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首页> 外文期刊>Applied mathematics and computation >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
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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

机译：带有订单规模相关贸易信贷以及确定性和恒定需求的一些最优库存模型系列的数学分析的完整解决方案

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摘要

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.
机译：通过适当地结合Ghare和Schrader（1963）[5]，Dolan（1987）[4]和Huang and Chung（2003）[7]的研究，Kreng和Tan（2011）[8]考虑并分析了最佳库存策略在延迟付款和现金折扣下具有与订单大小相关的贸易信贷。 Kreng and Tan（2011）[8]的数学分析是基于库存模型，该模型用于使具有恶化的商品的贸易信贷和现金折扣与订单数量相关联。受到诸如（例如）上述著作中所考虑的库存模型的实际应用潜力的启发，我们解决了Kreng和Tan（2011）[8]在2011年论文中的一些不足。我们强调了Kreng和Tan（2011）[8]的一个重要假设的无效性，即劣化率很小，提供了Kreng和Tan定理1的反例，并对Kreng和Tan定理2和3的结果提出了质疑。我们以定理和证明提出我们自己的观察和结果。因此，我们不仅消除了Kreng和Tan（2011）[8]在论文中提到的上述缺点，而且还为某些上述模型提供了完整的解决程序。最后，使用一些数值示例将本文介绍的结果与上述先前研究的结果进行比较。

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