A robust approximation for setting target inventory levels in a constrained production environment

Abstract

A model is developed to calculate the inventory target level required to provide a specified service level in a single-item single-stage inventory when production is subject to a capacity constraint. The model provides a reliable alternative when the exact Markov chain method is intractable, and where known approximations become unreliable due to high demand variability. The model derives the inventory shortfall distribution by simulating the unconstrained inventory process, from which the parameters of a continuous approximation are estimated. The inventory target level required to provide a desired service level can then be calculated efficiently. This new model requires that only one simulation trial is conducted, from which the optimization is then performed. It is thus an efficient alternative to conventional simulation-based optimization. By simulating the shortfall directly, the model makes no assumptions about the form of the demand distribution. By requiring no user modeling this new method is easily used by inventory managers in practice. The model is robust, with accuracy diminishing only by small degree under increased demand variability or production constraint. The degree of reliability increases as the desired service level increases. Sample size has little effect on the accuracy of forecast service levels.