Some results for the dynamic (s, S) inventory model *

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.