Quantifying Input Uncertainty in Simulation Output: Dependent Input Models of Diverse Types
Seminar by
Alp Akçay
Department of Industrial Engineering
Bilkent University
When we use simulation to estimate the performance of a stochastic system, the simulation model often includes multivariate input models (e.g., product demands and exchange rates in a global supply chain, processing times of a workpiece across several work centers) that are estimated using finite samples of real-world data. The finiteness of the samples introduces estimation errors in the input models, affecting the simulation output. However, the propogation of input model uncertainty to output uncertainty is rarely considered in simulation output analysis.
In this seminar, a discussion of input uncertainty issues and the state-of-the-art approaches for input uncertainty quantification -- that evolve around independent input models -- will be presented. There are very recent studies in the literature to account for input uncertainty with correlated input variables. However, their common input modeling technique assumes continuous marginal distributions for each input. In this study, we will use an alternative modeling methodology called normal copula graphical model that allows us to learn about the dependence between input variables which can be binary, categorical with ordered categories, count or continuous. In particular, we first encode the conditional indepedencies between input variables in an undirected graph. We then build a Markov chain Monte Carlo algorithm to obtain the posterior distribution of the precision matrix associated with a set of multivariate-normal latent variables that underlie the original multivariate input model. We use this posterior distribution to account for the input uncertainty due to the unknown dependence structure. Subsequently, we capture the input uncertainty due to the unknown marginal distribution of each input variable, and present a metamodel-assisted framework to propagate the input uncertainty to the output uncertainty. Finally, we consider a continuous- review assemble-to-order system with a correlated demand-arrival process, and show that our model improves the coverage of the confidence intervals for the per-period expected cost. The seminar will conclude with an overlook of the future research directions in this area.
