Inventory Control with Generalized Expediting

We consider a single-item, periodic review inventory control problem where discrete stochastic demand must be satisfied. When shortages occur, the unmet demand must be filled by some form of expediting. We allow a very general form for the cost structure of expediting, including the special case of lost sales. Examples of expediting are overtime production, where production is allowed above and beyond shortfall, and premium freight shipments, where backlogged products are built early the same period they are needed and then shipped very quickly. For the infinite horizon discounted problem, we characterize the structure of the optimal expediting policy and show that an (s, S) policy is optimal for regular production. In certain cases we demonstrate that it may be optimal to use overtime production to build up inventory over and above the shortfall. A numerical study is provided to add insight into the results.