The Inventory Model for Deteriorating Items under Conditions Involving Cash Discount and Trade Credit - Kun-Jen Chung; Jui-Jung Liao; Shy-Der Lin; Sheng-Tu Chuang; Hari Mohan Srivastava (Mathematics, 2019)
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 <semantics> Z ( T ) </semantics> 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 <semantics> Z ( T ) </semantics> . Secondly, this paper systematically revisits the annual total relevant cost <semantics> Z ( T ) </semantics> in Chang and Teng (2004) and presents in detail the mathematically correct ways for the derivations of <semantics> Z ( T ) </semantics> . 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 <semantics> Z ( T ) </semantics> , but it also demonstrates how Theorem 1 in this paper can locate all of the optimal solutions of <semantics> Z ( T ) </semantics> . The mathematical analytic investigation presented in this paper is believed to be useful for correct managerial considerations and managerial decisions.