Decision making on stock levels in cases of uncertain demand rate

Inventory control is a typical problem of decision making. In this paper a periodic replenishment of stock, the spare parts being of one kind, is discussed for some cases when the demand rate is uncertain. The first decision, before all others in the sequence, is done by assuming an a priori distribution of demand rate. In time, as the demand process goes on, corrections of parameters of the a priori distribution are made according to the accumulated knowledge about past demand. This Bayesian approach to decision making based on learning about the uncertain demand rate is known for the case when the demand rate is unknown but constant. It is shown that this same approach can be used in some cases when the demand rate is unknown and not constant. Results are given and used for inventory control.