In this paper, a model for an inventory whose stock decreases with time is considered. When a deliveryman arrives, if the level of the inventory exceeds a threshold $alpha$, no stock is delivered, otherwise a delivery is made. It is assumed that the size of a delivery is a random variable Y which is exponentially distributed. After assigning various costs to the model, we calculate the long-run average cost and show that there exist unique value of arrival rate of deliveryman $alpha$, unique value of threshold $alpha$ and unique value of average delivery m which minimize the long-run average cost.