Supply chain management with guaranteed delivery

We consider a two-stage supply chain under centralized control. The downstream facility faces discrete stochastic demand and passes supply requests to the upstream facility. The upstream facility always meets the supply requests from downstream. If the upstream facility cannot meet the supply requests from inventory on hand, the shortage must be filled by expediting, which will incur per unit and setup costs. Such expediting may take the form of overtime production, which occurs at the end of the period and incurs relatively high production costs, or premium freight shipments, which involves building products at the beginning of the period they are needed and shipping them very quickly with relatively high shipping costs. We consider the case where one method of filling shortages is available and determine novel optimal inventory policies under centralized control. At both stages, threshold policies that depend only on the current inventory in the system are optimal; for the total inventory in the system, a base-stock policy is optimal. Numerical analysis provides insight into the optimal policies and allows us to compare the supply chains under centralized and decentralized control.