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