A Family of Dynamic Inventory Models

Abstract

A family of inventory models in which demand is allowed to change with time is studied. One general model is presented which includes every member of the “family” as a special case. The general model assumes that demand is a random variable. The mean rate of demand may vary over time but demands in different time periods are assumed independent. It is assumed that there is a date of obsolescence for the item with no demands occurring after this date. The time of obsolescence may be either known or alternatively a finite number of obsolescence dates and their probable occurrence may be specified. Procurement lead times are allowed to be random variables, subject to certain restrictions which are discussed. Procurements are allowed only at a finite number of predetermined times which may be specified in any way desired. Demands occurring when the system is out of stock are assumed to be backordered. The procurement quantities are determined by solving a dynamic programming problem which minimizes the sum of the expected costs of procurement, carrying inventory, stockouts, and losses from obsolescence. The dynamic programming problem is within the range of feasibility computationally, because only tables involving a single parameter are required. A number of special cases of the general model are studied and it is shown that most dynamic models which have appeared in the literature are special cases of the general model.

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