Analytical and computational solution of adaptive inventory processes (Q1060674)

The authors consider a stochastic inventory model based on the early paper of \textit{H. Scarf} [Ann. Stat. 30, 490-508 (1959; Zbl 0089.368)], where the demand density is a member of the \(\Gamma\) family and is known up to an unknown parameter. Furthermore, it is assumed that there are no set-up costs. A mathematical model of the adaptive inventory control process is given and it is shown that the optimal policy is to order up to a certain inventory level. For the computation of this optimal level, a numerical method is devised. Finally, solutions are compared to the cases where the demand distribution is assumed to be exactly known or completely unknown.