A Saddle Point of aD Inventory Problem

When the demand distribution is unknown, that is, most of the informations of it are insufficient for a definite probability distribution, a minimax procedure is sometimes used in an inventory problem. The minimax inventory problem is considered as a 2-person zero-sum game, in which one player (manager) decides his ordering level and other player (nature) chooses her distribution in the prescribed class of distributions. We shall show the necessary and sufficient conditions for the existeuce of saddle points in this problem, and give the explicit formula for a set of saddle points and a saddle value. A multi-period model is also discussed.