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 lost-sales,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（s,S） policy,and the optimal allocation decision follows a state-dependent prioritization policy.
