The Uniform Distribution of Inventory Position for Continuous Review (s, Q) Policies

by R. M. Simon


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A demonstration that, under the widely used (s, Q) or periodic replenishment stockage policy with backlogging and procurement lead times that are random variables having arbitrary distributions, the stationary probability that the inventory position at any time is s + j = 1/Q. This equation has been proved by previous workers for various cases — for Poisson demand, for Markovian demand, for a periodic review case with the same demand distribution in each period — but none of the earlier proofs are readily generalized. Here the general review case is approached directly as a semi-Markov process, and the equation is shown to be valid for very general demand processes.

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