We consider a periodic review inventory system with two priority demand classes, one deterministic and the other stochastic. The deterministic demand must be met immediately in each period. However, the units of stochastic demand that are not satisfied during the period when demand occurs are treated as lost sales. At each decision epoch, one has to decide not only whether an order should be placed and how much to order, but also how much demand to fill from the stochastic source. The firm has the option to ration inventory to the stochastic source (i.e., not satisfy all customer demand even though there is inventory in the system). We first characterize the structure of the optimal policy. We show that, in general, the optimal order quantity and rationing policy are state dependent and do not have a simple structure. We then propose a simple policy, called (s, k, S) policy, where s and S (ordering policy) determine when and how much to order, while k (rationing policy) specifies how much of the stochastic demand to satisfy. We report the results of a numerical study, which shows that this simple policy works extremely well and is very easy to compute.

Abstract:We consider a make-to-order production system where two major components, one nonperishable (referred to as part 1) and one perishable (part 2), are needed to fulfill a customer order. In each period, replenishment decisions for both parts need to be made jointly before demand is realized and a fixed ordering cost is incurred for the nonperishable part. We show that a simple (s n , S 1 n , S 2 n ) policy is optimal. Under this policy, S 2 n along with the number of backorders at the beginning of a period if any and the availability of the nonperishable part (part 1) determines the optimal order quantity of the perishable part (part 2), while (s n , S 1 n ) guide when and how much of part 1 to order at each state. Numerical study demonstrates that the benefits of using the joint replenishment policy can be substantial, especially when the unit costs are high and/or the profit margin is low.