On the Equivalence and Performance of Distributionally Robust Optimization and Robust Satisficing Models

Problem definition: Distributionally robust optimization (DRO) is ubiquitous to address uncertainties inherent in operations management (OM) problems. Recently, an alternative goal-driven framework, robust satisficing (RS), is proposed. RS aims to attain a prescribed target, such as avoiding overshooting the cost budget, as much as possible under uncertainty. The goal-driven modeling philosophy fits many OM problems, yet there is a lack of direct comparisons between DRO and RS. In this paper, we uncover connections between DRO and RS. Methodology/results: Suppose both models are based on the Wasserstein metric and consider a risk-aware convex objective function affected by uncertain parameters. We demonstrate that they share the same solution family. We establish the correspondence between the radius parameter in DRO and the target parameter in RS such that the optimal solutions to the two models coincide. Inspired by the globalized distributionally robust counterpart (GDRC), we extend the analysis to GDRC and the globalized robust satisficing (GRS). We reveal that GDRC and GRS have the same solution families as DRO and RS, respectively. More importantly, we establish novel results on the equivalence of DRO, GDRC, RS, and GRS models under previously stated conditions. Managerial implications: The equivalence results help unify performance bounds of DRO and RS models. Specifically, each model now has an additional set of theoretical guarantees from the other model, and any bounds derived for one model automatically apply to other equivalent models via some parameter mapping. Despite the theoretical equivalence result, the performance of the DRO and RS models can vary depending on how the model parameters are selected. The experimental findings show how these differences emerge when transitioning from theory to practice. Additionally, the experiments provide insights for practitioners, such as how the use of cross-validation can help reflect the true model preferences, particularly when only a few validation points are set.