Distributionally Robust Optimization Under a Decision-Dependent Ambiguity Set with Applications to Machine Scheduling and Humanitarian Logistics

We introduce a new class of distributionally robust optimization problems under decision-dependent ambiguity sets. In particular, as our sets, we consider balls centered on probability distribution. The are based earth mover’s distances that includes both the total variation distance and Wasserstein metrics. discuss main computational challenges in solving interest provide an overview various settings leading to tractable formulations. Some arising side results, such mathematical programming expressions for robustified risk measures discrete space, also independent interest. Finally, rely state-of-the-art modeling techniques from machine scheduling humanitarian logistics arrive at potentially practical applications, present numerical study novel risk-averse problem with controllable processing times. Summary Contribution: this study, simultaneously address distributional uncertainty. unified framework along discussion possible ways specify key model components, complex Special care has been devoted identifying classes where these can be mitigated. reformulation including measures, describe how results utilized obtain formulations specific applied fields scheduling. Toward demonstrating value approach investigating performance proposed mixed-integer linear formulations, conduct derive insights regarding decision-making impact parameter choices.