# Analysis and Evaluation of Key Elements of Optimal Regulation of Green Supply Chain from the Perspective of Low Carbon

Authors: Zhenhua Dai; Chunming Ye
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

Economic globalization competition leads to rapid replacement of green products, large demand fluctuations, and prominent problems in green supply chain management. Based on the traditional supply chain performance evaluation theory, this paper introduces the low-carbon perspective, adopts the comprehensive optimization method to screen the indicators, and constructs the evaluation index system of the key elements of green supply chain optimization from the five dimensions of financial value, supply chain internal process, customer service level, innovation and learning, and low-carbon development. Then, the expert ranking method and the subjective and objective method of coefficient of variation are used to simulate the weight of indicators.


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## Body

## 1. Introduction

With the intensification of global warming, energy shortage and environmental pollution, low-carbon economy, energy conservation, and emission reduction have become the focus of social attention [1]. Building a green supply chain is of far-reaching significance to enterprises and society [2]. In recent years, with the rapid development of social economy, the supply chain system is restricted by many complex factors, such as the uncertainty of supply and demand in the supply chain system, the psychological behavior of system decision-makers, the environment of market competitors, and consumers’ low-carbon preference. The supply chain system becomes more and more complex, with the characteristics of nonlinearity, sensitivity, and complexity. Economic globalization competition leads to rapid renewal of green products and large demand fluctuations, which leads to prominent problems in green supply chain management. It is very important to identify the key elements in the supply chain and optimize the regulation of the green supply chain.At present, green supply chain management has attracted the high attention of many scholars at home and abroad. The research related to this paper mainly focuses on the following two aspects: first, the optimization and regulation of green supply chain. Tehrani and Gupta proposed a sustainable and environmentally friendly closed-loop green supply chain network for the tire industry and optimized the network using a robust fuzzy stochastic programming method [3]. Ahmadini et al. proposed a multiproject optimization inventory model considering green investment with the goal of protecting environment and demonstrated the effectiveness of the model numerically [4]. In order to minimize the cost and carbon emission of supply chain, Zhang et al. established a multiobjective uncertain equilibrium model of green supply chain network and used weighted ideal point method and constraint method to solve the multiobjective model [5]. Wang et al. studied the pricing decision of a dual-channel green supply chain composed of a single manufacturer and a single retailer, and on this basis proposed three pricing models to analyze the optimal decision of supply chain members [6]. Kumar et al. developed a strategy based on the manufacturers’ advanced payment policies and trade credit facilitation for retailers and finally obtained a green supply chain regulation model that optimized the retailers’ sales efforts, wholesale prices required by manufacturers, greenness of products, and sales prices influenced by retailers [7]. Aiming at a two-level green supply chain, Lin discusses the impact of retailers’ corporate social responsibility on supply chain pricing and manufacturing strategy through game theory. The results show that the manufacturers’ wrong estimation of retailers’ corporate social responsibility is unfavorable to themselves. However, when manufacturers overestimate, it is beneficial to consumers and retailers and gives the conditions for retailers’ information sharing [8]. Li et al. constructed a Stackelberg game model of dual-channel green supply chain composed of a single manufacturer and a single retailer in the context of fuzzy demand market, considering the fair preference behavior of manufacturers. The effects of consumers’ environmental awareness and green manufacturers’ fair preference behavior on the decision-making and benefits of green supply chain members are discussed through an example analysis [9]. Emergency disposal is a method to deal with major natural disasters or public health emergencies, including the location of emergency logistics center, material distribution, and transportation route planning [10, 11].On the other hand, the key elements of green supply chain are analyzed and evaluated. Based on the procurement management model proposed by Kraljic in 1983, Garzon et al. proposed a supplier green procurement evaluation method that included all green attributes [12]. Li and Liu adopted the analytic hierarchy process (AHP) to analyze the factors that affect the performance of fresh agricultural supply chain under the cloud logistic model and determine the influence degree of each factor [13]. After an in-depth analysis of the key elements of green supply chain, Chen and Xu established multiobjective programming model and network DEA model and determined the weight of each subsystem by AHP [14]. From the perspective of green supply chain management, Luo et al. adopted two methods of “R-clustering” and “coefficient of variation analysis” to construct a performance evaluation system of green supply chain in transportation industry [15]. Amini et al. evaluated the adverse outputs of GHG green supply chain management by establishing a multiobjective network data envelopment analysis model [16]. Lu and Song made an in-depth analysis of the key elements of the optimization and regulation of the green supply chain of retail enterprises and used the data envelopment analysis method to solve the constructed green supply chain performance evaluation index system [17]. Effendi et al. took PG Krebet Baru as an example to analyze the key elements of the company’s green supply chain performance evaluation and used the DEMATEL method to identify supply chain alternatives [18]. Liu et al. found that when the government adopts static measures, there is no stable equilibrium point in the game between the government and enterprises, while when the government adopts dynamic punishment or subsidies, there is a stable equilibrium point in the evolutionary game [19]. Amaladhasan et al. proposed the application of ecological balanced scorecard to evaluate key performance indicators of green supply chain of automobile enterprises [20].To sum up, many scholars have studied the optimization and regulation of green supply chain and the analysis and evaluation of key elements of green supply chain [21–25]. Few scholars consider optimizing the regulation of green supply chain through the analysis of key elements [26–29]. From this point of view, this paper introduces the low-carbon concept; establishes the green supply chain evaluation index including the low-carbon dimension through the comprehensive induction method; establishes the evaluation index system of key elements of green supply chain optimization and regulation by using the set filtering method, weight filtering method, and fuzzy cluster purification method; and finally calculates the importance of each evaluation index through simulation [30]. The innovation of this paper is reflected in the detailed analysis of the key factors affecting the optimal regulation of green supply chain and the integration of low-carbon concept into the index evaluation system of green supply chain. This research is of great significance for optimizing the operation of green supply chain, improving China’s environmental problems and maintaining the competitiveness of enterprises.


