Robust Optimization for Empty Repositioning Problems
Operations Research
Uncertain Linear Programs: Extended Affinely Adjustable Robust Counterparts
Operations Research
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
Efficient robust linear optimization for large repositioning problems
INOC'11 Proceedings of the 5th international conference on Network optimization
Theory and Applications of Robust Optimization
SIAM Review
A constraint sampling approach for multi-stage robust optimization
Automatica (Journal of IFAC)
IEEE/ACM Transactions on Networking (TON)
Robust Storage Assignment in Unit-Load Warehouses
Management Science
Journal of Combinatorial Optimization
The robust network loading problem with dynamic routing
Computational Optimization and Applications
Robust location transportation problems under uncertain demands
Discrete Applied Mathematics
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We describe a two-stage robust optimization approach for solving network flow and design problems with uncertain demand. In two-stage network optimization, one defers a subset of the flow decisions until after the realization of the uncertain demand. Availability of such a recourse action allows one to come up with less conservative solutions compared to single-stage optimization. However, this advantage often comes at a price: two-stage optimization is, in general, significantly harder than single-stage optimization. For network flow and design under demand uncertainty, we give a characterization of the first-stage robust decisions with an exponential number of constraints and prove that the corresponding separation problem is NP-hard even for a network flow problem on a bipartite graph. We show, however, that if the second-stage network topology is totally ordered or an arborescence, then the separation problem is tractable. Unlike single-stage robust optimization under demand uncertainty, two-stage robust optimization allows one to control conservatism of the solutions by means of an allowed “budget for demand uncertainty.” Using a budget of uncertainty, we provide an upper bound on the probability of infeasibility of a robust solution for a random demand vector. We generalize the approach to multicommodity network flow and design, and give applications to lot-sizing and location-transportation problems. By projecting out second-stage flow variables, we define an upper bounding problem for the two-stage min-max-min optimization problem. Finally, we present computational results comparing the proposed two-stage robust optimization approach with single-stage robust optimization as well as scenario-based two-stage stochastic optimization.