Calculating target inventory levels for constrained production: A fast simulation-based approximation

Abstract

An accurate model for the inventory shortfall distribution is necessary to calculate the target level required to give a desired service level in manufacturing systems under stochastic demand and production capacity constraint. Existing methods for modelling the inventory shortfall require that the demand distribution be expressible in functional form and that the coefficient of demand variation be small. When these conditions cannot be met, the only recourse to a practitioner is to set target levels using simulation-based optimisation, which is computationally intensive and time consuming. By contrast, this paper presents a model in which the inventory shortfall is approximated by sampling from a single simulation run of the inventory process. The target level required for a given service level can then be calculated efficiently, to a high degree of reliability, using an iterative search. This new model is thus an efficient alternative to conventional simulation-based optimisation. Because the shortfall distribution is generated by simulating demand directly, the model makes no assumptions about the form of the demand distribution. By requiring no user modelling of the functional form or parameters of the demand distribution, this new method is easily used by inventory managers in practice or implemented in software.