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A multiperiod single product nonstationary inventory problem is studied in which the system is reviewed at the beginning of each of a sequence of periods of equal length. The model has the following features. There are several classes of demand for the product in each period. The demands in different periods are independent but not necessarily identically distributed. The cost structure is nonstationary with the ordering cost being proportional to the amount ordered. Conditions are given that ensure that the base stock ordering policy is optimal and that the base stock levels in each period are easy to calculate. The results are based on the work given in the literature and on properties of stochastically ordered distributions that are developed in the paper. The case of a linear holding cost and a linear shortage cost is studied in detail.
Arthur F. Veinott (Fri,) studied this question.