Accounting for Multivariate Input Uncertainty in Large-Scale Stochastic Simulations

Two important components of a large-scale stochastic simulation are the generation of random variates from multivariate input models and the analysis of simulation output data to estimate mean performance measures and confidence intervals. The common practice is to obtain the multivariate input models applying statistically valid fitting algorithms to historical data sets of finite length and construct the confidence intervals accounting for the stochastic uncertainty, but ignoring the uncertainty around the multivariate input-model fits. This leads not only to inaccurate estimation of mean performance measures, but also to confidence intervals with low coverage probabilities. In this paper we introduce a framework for large-scale stochastic simulations to obtain credible point estimates and confidence intervals with high coverage by accounting for both stochastic uncertainty and multivariate input uncertainty. Specifically, we develop a Bayesian formulation, which utilizes the flexible Johnson translation system, the Sklar’s marginal-copula representation, and the Cooke’s copula-vine specification, for a multivariate input model. We demonstrate that the resulting formulation extends the Bayesian simulation replication algorithm and the Bayesian output analysis, both of which have been used successfully for stochastic simulations with independent inputs, to stochastic simulations with correlated inputs. We illustrate the value of the framework and the importance of the joint representation of stochastic uncertainty and multivariate input uncertainty for multi-product inventory simulations.