Optimal Policy For An Inventory System With Stochastic And Deterministic Demand

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 will use rationing policy to manage inventory system.We first give an example of the inventory system, and propose a dynamic programming model. Then we 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 asimple structure. Finally, we propose a simply policy, called (s,w,S) policy, wheres and S (ordering policy) determine when and how much to order, while w(rationing policy) specifies how much of total demand to satisfy. We report the results of a numerical study, which shows that this simple policy works very well.