The complete proof on the optimal ordering policy under cash discount and trade credit

Huang (2005) investigates the buyer's optimal ordering policy and payment policy under supplier credit. His inventory model is correct and interesting. Basically, he uses an algebraic method to locate the optimal solution of the annual total relevant cost TRC(T) and ignores the role of the functional behaviour of TRC(T) in locating the optimal solution of it. However, as argued in this article, Huang needs to explore the functional behaviour of TRC(T) to justify his solution. So, from the viewpoint of logic, the proof about Theorem 1 in Huang has some shortcomings such that the validity of Theorem 1 in Huang is questionable. The main purpose of this article is to remove and correct those shortcomings in Huang and present the complete proofs for Huang.