# Distributionally Robust Selection of the Best

## TL;DR

This paper addresses the challenge of selecting the best among multiple simulation alternatives under input uncertainty by proposing robust procedures that guarantee a high probability of correct selection, demonstrated through numerical and real-world case studies.

## Contribution

It introduces a novel robust selection framework using ambiguity sets of input distributions, with proven procedures that outperform existing methods in accuracy and efficiency.

## Key findings

- Proposed procedures achieve at least the desired probability of correct selection.
- Numerical experiments show improved computational efficiency.
- Application to real data demonstrates better decision quality.

## 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.