Ranking and selection under input uncertainty: A budget allocation formulation

A widely acknowledged challenge in ranking and selection is how to allocate the simulation budget such that the probability of correction selection (PCS) is maximized. However, there is yet another challenge: when the input distributions are estimated using finite real-world data, simulation output is subject to input uncertainty and we may fail to identify the best system even using infinite simulation budget. We propose a new formulation that captures the tradeoff between collecting input data and running simulations. To solve the formulation, we develop an algorithm for two-stage allocation of finite budget. We use numerical experiment to demonstrate the performance of our algorithm.