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The Use of Decision-dependent Uncertainty Sets in Robust Optimization

This paper contemplates the amenability of Robust Optimization to address problems that involve endogenous uncertainty, i.e., uncertainty that is affected by the decision maker’s strategy. To that end, we extend generic polyhedral uncertainty sets that are typically considered in RO into sets that depend on the actual decisions. Such dependency allows us not only to capture functional changes in correlations that may be induced by given decisions, but also to alleviate conservatism effects from non-materialized model parameters. Case studies from process network capacity expansion, offshore oilfield development, and clinical trial planning showcase the effect of various levels of uncertainty in the optimal solutions as well as the modeling potential and favorable computational tractability characteristics of the proposed framework, which can be utilized in both short-term and long-term decision making.