Optimal policies of an inventory system with multiple demand classes

This paper deals with a periodic review inventory system serving multiple demand classes that are differentiated by the treatment for shortages. Shortages of some classes were treated according to lostsales, while those of the others were backlogged. In each period, both replenishment decisions of inventory and allocation for all classes were made by a setup cost for each replenishment. By using the approach of stochastic dynamic programming formulation, the optimal replenishment policy is a state-dependent (8, S) policy, and the optimal allocation decision follows a state-dependent prioritization policy.