Inventory models with a mixture of backorders and lost sales

This article presents several single‐echelon, single‐item, static demand inventory models for situations in which, during the stockout period, a fraction b of the demand is backordered and the remaining fraction 1 ‐ b is lost forever. Both deterministic and stochastic demand are considered. although the case of stochastic demand is treated heuristically. In each situation, a mathematical model representing the average annual cost of operating the inventory system is developed. and an optimum operating policy derived. At the extremes b =1 and b =0 the models presented reduce to the usual backorders and lost sales cases, respectively.