## 2. Analysis of Supply Chain Elements

Traditional supply chain management takes customer demand as the center, coordinates, and controls information flow, logistics, and capital flow in each link of supply chain in a planned and organized way. Green supply chain management focuses on resource utilization and environmental impact on the traditional management mode. It is a modern management mode based on the green manufacturing theory and supply chain management technology, which minimizes the impact of products on the environment during the life cycle and maximizes the resource utilization. As a process that the industry must go through, the development of green supply chain is still in the process of continuous exploration, facing many problems that need to be solved, among which, how to realize the key elements of optimal regulation of green supply chain is an important perspective. In order to reduce costs and improve production factors, circulation enterprises mainly realize the objectives of the supply chain by optimizing the division of labor and cooperation between circulation enterprises, producers, and consumers, strengthening the control of the supply chain and making up for weaknesses through management innovation.Around this problem, the key elements of supply chain are studied, aiming to find a suitable operation mode for the development of low-carbon economy by optimizing and adjusting the key elements. There are four main research methods for constituent elements in existing research theories: three-point method, four-point method, five-point method, and nine-point method. Alt, Zimmerman, Betz, and other scholars have also made different divisions. The above methods are complementary in content and can be integrated with the operation system, value proposition, and profit model based on value triangle logic. The elements of the supply chain are classified in Table1.Table 1
Composition of supply chain elements.
General categorySubclassResources and activities to provide valueEnterprise internal value chainCore competenceCostNetwork of partnerships with other stakeholders in value deliveryCooperative networkForm of valueProducts or servicesChannelCustomer relationshipFor whom to create valueWays of value realization and ways of income


## 3. Evaluation Model of Key Elements of Supply Chain Optimization

### 3.1. Acquisition and Selection of Evaluation Indicators

The selection of index system is directly related to the scientific nature, objectivity, and accuracy of the research conclusion and is the core step of the evaluation of key elements. Figure1 is the relationship between indicator selection principles.Figure 1
Relationship between indicator selection principles.There are many methods of index screening, such as principal component analysis, factor analysis, AHP, K-L information method, peak valley correspondence method, TDOA correlation analysis method, cluster analysis method, and comprehensive induction method. Based on the theoretical research on supply chain optimization and regulation, the key indicators are selected through analysis and evaluation, and then the comprehensive induction method is adopted to further optimize the selection of indicators. Comprehensive induction can combine objective statistical analysis data with subjective scientific description data and ensure the scientific nature and effectiveness of index selection to a certain extent. Figure2 shows specific process for determining the index system.Figure 2
Specific process for determining the index system.


