【学术视点】分布稳健的最佳选择

Distributionally Robust Selection of the Best

Weiwei Fan, L. Jeff Hong, Xiaowei Zhang

MANAGEMENT SCIENCE

About the author

Weiwei Fan: Advanced Institute of Business and School of Economics and Management, Tongji University,

L. Jeff Hong: School of Management and School of Data Science, Fudan University

Xiaowei Zhang: Department of Management Sciences, College of Business, City University of Hong Kong

Keywords

selection of the best • distributional robustness • input uncertainty • probability of correct selection

Abstract

Specifying a proper input distribution is often a challenging task in simulation modeling. In practice, there may be multiple plausible distributions that can fit the input data reasonably well, especially when the data volume is not large. In this paper, we consider the problem of selecting the best from a finite set of simulated alternatives, in the presence of such input uncertainty. We model such uncertainty by an ambiguity set consisting of a finite number of plausible input distributions and aim to select the alternative with the best worst-case mean performance over the ambiguity set. We refer to this problem as robust selection of the best (RSB). To solve the RSB problem, we develop a two-stage selection procedure and a sequential selection procedure; we then prove that both procedures can achieve at least a user-specified probability of correct selection under mild conditions. Extensive numerical experiments are conducted to investigate the computational efficiency of the two procedures. Finally, we apply the RSB approach to study a queueing system’s staffing problem using synthetic data and an appointment-scheduling problem using real data from a large hospital in China. We find that the RSB approach can generate decisions significantly better than other widely used approaches.