Optimal adaptive estimators for partially observed numbers of defective items in inventory models

In this paper, three discrete time integer-valued inventory models for perishable items are introduced. In these models, each item in the stock is assumed to perish in a given period with some probability. The dynamics of the models are affected by a demand process, a replenishment process, and perishability. However perished items are not observed while in stock, unless sold. Recursive estimates for the probability of the number of the perished items are derived.