Abstract
Summary The periodic review, single item, stationary (s, S) inventory model is considered. There is a fixed lead time, a linear purchase cost, a fixed set‐up cost, a holding and shortage cost function, a discount factor 0 < α≤ 1 and backlogging of unfilled demand. The solution for the total expected discounted cost for the finite period (s, S) model is found. In addition the time dependent behaviour of the inventory process is found. Further a limit theorem is given, which relates the total expected cost for the finite period (s, S) model with no discounting to the average expected cost per period for the infinite period (s, S) model. As a by‐product we obtain known results for the infinite period (s, S) model.
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