Wardrop Equilibria with Risk-Averse Users
Transportation Science
Communication: Robust network optimization under polyhedral demand uncertainty is NP-hard
Discrete Applied Mathematics
INFORMS Journal on Computing
On 2-stage robust LP with RHS uncertainty: complexity results and applications
Journal of Global Optimization
Theory and Applications of Robust Optimization
SIAM Review
Computers and Operations Research
The maximum flow problem of uncertain network
Information Sciences: an International Journal
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We consider the problem of expanding arc capacities in a networksubject to demand and travel time uncertainty. We propose a robustoptimization approach to obtain capacity expansion solutions thatare insensitive to this uncertainty. Our results show that, underreasonable assumptions for network flow applications, such robustsolutions can be computed by solving tractable conic linearproblems. For example, the robust solution for a multicommodityflow problem is obtained by solving a linear program if the problemhas a single source and sink per commodity and the uncertainty indemand and travel time is given by independent bounded polyhedralsets. Preliminary computational results show that the robustsolution is attractive, as it can reduce the worst case cost bymore than 20%, while incurring a 5% loss in optimality whencompared to the optimal solution of a representative scenario.© 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 50(2), 1361452007