Analysis of net inventory in continuous review models with random lead time

This paper derives the steady state distribution of net inventory in a continuous review inventory system under an (s,S) policy in which the demand process is Poisson, ordering decisions are based on net inventory, and lead times are random. The paper assumes that a single supplier satisfies the system’s orders and may supply other similar systems as well. It develops useful approximations for the stationary distribution of net inventory, and also relates our results to previous work which utilizes ordering policies based on inventory position. The analysis of the model applies level crossing theory.