Optimal policies for inventory systems with two priority demand classes

We consider a periodic review inventory system with two priority demand classes, one deterministic and other stochastic. The units of deterministic demand that are not satisfied will be punished in terms of the quantity, and the units of stochastic demand that are not satisfied are treated as lost sales. We propose a finite-horizon dynamic programming model, and characterize the structure of the optimal policy (include when to order, order quantity and how to fill the different demand). We show that the optimal order quantity and rationing policy are state dependent and do not have a simple structure.