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【明理讲堂2023年第81期】11-14香港中文大学龙卓瑜副教授:Supermodularity in Two-Stage Distributionally Robust Optimization

报告题目:Supermodularity in Two-Stage Distributionally Robust Optimization





Daniel Zhuoyu LONG is an associate professor at the Department of Systems Engineering & Engineering Management, The Chinese University of Hong Kong (CUHK). Before joining CUHK, he received his Ph.D. degree from the Department of Analytics and Operations at the National University of Singapore in 2013, his master degree from the Chinese Academy of Science in 2008, and his bachelor degree from Tsinghua University. His research interests revolve around distributionally robust optimization, risk management, and broad applications in supply chain management and project management.


In this paper, we solve a class of two-stage distributionally robust optimization problems which have the property of supermodularity. We exploit the explicit worst-case expectation of supermodular functions and derive the worst-case distribution for the robust counterpart. This enables us to develop an efficient method to obtain an exact optimal solution to these two-stage problems. Further, we provide a necessary and sufficient condition for checking whether any given two-stage optimization problem has the supermodularity property. We also investigate the optimality of the segregated affine decision rules when problems have the property of supermodularity. We apply this framework to several classic problems, including the multi-item newsvendor problem, the facility location problem, the lot-sizing problem on a network, the appointment scheduling problem, and the assemble-to-order problem. While these problems are typically computationally challenging, they can be solved efficiently under our assumptions. Finally, numerical examples are conducted to illustrate the effectiveness of our approach.