Review on ranking and selection: A new perspective

Abstract

In this paper, we briefly review the development of ranking and selection (R&S) in the past 70 years, especially the theoretical achievements and practical applications in the past 20 years. Different from the frequentist and Bayesian classifications adopted by Kim and Nelson (2006b) and Chick (2006) in their review articles, we categorize existing R&S procedures into fixed-precision and fixed-budget procedures, as in Hunter and Nelson (2017). We show that these two categories of procedures essentially differ in the underlying methodological formulations, i.e., they are built on hypothesis testing and dynamic programming, respectively. In light of this variation, we review in detail some well-known procedures in the literature and show how they fit into these two formulations. In addition, we discuss the use of R&S procedures in solving various practical problems and propose what we think are the important research questions in the field.

Unbiased decision making in location-routing problems with uncertain customer demands

“…be good alternatives. According to the definition of indifference zone, the decision maker should be indifferent if one of these good alternatives is selected as the best (Hong et al 2021). The solution obtained by the ranking and selection method is different with respect to the solution of the deterministic counterpart.…”

“…Among the selection methods, there are the ranking and selection techniques that provide "statistical guarantees" on the chosen solution. For a comprehensive overview, we refer the reader to the recent paper by Hong et al (2021) in which theoretical achievements on ranking and selection and practical applications in the past 20 years are discussed. Hong et al (2021) also explain the philosophy of the indifference zone approach to ranking and selection.…”

“…For a comprehensive overview, we refer the reader to the recent paper by Hong et al (2021) in which theoretical achievements on ranking and selection and practical applications in the past 20 years are discussed. Hong et al (2021) also explain the philosophy of the indifference zone approach to ranking and selection. This approach has a rich literature.…”

“…To this end, an indifference zone method like the Rinott's procedure can be used (Hong et al 2021). The difficulty in applying the procedure depends on how much i * is better than the other alternatives.…”

Dynamic Sampling Allocation for Selecting a Good Enough Alternative

“…R&S has been widely studied in simulation, which aims to allocate simulation replications to alternatives for efficiently selecting the best alternative. There are fixed-precision and fixed-budget procedures for R&S [3], where the former allocates samples to guarantee a probability of correct selection (PCS) up to a certain level, whereas the latter optimizes performance metrics under a fixed simulation budget constraint. A well-researched paradigm is an indifference zone (IZ) framework [4], [5], which aims to guarantee a PCS level in the least favorable configuration.…”