On the optimality of (s,S)-strategies in a minimax inventory model with average cost criterion

A stochastic dynamic inventory problem is considered in which the distribution function of the demand and the holding and shortage cost depend on an unknown parameter. This problem is interpreted as a Markov game with complete information. It is shown that for the average cost criterion as for the discounted cost criterion an optimal (s,S)-strategy exists. Bounds for the parameters of such a strategy are given.