The complete solution procedures for the mathematical analysis of some families of optimal inventory models with order-size dependent trade credit and deterministic and constant demand

By suitably combining the investigations by Ghare and Schrader (1963) [5], Dolan (1987) [4] and Huang and Chung (2003) [7], Kreng and Tan (2011) [8] consider and analyze the optimal inventory policies with order-size dependent trade credit under delayed payment and cash discount. The mathematical analysis of Kreng and Tan (2011) [8] is based upon an inventory model for deteriorating items with trade credit and cash discount linked to the order quantity. Motivated by the potential for practical applications of such inventory models as those that are considered in (for example) the aforecited works, we address some shortcomings in the 2011 paper by Kreng and Tan (2011) [8]. We emphasize upon the invalidity of an important assumption by Kreng and Tan (2011) [8], namely that the deterioration rate is small, provide a counterexample to Kreng and Tan's Theorem 1 and question the results of Kreng and Tan's Theorems 2 and 3. We present our own observations and results as theorems and proofs. We thus have not only removed the aforementioned shortcomings in the paper by Kreng and Tan (2011) [8], but we have also provided the complete solution procedures for some of the aforementioned models. Finally, some numerical examples are used to compare the results, which are presented in this paper, with those of the aforecited earlier investigations.