In this paper we present a methodology to decide capacity expansions for a transit network that finds a robust solution with respect to the uncertainty in demands and travel times. We show that solving for a robust solution is a computationally tractable problem under conditions that are reasonable for a transportation system. For example, the robust problem is tractable for a multicommodity flow problem with a single source and sink per commodity and uncertain demand and travel time represented by bounded convex sets. Preliminary computational results show that the robust solution can reduce the worst case cost by more than 20%, while incurring on a 5% loss in optimality when compared to the optimal solution of a representative scenario.
Working Paper #2004-01, Industrial and Systems Engineering, USC, June 2004