The essence of Robust Optimization is to find optimal solutions that remain feasible under all the deviations included in a specified uncertainty set that should reflect the risk aversion of the decision maker. In this talk, we focus on uncertainty sets built through Multiband Uncertainty Set. This set extends the classical concept of Bertsimas and Sim, where a single band for each uncertain parameter is given and the number of deviating values is limited. The new set breaks the single band in into multiple sub-bands to get a higher modeling resolution.
We will give an overview on our theoretical results for robust optimization problems under multiband uncertainties: a compact formulation for the robust counterpart of a MILP; an efficient method for the separation of robustness cuts (i.e., cuts that impose robustness), based on solving a min-cost flow instance; an analysis of 0-1 optimization problems with cost uncertainties given by a multiband scenario set. Finally, we present first computational results on the price of robustness and the stability according to different rules for building these scenario sets.