On the incorporation of parameter uncertainty for inventory management using simulation

The main purpose of this paper is to discuss how a Bayesian framework is appropriate to incorporate the uncertainty on the parameters of the model that is used for demand forecasting. We first present a general Bayesian framework that allows us to consider a complex model for forecasting. Using this framework, we specialize (for simplicity) in the continuous‐review (Q,R) system to show how the main performance measures that are required for inventory management (service levels and reorder points) can be estimated from the output of simulation experiments. We discuss the use of two estimation methodologies: posterior sampling (PS) and Markov chain Monte Carlo (MCMC). We show that, under suitable regularity conditions, the estimators obtained from PS and MCMC satisfy a corresponding Central Limit Theorem, so that they are consistent, and the accuracy of each estimator can be assessed by computing an asymptotically valid half‐width from the output of the simulation experiments. This approach is particularly useful when the forecasting model is complex in the sense that analytical expressions to obtain service levels and/or reorder points are not available.