Optimal computing budget allocation for complete ranking with input uncertainty

Existing research in ranking and selection has focused on the problem of selecting the best design, subset selection and selecting the set of Pareto designs. Few works have addressed the problem of complete ranking. In this research, we consider the problem of ranking all alternatives completely with consideration of input uncertainty. Given a fixed simulation budget, we aim to maximize the probability of correct ranking among all designs based on their worst-case performances. The problem is formulated as an optimal computing budget allocation model. To make this optimization problem computationally tractable, we develop an approximated probability of correct ranking and derive the asymptotic optimality condition based on it. A sequential ranking procedure is then suggested to implement the proposed simulation budget allocation rule. The high efficiency of the proposed simulation procedure is demonstrated via a set of numerical experiments. In addition, useful insights and analysis on characterizing the optimality condition and implementing the efficient budget allocation rule are provided.