Review on Ranking and Selection: A New Perspective
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In this paper, we briefly review the development of ranking-and-selection (R S) in the past 70 years, especially the recent theoretical achievements and practical applications in the last 20 years. Different from the frequentist and Bayesian classifications in the review chapters of Kim and Nelson (2006b) and Chick (2006), we categorize the existing R S procedures into the 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. In particular, they are built on the hypothesis-testing and dynamic-programming formulations, respectively. In light of this, we further explain in detail how several well-known procedures in the literature are designed under these two formulations. Moreover, we discuss about practical integration of using R S to solve various problems as well as emerging variations of new R S problems.
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