Optimal Ordering and Rationing Policies in a Nonstationary Dynamic Inventory Model with n Demand Classes

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Abstract
We consider the problems associated with an inventory system in which demands for stock are of n classes of varying importance. When demand from a given class arrives one must decide whether to satisfy it or to not satisfy it and conserve stock for possible use later to satisfy demand from a more important class. Conditions are given under which the optimal rationing policy between successive procurements of new stock is determined by a set of critical rationing levels such that at a given time one satisfies demand of a given class only if no demand of a more important class remains unsatisfied and as long as the stock level does not fall below the critical rationing level for that class at that time. Conditions are also given under which the optimal procurement policy at a given time is determined by a single critical level in the usual manner. Further conditions are given which assure that the optimal rationing and procurement policies may be determined myopically.

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