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Stochastic simulation models are increasingly popular for analyzing complexstochastic systems. However, the input distributions required to drive thesimulation are typically unknown in practice and are usually estimated fromreal world data. Since the amount of real world data tends to be limited, theresulting estimation of the input distribution will contain errors. Thisestimation error is commonly known as input uncertainty. In this paper, weconsider the stochastic simulation optimization problem when input uncertaintyis present and assume that both the input distribution family and thedistribution parameters are unknown. We adopt a nonparametric Bayesian approachto model the input uncertainty and propose a nonparametric Bayesian riskoptimization (NBRO) framework to study simulation optimization under inputdistribution uncertainty. We establish the consistency and asymptotic normalityof the value of the objective function, the optimal solution, and the optimalvalue for the NBRO problem. We further propose a simulation optimizationalgorithm based on Efficient Global Optimization (EGO), which explicitly takesinto account the input uncertainty so as to efficiently solve the NBRO problem.We study the consistency property of the modified EGO algorithm and empiricallytest its efficiency with an inventory example and a critical care facilityproblem.

A nonparametric Bayesian approach for simulation optimization with input uncertainty