First-Stage Sampling in Ranking and Selection: Beyond Variance Estimation

• 成果类型: Article; Early Access
• 署名作者: Fan, Weiwei; Li, Xuewen; Luo, Jun; Tsai, Shing Chih
• 署名单位: Tongji University; Shanghai Jiao Tong University; National Cheng Kung University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2023.0705
• 发表日期: 2025
• 关键词: simulation

摘要

Ranking-and-selection (R&S) procedures, which seek to select the best system among a finite set of stochastic systems, often conduct a first-stage sampling to estimate the unknown variances of the systems. In this paper, we assume that system samples are normally distributed and demonstrate that the first-stage sample size n0 affects the performance of sequential R&S procedures in the manner beyond variance estimations. Specifically, we prove that the presence of n0 could reduce the achieved probability of incorrect selection (PICS). However, this issue has long been ignored, leading to undesired conservativeness of existing procedures. To quantify this conservativeness, we derive formulas for both the indifference-zone (IZ) and IZ-free procedures that depict the relationship between the achieved PICS and n0. These formulas are exact under the least favorable configurations of means, indicating that the impacts of n0 are fully taken into consideration. Based on these analyses, we offer new guidelines on the choice of n0 for the existing procedures. Furthermore, we leverage these formulas to design an improved version of classic IZ-free procedures, which is easy to implement. Lastly, we conduct extensive numerical experiments to demonstrate the superior performance of our proposed procedures.