Optimal retailer's replenishment policy for the EPQ model under the supplier's trade credit policy

This paper investigates the optimal replenishment policy under conditions of permissible delay in payments within an economic production quantity (EPQ) framework. In 1985, Goyal assumed that: (1) The unit selling price and the unit purchasing price are equal. (2) The replenishment rate is infinite. (3) At the end of the credit period, the account is settled. The retailer starts paying for higher interest charges on the items in stock and returns money of the remaining balance immediately when the items are sold. The main purpose of this paper is to modify Goyal's model to presume that the unit selling price and the unit purchasing price are not necessarily equal to reflect the real-life situations, and assumes the replenishment rate is finite. Furthermore, this paper will propose that at the end of the credit period, the retailer will make a partial payment on total purchasing cost and pay off the remaining balance by loan from the bank. One theorem is obtained to explore the convexity of the total annual relevant cost function. Three theorems are developed to determine the optimal cycle time and the optimal order quantity. Numerical examples are given to illustrate these theorems.