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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》，上次对阅读该文章的摘要部分，本期进入引言的阅读。

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 . Last time we read the abstract section of the article, and in this issue we move on to the introduction.

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

【研究背景/必要性】

引言部分，首先还是指出研究背景，指出回收是一个为旧产品或可修复产品增加重要价值的过程，它有助于企业和政府节约成本和自然资源。在现实中，不同产品的生产创新会导致产品寿命缩短，为了给未来的世代节约能源，回收再造则是一种即经济又环保的方法。作者提出这一概念之后，回顾了前人学者关于闭环供应链，回收再造的研究，指明关于这一问题研究的必要性。

The introduction section, again, begins by pointing out the background of the study, stating that recycling is a process that adds significant value to old or repairable products, which helps companies and governments to save costs and natural resources. In reality, innovations in the production of different products can lead to shorter product lifetimes, and recycling is an economical and environmentally friendly way to save energy for future generations. After introducing this concept, the authors review the previous research on closed-loop supply chains, recycling, and indicate the need for research on this issue.

随后，文章指出不同质量等级的退货是由预先定义的比例决定的，这些比例是由历史数据、专家意见等获得的，在可用数据较少的不确定情况下，可以利用概率理论对回报进行适当的分类。在此文中，作者提出与年龄有关的二手产品质量等级，退货的质量取决于他们的年龄。

The article then shows that returns of different quality grades are determined by predefined proportions obtained from historical data, expert opinions, etc. In the case of uncertainty with little available data, the returns can be classified appropriately using probability theory. In this paper, the authors propose age-related quality grades for used products, where the quality of returns depends on their age.

基于上述研究，作者指出文章以一个多周期的CLSC（闭环供应链）为研究对象，提出一个处理CLSC模型中价格敏感需求、购置成本和保修成本领域的流的数学模型，必要确定一个适当的策略，包括定价、保修期和收购成本，作为激励顾客购买二手产品。

Based on the above research, the authors point out that the article takes a multi-cycle CLSC (closed-loop supply chain) and proposes a mathematical model that deals with the flow of price sensitive demand, acquisition cost and warranty cost areas in the CLSC model necessary to determine an appropriate strategy, including pricing, warranty period and acquisition cost, as an incentive for customers to purchase used products.

【文献综述】

相关文献综述，第一类是研究人员对CLSC中价格依赖需求和收购成本管理相关问题进行了研究。大部分学者通过模型构建基于不同因素下，研究了产品质量、价格的策略制定。另一个文献研究与CLSC问题中的产品保修有关。学者们对保修期对产品的购买意愿等方面的影响进行了研究分析。

The first category of the related literature review is that researchers have studied the issues related to price dependent demand and acquisition cost management in CLSC. Most of the scholars have studied the strategy development of product quality and price through model construction based on different factors. Another literature study is related to the product warranty in CLSC problem. Scholars have studied and analyzed the effect of warranty period on aspects such as purchase intention of the product.

【研究贡献】

倒数第二段作者对文的贡献做了总结。

一是文章考虑了一个多时期的闭环供应链，将计算出维修的最佳次数以提升旧产品的质量。

The authors of the penultimate paragraph summarize the contributions of the article.

One is that the article considers a multi-period closed-loop supply chain that will calculate the optimal number of repairs to improve the quality of the used product.

二是产品的需求是关于保修期时间和销售价格的函数；二手产品的退货率是二手产品的购置成本和退货年龄的函数。

Two, the demand for the product is a function about the duration of the warranty period and the sales price; the return rate of the used product is a function of the acquisition cost of the used product and the age of the return.

三是此文对退货产品的收购成本，产品的销售价格，库存成本，以及为生产计划安装额外能力的成本的确定进行求解，并优化。

Third, this paper solves for and optimizes the determination of the acquisition cost of the returned product, the selling price of the product, the inventory cost, and the cost of installing additional capacity for the production plan.

四是文章提供遗传算法、粒子群优化算法和入侵性杂草优化算法来解决所提出的混合整数井线性（MINLP）模型。

Fourth, the paper provides genetic algorithm, particle swarm optimization algorithm and invasive weed optimization algorithm to solve the proposed mixed integer well linear (MINLP) model.

【研究思路与框架】

文章在第2节介绍了模型所需假设和符号。第3节描述了一个闭环供应链的MINLP模型。在第4节中介绍了三种不同的解决方案。第5节介绍了三种元后发式算法的解决程序，用上述算法求解的数值例子，并用相对性能偏差方法对其主要参数进行了校准。在第6节中，提供了管理方面的见解。最后，第7节捋提出结论和未来方向。

The article presents the required assumptions and notation for the model in Section 2. Section 3 describes a MINLP model for a closed-loop supply chain. Three different solutions are presented in Section 4. Section 5 presents the solution procedures for the three meta-posteriori algorithms, numerical examples solved with the above algorithms, and calibrated with relative performance deviation methods for their main parameters. In Section 6, management insights are provided. Finally, Section 7 stroke presents conclusions and future directions.

知识补充

混合整数非线性规划

当数学模型中需要对整数变量或者离散变量进行优化，且目标函数或者约束函数为非线性函数，则为整数非线性规划。但是当变量既有部分为整数变量也有部分为连续变量时就成为混合整数非线性规划。

When the mathematical model requires optimization of integer variables or discrete variables, and the objective function or constraint function is nonlinear, then it is integer nonlinear programming. However, when the variables are both partly integer and partly continuous, it becomes mixed integer nonlinear programming.

具体的混合整数非线性规划模型可以表述为下图所示的公式。

The specific mixed-integer nonlinear programming model can be formulated as shown in the following equation.

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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).

[2]达林. 切平面在混合整数非线性规划中的应用[D].北京交通大学,2009.

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