Optimal replenishment and payment policies in the EOQ model under cash discount and trade credit

This paper deals with the problem of determining the economic order quantity under conditions of cash discount and trade credit. Goyal is the first person to consider the economic order quantity under condition of permissible delay in payments. In this paper, incorporating the cash discount policy for early payment into Goyal's model is a new issue. The main purpose of this paper is to extend Goyal's model with cash discount to reflect the real-life business situations. Mathematical models have been derived for obtaining the optimal cycle time and optimal payment policy for item under cash discount and trade credit so that the annual total relevant cost is minimized. First, this paper shows that the annual total relevant cost functions are convex. Second, with convexity, two theorems are developed to determine the optimal cycle time, optimal order quantity and the optimal payment policy. Finally, numerical examples are solved to illustrate the results given in the paper.