INPUT-OUTPUT UNCERTAINTY COMPARISONS FOR OPTIMIZATION VIA SIMULATION

When an optimization via simulation (OvS) procedure designed for known input distributions is applied to a problem with input uncertainty (IU), it typically does not provide the target statistical guarantee. In this paper, we focus on a discrete OvS problem where all systems share the same input distribution estimated from the common input data (CID). We define the CID effect as the joint impact of IU on the outputs of the systems caused by common input distributions. Our input-output uncertainty comparison (IOU-C) procedure leverages the CID effect to provide the joint confidence intervals (CIs) for the difference between each system's mean performance and the best of the rest incorporating both input and output uncertainty. Under mild conditions, IOU comparisons provide the target statistical guarantee as the input sample size and the simulation effort increase.