Time Dependent Solutions to the (s, S) Inventory Problem

The transient solution for the probability density of the stock level is found for the (s, S) inventory model. The density is found at the end of each demand period and thus the solution is for discrete time. Results are obtained for general demand where there is zero delay in delivery of orders and where there is a λ-period delay in delivery. Examples are given for exponential demand and for gamma distributed demand.