Accounting for parameter uncertainty in large-scale stochastic simulations with correlated inputs

Abstract

This paper considers large-scale stochastic simulations with correlated inputs having normal-to-anything (NORTA) distributions with arbitrary continuous marginal distributions. Examples of correlated inputs include processing times of workpieces across several workcenters in manufacturing facilities and product demands and exchange rates in global supply chains. Our goal is to obtain mean performance measures and confidence intervals for simulations with such correlated inputs by accounting for the uncertainty around the NORTA distribution parameters estimated from finite historical input data. This type of uncertainty is known as the parameter uncertainty in the discrete-event stochastic simulation literature. We demonstrate how to capture parameter uncertainty with a Bayesian model that uses Sklar's marginal-copula representation and Cooke's copula-vine specification for sampling the parameters of the NORTA distribution. The development of such a Bayesian model well suited for handling many correlated inputs is the primary contribution of this paper. We incorporate the Bayesian model into the simulation replication algorithm for the joint representation of stochastic uncertainty and parameter uncertainty in the mean performance estimate and the confidence interval. We show that our model improves both the consistency of the mean line-item fill-rate estimates and the coverage of the confidence intervals in multiproduct inventory simulations with correlated demands.