Robust capacity expansion of network flows

We consider the problem of expanding arc capacities in a network subject to demand and travel time uncertainty. We propose a robust optimization approach to obtain capacity expansion solutions that are insensitive to this uncertainty. Our results show that, under reasonable assumptions for network flow applications, such robust solutions can be computed by solving tractable conic linear problems. For example, the robust solution for a multicommodity flow problem is obtained by solving a linear program if the problem has a single source and sink per commodity and the uncertainty in demand and travel time is given by independent bounded polyhedral sets. Preliminary computational results show that the robust solution is attractive, as it can reduce the worst case cost by more than 20%, while incurring a 5% loss in optimality when compared to the optimal solution of a representative scenario.