Supply Chain Management with Overtime and Premium Freight

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 can not meet the supply requests from inventory on hand, the shortage must be filled by either overtime production and/or premium freight shipments, both incurring per unit and setup costs. Overtime production occurs at the end of the period and incurs relatively high production costs; premium freight refers to building products at the beginning of the period they are needed and shipping them very quickly with relatively high shipping costs. Focusing primarily on the case where only one method of filling shortages is available, we 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 chain under centralized and decentralized control.