In this paper, we solve a class of two-stage distributionally robust optimization problems which have the property of supermodularity. We exploit the explicit upper bounds on the expectation of supermodular functions and derive the worst-case distribution for the robust counterpart. This enables us to develop an efficient method to derive an exact optimal solution of these two-stage problems. Further, we provide a necessary and sufficient condition to check whether any given two-stage optimization problem has supermodularity. We apply this framework to classic problems, including the multi-item newsvendor problem, the appointment scheduling problem and general assemble-to-order (ATO) systems. While these problems are typically computationally challenging, they can be solved efficiently using our approach.
Long, Qi, Zhang (2019), The Chinese University of Hong Kong, working paper
View Supermodularity in Two-Stage Distributionally Robust Optimization