An Algebraically Derived Minimal Cost Solution Technique of the EOQ Model Under Conditional Trade Credit

In 1985, Goyal considered the retailer’s inventory replenishment problem under trade credit independent of the order quantity and the retailer’s unit selling price and the purchasing price per unit were equal. In this paper, the restrictive assumptions of the trade credit independent of the order quantity and the retailer’s unit selling price equaled to the purchasing price per unit are relaxed to fit real business situations. This paper investigates the retailer’s inventory problem under trade credit dependent of the order quantity and the retailer’s unit selling price not necessarily equals to the purchasing price per unit within the economic order quantity (EOQ) framework. In addition, we adopt the algebraic procedure to determine the retailer’s optimal ordering policy under minimizing the annual total variable cost. This algebraic approach could therefore be used easily to introduce the basic inventory theories to younger students who lack the knowledge of calculus. Then, two theorems are developed to efficiently determine the optimal cycle time and optimal order quantity for the retailer. Finally, numerical examples are given to illustrate these theorems and obtain a lot of managerial insights.