A finite-horizon inventory system with partial backorders and inventory holdback

Abstract We consider a periodic-review base stock inventory system with partial backorders. At the beginning of each period t of a T period problem, an order of size q t is placed for delivery one period later. As the stochastic demand is realized, as much as possible of it is filled immediately from the inventory on-hand. If the realized demand exceeds the inventory on-hand, up to q t – k t units of excess demand are backordered to be filled from the pipeline inventory or future orders. The on-order quantity k t denotes the reservation quantity held back for use in subsequent periods. The case k t = q t yields the full lost sales model while the case k t = − ∞ yields the full backorder model.