Robust Satisficing

Abstract

We present a general framework for robust satisficing that favors solutions for which a risk-aware objective function would best attain an acceptable target even when the actual probability distribution deviates from the empirical distribution. The satisficing decision maker specifies an acceptable target, or loss of optimality compared with the empirical optimization model, as a trade-off for the model’s ability to withstand greater uncertainty. We axiomatize the decision criterion associated with robust satisficing, termed as the fragility measure, and present its representation theorem. Focusing on Wasserstein distance measure, we present tractable robust satisficing models for risk-based linear optimization, combinatorial optimization, and linear optimization problems with recourse. Serendipitously, the insights to the approximation of the linear optimization problems with recourse also provide a recipe for approximating solutions for hard stochastic optimization problems without relatively complete recourse. We perform numerical studies on a portfolio optimization problem and a network lot-sizing problem. We show that the solutions to the robust satisficing models are more effective in improving the out-of-sample performance evaluated on a variety of metrics, hence alleviating the optimizer’s curse. Funding: D. Z. Long is supported by the Hong Kong Research Grants Council [Grant 14207819]. M. Sim and M. Zhou are supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 [Grant MOE-2019-T3-1-010]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/opre.2021.2238 .