The Inventory Models for Deteriorating Items in the Discounted Cash-Flows Approach Under Conditional Trade Credit and Cash Discount in a Supply Chain System

Yang [20] studies a deteriorating inventory model in which the supplier simultaneously offers the retailer either a conditional delay in payments or a cash discount. While considering the same inventory problem as that of Yang [20] in a systematic manner, the main purpose of this paper is twofold: First of all, since Yang [20] does not seem to have defined his inventory problem precisely, this paper aims at remodeling this inventory problem from different viewpoints in order to derive formulations for APV(T), that is, the present value of all future cash flows, so that researchers and practitioners can understand the situation much more easily. Secondly, since the processes of proofs of Lemmas 1 and 2, and also of Theorems 1, 2 and 3 in Yang’s paper [20], have some shortcomings from the mathematical viewpoints, this paper applies rigorous analytic methods of mathematics to explore the functional behaviors of APV(T), not only to remove all of the shortcomings in Yang’s work [20], but also to present the complete rigorous mathematical proofs for the results asserted by Yang [20]