  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.
