Robust Satisficing

We present a model for optimization under uncertainty called robustness optimization that favors solutions for which the model’s constraint would be the most robust or least fragile under uncertainty. The decision maker does not have to size the uncertainty set, but specifies an acceptable target, or loss of optimality compared to the baseline model, as a tradeoff for the model’s ability to withstand greater uncertainty. We axiomatize the decision criterion associated with robustness optimization, termed as the fragility measure, which is a class of Brown and Sim (2009) satisficing measure, and it satisfies the properties of monotonicity, positive homogeneity, subadditivity, pro-robustness, and anti-fragility. We provide a representation theorem and connect it with known fragility measures including the decision criterion associated with the GRC-sum of Ben-Tal et al. (2017) and the riskiness index of Aumann and Serrano (2008). We present a suite of practicable robustness optimization models for prescriptive analytics including linear, adaptive linear, data-driven adaptive linear, combinatorial, and dynamic optimization problems. Similar to robust optimization, we show that robustness optimization via minimizing the fragility measure can also be done in a tractable way. We also provide numerical studies on static, adaptive, and data-driven adaptive problems and show that the solutions to the robustness optimization models can withstand greater impact of uncertainty compared to the corresponding robust optimization models without increasing the cost or incurring additional computational effort.