Probabilistic order level system with a mixture of backorders and lost sales

This article presents probabilistic order level inventory model for situations in which during the stockout period, αth fraction of the demand is back ordered and the remaining fraction (1−α) is lost. A mathematical model representing the average annual cost of inventory system and optimum order level is derived. At extremes α = 1 and α = 0, the models reduce to the usual back order and lost sales cases respectively.