A lot-size model with partial backlogging when the amount received is uncertain for deteriorating items

In most of the existing economic lot-size models, the demand during the stockout period is either completely backordered or lost, and units in inventory do not deteriorate. A lot-size model is developed in which the demand during the stockout period is partially backordered and partially lost, the quantity received is uncertain, and units in the inventory deteriorate at a constant rate. The standard deviation of the quantity received is taken to be either independent of or proportional to the quantity ordered. The results obtained are shown to be extensions of well-known results of a lot-size model with backordering.