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内容提要

今天我们继续阅读英文期刊文献《Modeling and optimizing a multi‑period closed‑loop supply chain for pricing, warranty period, and quality management》，中文翻译可理解为《关于产品定价、保修期和质量管理的多周期闭环供应链模型与优化》，上期我们将学习了目标函数1，今天将继续学习目标函数的剩余部分。

Today we continue our reading of the English journal article Modeling and optimizing a multi-period closed-loop supply chain for pricing, warranty period, and quality management . In the last issue we will learn the objective function 1, and today we will continue to learn the remaining part of the objective function.

本期内容将从思维导图、精读内容和知识补充三部分展开。

In this issue, we will start with three parts: mind map, intensive reading content and knowledge supplement.

思维导图

精读内容

【库存持有成本】

文章指出库存持有成本是供应链的主要成本之一，是不可以忽略的关键因素。文章强调不允许出现短缺情况，即企业需要在任何周期内均满足消费者所有的新产品或维修产品的需求。

因此确定适当的库存控制政策对供应链的适当管理起着重要作用， 文章模型中的库存程序如下图图所示。

图的纵坐标为库存水平，横坐标为时间。可以看到在每一阶段，随着时间的增加，库存水平也在上升；在满足消费需求之后，会有部分产品剩余，依旧放在仓库中，产生库存成本。

The article identifies inventory holding costs as one of the major costs of the supply chain and a key factor that cannot be ignored. The article emphasizes that shortages are not allowed, i.e., companies need to meet all consumer demand for new or repaired products in any cycle.

Therefore, determining the appropriate inventory control policy plays an important role in the proper management of the supply chain, and the inventory procedure in the article's model is shown in the figure below.

The vertical coordinate of the graph is the inventory level and the horizontal coordinate is the time. It can be seen that at each stage, as time increases, the inventory level rises; after the consumer demand is met, there will be some products left over and remain in the warehouse, incurring inventory costs.

下面来看文章关于库存成本的具体模型构建。首先，

方程（8）显示了t-1期末的库存水平与t期初的库存水平相等，这里是可以从库存成本结构图中可以直接看出来的。

See the article below for a specific model construction on inventory costs. First.

Equation (8) shows that the inventory level at the end of period t-1 is equal to the inventory level at the beginning of period t. Here is what can be seen directly from the inventory cost structure diagram.

从公式（9）中，我们又可以得到t期结束时的库存数量。整个公式结合库存结构图来看，就是1阶段的剩余库存、t期末的需求量以及维修数量之和减去市场实际的需求。

From equation (9), we again get the quantity in stock at the end of period t. The whole formula, when viewed in conjunction with the inventory structure diagram, is the sum of the remaining inventory in period 1, the demand at the end of period t, and the number of repairs minus the actual demand in the market.

下面计算库存成本，其中Tt是生产Qt产品所花费的时间，等于Qt/ pr，其中pr是生产速度。

The following calculates the inventory cost, where Tt is the time taken to produce Qt products and is equal to Qt/ pr, where pr is the production rate.

库存成本计算完成之后，接着确定了销售新产品和维修产品中获得的总收入。

Once the inventory costing was completed, the total revenue earned from the sale of new and repaired products was then determined.

收入与成本计算完成后，最后提出了目标函数，即 最大化的CLSC模型的总利润如下。（收入减成本）

After the revenue and cost calculations are completed, the objective function is finally proposed. The total profit of the maximized CLSC model is as follows. (revenue minus cost)

知识补充

库存持有成本，则是指与企业产品库存相关的成本，包括库存投资资金成本、库存服务成本、仓储空间成本、库存风险成本等在内的相关成本。

库存会影响企业货物的周转率，以及是否能够快速响应消费者的需求。

在常规情况下，企业一般会考虑到经济订货批量，从经济的观点出发，在考虑库存的情况下，选择订货批量，使库存成本和订货成本合计最低。

Inventory holding costs, on the other hand, are the costs associated with a company's product inventory, including inventory investment capital costs, inventory service costs, storage space costs, inventory risk costs, and other related costs.

Inventory affects the turnover rate of a company's goods and its ability to respond quickly to consumer demand.

Under regular circumstances, companies generally consider the economic order lot, and from an economic point of view, choose an order lot that minimizes the combined cost of inventory and order cost while taking inventory into account.

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参考资料：谷歌翻译、百度百科；

参考文献：

[1] Keshavarz-Ghorbani F , Khamseh A A . Modeling and optimizing a multi-period closed-loop supply chain for pricing, warranty period, and quality management[J]. Journal of Ambient Intelligence and Humanized Computing, 2021(6).

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