### 3.2. Construction of Evaluation Index for Key Elements of Supply Chain Optimization

Based on the existing theoretical research on supply chain optimization and regulation, further analyze and sort out the influencing factors and constituent elements of supply chain optimization and build the evaluation model of key elements of supply chain optimization, as shown in Table2:Table 2
Model of main elements of supply chain optimization.
Evaluation dimensionsSortingPrimary evaluation indexSecondary evaluation indexEnvironment3Low-carbon greenGrowth rate of carbon dioxide emissionConsumption per unit output value of carbon dioxideGrowth rate of environmental protection investmentRecycling resource utilizationFinance4Financial valueClean energy utilization rateAsset liability ratioProfit growth rateAsset turnoverService5Customer serviceDelivery timeCustomer satisfactionProcess1Internal processOperating costsRate of sale of marketed goodsGrowth rate of information Equipment investmentScientific research2Innovation and learningAccuracy of market forecastRatio of scientific researchers


### 3.3. Key Elements of Supply Chain Optimization Model Evaluation Index Screening Technology Processing

The comprehensive optimization method is based on scientific calculation methods, expert dialectical decision-making, and typical data calculation. The whole screening process combines qualitative and quantitative. Firstly, six methods are used to screen the indicators in order, and then the established index system is modified and improved. One or more methods can be selected or reused until it meets the needs. The index system established by this method has high scientific nature and rationality. The specific process is shown in Figure3.Figure 3
Specific process of comprehensive optimization method.According to the screening principles of the above index system, the initial index set is determined by consulting data, and then a number of valuable index systems with unanimous expert opinions are selected by inviting senior experts of relevant enterprises according to the above principlesZ=Z1,Z2,Z3⋯Zn.Step 1.
Set filtering method.
The unnecessary indicators are filtered out through the collection method, leaving the selected indicators. Set the initial index systemZ=Z1,Z2,Z3⋯Zn. Suppose K experts are invited to screen n indicators, respectively, leaving more important and indispensable indicators.
Suppose the first expert selectst1 indicators Z=Z21,Z22,Z23⋯Z2t1, the second expert selected t2 indicators Z1=Z21,Z22,Z23⋯Z2t2, the K expert selected tK indicators Zi=Zk1,Zk2,Zk3⋯Zktk, so UiK=1Zi is the index system recognized by all experts;
UiK=1Ziis a complete index system accepted by experts;
−UiK=1Ziis the filtered indicator set, which may also be an empty set;
Z0=UiK=1ZK=Z10,Z20,Z30⋯ZK0is the selected index system.Step 2.
Weight filtering method.
According to the weight coefficient of the indicator, the indicator with smaller weight coefficient is filtered out, and the selected indicator is left.
Set index systemZ=Z1,Z2,Z3⋯Zn, the corresponding weight coefficient isai=a1,a2,⋯,an.
For a givena∈0,1.
(1)Z∗=Za=Zi∣ai≥a,i=1,2,⋯,n=X1∗,X2∗,⋯,Xn∗.
Z∗ here is the filter index system relative to a. Where a is a very small positive number, and its value should be determined by experts according to specific principles and actual conditions.Step 3.
Purify the validity of the index set.
This step can improve the rationality of the index system, which is recorded asβ.
Set index systemZ=Z1,Z2,Z3⋯Zn, the evaluation object is S, the score set for indicator Zi is F1i,F2i,F3i⋯,FSi, they were divided into three groups according to the size of score F1i,F2i,F3i⋯FSi, the number of high group and low group should account for about 1/4 of the total number S.
SetF¯1i as the average score of the high group of index, Zi, F¯2i is the average score of the low group of index, and Zi, Fi is the full score of indicatorZi.
Then, the validity of indicatorZi is βi=F1i¯/Fi−F2i¯/Fi, i=1,2,⋯,n, the average validity of indicator system Z is βi¯=1/n∑i=1nβi in general:
When the evaluation result ofβi or β¯ is better than that of Zi, it shall be retained;
Whenβi is between 0.2 and 0.4, the evaluation result is general, and Zi should be corrected at this time;
Whenβi is less than 0.2, the evaluation result is poor, and Zi should be modified or eliminated.Step 4.
Purify the reliability of the index set.
