with step-increasing cost and capacity functions should be installed on the edges. This problem is a fundamental network design problem having many important applications in contemporary telecommunication networks. We describe an exact constraint generation approach and we show that the conjunctive use of valid inequalities, bipartition inequalities that are generated using max-flow computations, as well as an exact separation algorithm of metric inequalities makes it feasible to solve to optimality instances with up to 50 nodes and 100 edges.