Managing Supply Chains with Expediting and Multiple Demand Classes

We consider a periodic review, single-stage inventory system with multiple demand classes and a fixed replenishment lead time. Inventory expediting is allowed to alleviate demand-supply mismatches. Priority demands are commonly used in practice to provide differentiated services for customers, and inventory expediting is an effective strategy to improve the service levels of high-priority demands. However, it is challenging to coordinate the inventory ordering, expediting and allocation decisions in supply chains. We partially characterize the structure of the optimal policy. We also derive various monotone properties of the optimal policy with limited sensitivities. Moreover, we show that a state-dependent rationing level policy is optimal for inventory allocation and the optimal rationing levels are in fact independent of the backorder quantity of each demand class. We also show when some simple policies are indeed optimal. Numerically, we illustrate the optimal policy and investigate the performances of three proposed simple heuristics. Finally, we extend the results to more general systems, such as serial systems, systems with convex backordering costs, etc.