The purpose of this paper concentrates on an economic production quantity model with the factors of imperfect quality and quantity discounts, in which the inspection action occurs during the production stage. There is specific consideration of there being a finite production rate, and the quantity discounts offered by the supplier serves the purpose of stimulating buying greater quantities. This is in contrast to EPQ models that do not take these added factors into consideration. The objective of this paper is to determine the setup cost reduction, which is a function of capital investment, and inventory lot size. An alternative solution procedure was developed that does not employ the Hessian Matrix concavity in the expected total profit. We develop an algorithm to determine the optimal solution for this model. Theoretical results are discussed and a numerical example is proposed. Managerial insights are also examined.

中文翻译：

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质量和数量折扣不完善的经济生产数量模型的最佳设置成本降低和批量大小

本文的目的集中在具有不完善的质量和数量折扣因素的经济生产数量模型中，其中在生产阶段进行检查动作。需要特别考虑的是生产速度有限，并且供应商提供的数量折扣是为了刺激购买更多数量。这与未考虑这些附加因素的EPQ模型形成对比。本文的目的是确定安装成本的降低，这是资本投资和库存批量的函数。已开发了一种替代解决方案，该解决方案未在预期的总利润中使用Hessian矩阵凹度。我们开发了一种算法来确定此模型的最佳解决方案。讨论了理论结果，并给出了数值例子。还对管理见解进行了检查。