Integer and combinatorial optimization
Integer and combinatorial optimization
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Wireless Communications: Principles and Practice
Wireless Communications: Principles and Practice
Operations Research
Theory and Applications of Robust Optimization
SIAM Review
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"The Price of Robustness" by Bertsimas and Sim [4] represented a breakthrough in the development of a tractable robust counterpart of Linear Programming Problems. However, the central modeling assumption that the deviation band of each uncertain parameter is single may be too limitative in practice: experience indeed suggests that the deviations distribute also internally to the single band, so that getting a higher resolution by partitioning the band into multiple sub-bands seems advisable. In this work, we study the robust counterpart of a Linear Programming Problem with uncertain coefficient matrix, when a multi-band uncertainty set is considered. We first show that the robust counterpart corresponds to a compact LP formulation. Then we investigate the problem of separating cuts imposing robustness and we show that the separation can be efficiently operated by solving a min-cost flow problem. Finally, we test the performance of our new approach to Robust Optimization on realistic instances of a Wireless Network Design Problem subject to uncertainty.