This paper presents a single-echelon, single item, stochastic lead time and static demand inventory model for situations in which, during the stockout period, a fraction ${eta}$ of the demand is backordered and the remaining fraction $(1-{eta})$ is lost. In this situations, an objective function representing the average annual cost of inventory system is obtained by defining a time-proportional backorder cost and a fixed penalty cost per unit lost. The optimal operating policy variables minimizing the average annual cost are calculated iteratively. At the extremet ${eta}=1$, the model presented reduces to the usual backorder case. A numerical example is solved to illustrate the algorithm developed.