Technical Note—Comments on the Distribution of Inventory Position in a Continuous-Review (s,S) Inventory System

Abstract

This paper comments on the limiting distribution of the inventory position in a continuous-review ( s , S ) inventory system with arbitrary customer interarrival-time distribution. The limiting distribution is derived for the general case in which the demand quantity is random. We show that the limiting distribution is uniform on ( s + 1, …, S ) if and only if units are demanded one at a time. However, with a slight modification of the procurement policy, the uniform distribution is recaptured even with random demand quantities.