An Inventory Problem with Discrete Time Review and Replenishment by Batches of Fixed Size

An inventory system under periodic review is considered. If at the time of review the stock has fallen below a given level, L, a fixed quantity, Q, is ordered; otherwise no action is taken. It is assumed that delivery time is negligible. Two costs are considered to be of importance: one proportional to the average overage, the second proportional to the average shortage. Under exponential demand assumptions optimal values of L and Q are obtained.