Distributionally Robust Selection of the Best

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.

A worst‐case formulation for constrained ranking and selection with input uncertainty

“…By doing so, the problem scale is reduced from km to k + m − 1, and thus the computing efficiency has the potential to be substantially improved. This observation is consistent with the selection rules for unconstrained robust R&S (Fan et al, in press; Gao, Xiao, et al, ).…”

“…Due to the lack of complete knowledge, P is usually estimated from the information available in order to drive the simulation model, which leads to some degree of uncertainty. In order to account for this uncertainty in our formulation, we adopt a similar approach as in Fan et al (in press) and assume that for each design in , the set of possible distributions of ξ is identical and contains a finite number of scenarios, denoted as and called the uncertainty set. This set incorporates the uncertainty from both the input distributions and their associated parameters.…”

“…To assess the system performance of a design, we use the worst‐case performance among the β scenarios in , that is, for l = 0, 1, …, m (Ben‐Tal & Nemirovski, ; Fan et al, in press; Gülpinar & Rustem, ). Since decisions made based on the worst‐case scenario can prevent potential high risk, this setting is preferred by conservative decision makers.…”

“…Following this direction, Corlu and Biller () developed a robust R&S procedure for subset selection. Fan, Hong, and Zhang (in press) and Gao, Xiao, Zhou, and Chen () selected the best design with respect to the worst‐case choices among a finite collection of possible input models using the IZ and OCBA approaches respectively. However, none of these developments address the input uncertainty for R&S under stochastic constraints.…”

Review on ranking and selection: A new perspective

“…Particularly, the RSB formulation includes all the possible scenarios of input distribution into an ambiguity set and then takes a robust perspective to define the best alternative with respect to the worst-case mean performance measures over the ambiguity set. Fan et al (2020) further improved their work and proposed both two-stage and sequential procedures that can achieve the user-specified PCS. These RSB procedures are also tested by a healthcare queueing system with both synthetic and real hospital data.…”