Inventory policies for systems with stochastic and deterministic demand

We consider a periodic review inventory system with demand arriving simultaneously from a deterministic source and a random source. The deterministic demand has to be satisfied immediately and the stochastic demand can be backordered. Assuming that the stochastic demand is never backlogged if there is stock in the system, we prove that a modified (s, S) policy is optimal under general conditions if there is a setup cost. If there is a smoothing cost instead of the setup cost, we observe that the problem corresponds to a standard model with one source of demand.