The Dynamic Inventory Problem with Unknown Demand Distribution

In this paper we consider the dynamic inventory problem in which the demand distribution possesses a density belonging to either the exponential or range family of densities and having an unknown parameter. An a priori density is chosen for the unknown parameter. Using a Bayesian estimation scheme, inequalities are obtained for the optimal purchase policies as the amount of demand information varies. In addition, asymptotic expansions for the optimal policies are found as the number of observations of the demand becomes large. This paper extends the results of Scarf, [8].