On the optimality of a variable parameters inventory model for deteriorating items under trade credit policy

In most inventory models it is assumed that the parameters of the model do not vary with time, and that the payment of orders from the retailer to the supplier are made immediately on the receipt of these orders. Some suppliers, however, allow a certain fixed period to settle payment accounts. During this fixed period no interest is charged by the supplier, but beyond that period an interest, with the conditions agreed upon, is charged on the retailer. However, an interest can be earned by the retailer from the revenue that he receives during the given credit period. The objective of the retailer is to minimize his total relevant costs. In this paper we formulate and solve the problem for a general EOQ model in which shortages are allowed, but are partially backlogged, and all model parameters, including the cost parameters, are arbitrary functions of time. Then, we use rigorous mathematical methods to show that the obtained solution is unique and global optimal.