A simple method to locate the optimal solution for exponentially deteriorating items under trade credit financing

In this paper, we discuss a paper of Chang and Teng [C.T. Chang, J.T. Teng, Retailer’s optimal ordering policy under supplier credits, Mathematical Methods of Operations Research 60 (2004) 471–483], they established an inventory model for deteriorating items when the supplier permits not only a cash discount but also a permissible delay. They also proved a closed-form solution of the inventory system under their assumption. Herein, we consider a deteriorating item that follows an exponential distribution. Thus, Chang and Teng [C.T. Chang, J.T. Teng, Retailer’s optimal ordering policy under supplier credits, Mathematical Methods of Operations Research 60 (2004) 471–483] is a special case in our model. The main purpose of this paper is threefold: First, we show that the total variable cost per unit time is convex by a rigorous proof. Second, with convexity, the optimal solution procedures to find the optimal ordering policy, which is independent of Chang and Tengs’ assumption, and bounds for the optimal ordering time are provided. Third, we compare optimal solutions obtained by using our approach and Chang and Tengs’ approach. Finally, sensitivity analysis is performed to study the effects of changing parameters values on the optimal solution.