The Inventory Model for Deteriorating Items under Conditions Involving Cash Discount and Trade Credit

In the year 2004, Chang and Teng investigated an inventory model for deteriorating items in which the supplier not only provides a cash discount, but also allows a permissible delay in payments. The main purpose of the present investigation is three-fold, as follows. First, it is found herein that Theorem 1 of Chang and Teng (2004) has notable shortcomings in terms of their determination of the optimal solution of the annual total relevant cost Z(T) by adopting the Taylor-series approximation method. Theorem 1 in this paper does not make use of the Taylor-series approximation method in order to overcome the shortcomings in Chang and Teng (2004) and alternatively derives all the optimal solutions of the annual total relevant cost Z(T). Secondly, this paper systematically revisits the annual total relevant cost Z(T) in Chang and Teng (2004) and presents in detail the mathematically correct ways for the derivations of Z(T). Thirdly, this paper not only shows that Theorem 1 of Chang and Teng (2004) is not necessarily true for finding the optimal solution of the annual total relevant cost Z(T), but it also demonstrates how Theorem 1 in this paper can locate all of the optimal solutions of Z(T). The mathematical analytic investigation presented in this paper is believed to be useful for correct managerial considerations and managerial decisions.