(461a) Robust Optimization with Decision-Dependent Uncertainty Sets
In this context, we investigate the numerical performance of applying the standard, duality-based reformulation approach to solve RO problems with decision-dependent sets. We also present a novel algorithmic solution approach based on the Kelley's cutting plane method  within a tailored branch-and-bound framework, which can improve tractability. Furthermore, we show the capability of our proposed methodology to incorporate for the first time near-optimal recourse actions, such as piece-wise linear or piece-wise constant decision rules , in multi-stage stage setups with endogenous uncertainty. This feature is of great importance since it has been shown  that deferring a subset of the decisions for later (âwait-and-seeâ) can lead to more profitableâyet equally robustâsolutions compared to traditional RO, where all of the decisions are considered as âhere-and-nowâ.
The modeling capabilities afforded to us by using these new decision-dependent sets is showcased via a number of case studies, for which we quantify the additional benefits that can be gained by introducing recourse actions in a non-anticipative fashion to multi-stage problems involving endogenous uncertainty.
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