Effective Budget of Uncertainty for Classes of Robust Optimization

Robust optimization (RO) tackles data uncertainty by optimizing for the worst-case scenario of an uncertain parameter and, in its basic form, is sometimes criticized for producing overly conservative solutions. To reduce the level of conservatism in RO, one can use the well-known budget-of-uncertainty approach, which limits the amount of uncertainty to be considered in the model. In this paper, we study a class of problems with resource uncertainty and propose a robust optimization methodology that produces solutions that are even less conservative than the conventional budget-of-uncertainty approach. We propose a new tractable two-stage robust optimization approach that identifies the “ineffective” parts of the uncertainty set and optimizes for the “effective” worst-case scenario only. In the first stage, we identify the effective range of the uncertain parameter, and in the second stage, we provide a formulation that eliminates the unnecessary protection for the ineffective parts and, hence, produces less conservative solutions and provides intuitive insights on the trade-off between robustness and solution conservatism. We demonstrate the applicability of the proposed approach using a power dispatch optimization problem with wind uncertainty. We also provide examples of other application areas that would benefit from the proposed approach.