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

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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.

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