Abstract This work analyzes an inventory system with stock-dependent demand and non-linear holding cost. It presents a new approach to maximize the return on investment, that is, the profit/cost ratio. When an inventory manager can invest in different projects and the resources are limited, it seems sensible to select those projects that provide a higher return on investment. Thus, the goal of the manager will be to find the inventory policy that gives a major return on investment. Note that the solution for the maximum profit per unit time does not necessarily match the solution of the maximum profit/cost ratio. Consequently, a new procedure to obtain the inventory policy that maximizes the return on investment should be proposed. In this paper, it is proved that maximizing the profit/cost ratio is equivalent to minimizing the inventory cost per unit of an item, instead of minimizing the inventory cost per unit time. The optimal policy can be obtained in a closed form and the replacement should be done when the stock is depleted. Thus, the inventory manager does not need to process a new order while there are items available in stock. This optimal solution is different from the other policies proposed for the problems of minimum cost or maximum profit per unit time. Finally, numerical examples are solved to illustrate the theoretical results and the solution methodology proposed in the work.

中文翻译：

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一种在依赖于库存的需求库存模型中最大化利润/成本比的新方法

摘要 这项工作分析了具有依赖于库存的需求和非线性持有成本的库存系统。它提出了一种最大化投资回报的新方法，即利润/成本比。当库存经理可以投资不同的项目并且资源有限时，选择那些提供更高投资回报的项目似乎是明智的。因此，经理的目标将是找到能够带来重大投资回报的库存政策。请注意，单位时间最大利润的解决方案不一定与最大利润/成本比的解决方案相匹配。因此，应该提出一个新的程序来获得最大化投资回报的库存政策。在本文中，事实证明，最大化利润/成本比相当于最小化一个物品的单位库存成本，而不是最小化单位时间的库存成本。最优策略可以以封闭形式获得，并在库存耗尽时进行替换。因此，库存经理无需在库存中有可用物品时处理新订单。这种最优解不同于针对单位时间最小成本或最大利润问题提出的其他策略。最后，对数值例子进行了求解，以说明工作中提出的理论结果和求解方法。当库存中有可用物品时，库存经理不需要处理新订单。这种最优解不同于针对单位时间最小成本或最大利润问题提出的其他策略。最后，对数值例子进行了求解，以说明工作中提出的理论结果和求解方法。当库存中有可用物品时，库存经理不需要处理新订单。这种最优解不同于针对单位时间最小成本或最大利润问题提出的其他策略。最后，对数值例子进行了求解，以说明工作中提出的理论结果和求解方法。