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Optimal retailer's replenishment decisions for EPQ model under up-stream and down-stream trade credit financing

The traditional economic order quantity models usually assume that the purchasing cost must be paid for the items as soon as the items are received. However, in practice trade credit is one of the main measures to promote the sale of goods. On the other hand, the retailer would offer the trade credit period to his/her customers. That is a two-level trade credit. In this paper, we develop an EPQ model for deteriorating items under two-level trade credit, where the demand rate of the items is dependent on the current stock level, and the inventory system with inventory-level-dependent demand rate is further extended. Then we provide the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions that could make the average cost per unit time to a minimum. Easy solution methods are shown to find the optimal replenishment policy of the considered problem and some theoretical evidences are provided for retailers to make the practical inventory decision. At last, numerical examples are presented to illustrate the developed model.