Inventory model with partial backorders

This article presents a deterministic inventory model for situations in which, during the stockout period, a fraction j8 of the demand is backordered and the remaining fraction 1 — β is lost. By defining a time proportional backorder cost and a fixed penalty cost per unit lost, a convex objective function representing the average annual cost of operating the inventory system is obtained. The optimal operating policy variables are calculated directly. At the extremes β = 1 and β = 0 the model presented reduces to the usual backorders and lost sales case, respectively.