Abstract We consider the Economic Order Quantity (EOQ) model for exponentially deteriorating items in which the items deteriorate at a rate proportional to the inventory level per unit time, which leads to an exponentially decreasing inventory level function over time. The coexistence of the exponential and polynomial terms in the total cost function makes closed-form exact solutions impossible, so approximations are used. Methods that optimize management science models without derivatives have recently been used to provide insights to managers who may not have a background in calculus. We propose such an approach for the deteriorating items inventory model with and without planned backorders and compare it with an existing one. Our derivation is much simpler and succinct; our closed-form solution is more intuitive than the existing one. We conduct numerical experiments to analyze the accuracy of the closed-form solution.

中文翻译：

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EOQ 模型优化解决方案的简单推导，用于有计划延期交货的恶化项目

摘要 我们考虑了经济订货量 (EOQ) 模型，用于指数恶化的物品，其中物品的恶化速度与每单位时间的库存水平成正比，这导致库存水平函数随着时间的推移呈指数下降。总成本函数中指数项和多项式项的共存使得封闭形式的精确解不可能，因此使用近似值。最近，在没有导数的情况下优化管理科学模型的方法已被用于为可能没有微积分背景的管理人员提供见解。我们为有和没有计划缺货的不断恶化的物品库存模型提出了这样一种方法，并将其与现有的方法进行比较。我们的推导要简单得多；我们的封闭式解决方案比现有解决方案更直观。