This method is a purification of the stability and reliability of the index set. SupposeY¯ is the average of the first evaluation of indicator Zi, and X¯ is the average of the second evaluation of indicatorZi.
(2)Y¯=1n∑i=1nYi.(3)X¯=1n∑i=1nXi.
Then, the reliability of index systemZ=Z1,Z2,Z3⋯Zn is
(4)ρ=∑i=1nYi−Y¯−Xi−X¯∑i=1nYi−Y¯2·∑i=1nXi−X¯2
If the evaluation objects involved in the evaluation are all carried out under stable normal conditions and there is no significant change in the evaluation objects during the two evaluations, then(i)
whenρ is between 0.90 and 0.95, the index system has excellent stability and reliability(ii)
whenρ is between 0.80 and 0.90, the index system has good stability and reliability(iii)
whenρ is between 0.65 and 0.80, the index system has general stability and reliability(iv)
whenρ is below 0.65, the index system has poor stability and reliability; At this time, it means that there are significant differences in some indicators in the index system in the two evaluations. The following methods can be adopted to find out these indicators
SupposeRi1=Yi11,Yi21,Yi31⋯Yim1,Ri2=Yi12,Yi22,Yi32⋯Yim2 are the evaluation vectors of the evaluation object corresponding to Zi, respectively, i=1,2,⋯,n, clusters setR11,R21⋯Rn1,R12,R22⋯Rn2.
If the designed stored valuesRi1andRi2 are divided into different categories, take out Zi for qualitative analysis. If the difference between the two evaluation results is really the cause of Zi itself, modify or eliminate index Zi.Step 5.
Fuzzy clustering purification method.
This method is a purification of the compatibility between indicators. Through this method, the indicators with greater compatibility between indicators can be combined into one item or modified, or the compatibility between indicators can be reduced, so as to make the index system more independent, scientific, and concise.
Assuming that all the data involved are obtained in a steady state, the index system is set asZ=Z1,Z2,Z3⋯Zn,
Fuzzy relation matrix:(5)Q=q11⋯q1n⋮⋱⋮qm1⋯qnn,
in which,Q1i represents the similarity coefficient of Z1 and Zi, which can be calculated by the following formula:
(6)qij=∑k=1mrik−ri¯−rjk−rj¯∑k=1mrik−ri¯2·∑k=1mrjk−rj¯2,
in which,rik is the evaluation vector corresponding to Z for the evaluation object Pt (representative typical evaluation object). And
(7)ri¯=1m∑k=1mrik,(8)rj¯=1m∑k=1mrjk.
According to the relevant fuzzy theory, we assume(9)qii=1,∀i∈0,1,qij=qjk,∀i,j,qij∈0,1,qij≤qjk≤qik,∀i,j,k=1,2,3⋯n.
Operation symbol⊲ indicates a⊲b=mina,b.
At this time, matrixQ=qijn×n is called fuzzy equivalent matrix Q=qijλm×n, among qijλ=0,qij<λ1,qij≥λ.Obviously, there are different Qλ for different λ. For a given λ, it is a matrix consisting of 0 and 1. If the elements in column i and column j are completely equal, we think that indicator Zi and indicator Zj are of the same class. In this way, the classification of different λ is also different. We should select such λ, which makes the index difference in the same category very small, but the difference between classes is significant. Such λ is the best, and the selection of the best λ is not introduced. The cluster corresponding to the best λ is called the best cluster. And recorded as
(10)Zpt=Z1c,Z2c,Z3c⋯Zncc⋯Zpt1⋯ZptcZ11,Z21,Z31⋯Zn11,Z12,Z22,Z32⋯Zn22⋯,
Zpti=Z1i,Z2i,Z3i⋯Zniiis called a subclass of Zpt.
Set the evaluation objectS, set Zpt∣t=1,2,3⋯s, where Zpt is the best clustering relative to the evaluation object. Obviously, Zi must belong to a subclass of Zpt. If Zi1,Zi2,Zi3⋯Zib belongs to subclass, Zi1,Zi2,Zi3⋯Zib is said to be relative to the same kind. Suppose Zi1,Zi2,Zi3⋯Zib is the same as k elements in Zpt∣t=1,2,3⋯s, then φ=k/s,1≤k≤s, Zi1 is the degree of clustering between Zi1,Zi2,Zi3⋯Zib, obviously 0≤φ≤1. If φ≥0.8, Zi1,Zi2,Zi3⋯Zib can be merged into one item. If φ<0.8, it will not be merged and shall be retained. For indicators that can be incorporated into two or more items at the same time, they should be adjusted so that they can be incorporated into only one item.
There are many factors affecting supply chain optimization, such as government policies and regional political stability. because many factors are not quantifiable and lack of statistical data, they are not included in the research scope. Therefore, this chapter constructs the comprehensive regression method system of key elements of supply chain optimization and regulation and finally establishes the evaluation index system model of key elements of supply chain optimization and regulation as shown in Table3.Table 3
Evaluation model of key elements of supply chain optimization.
Evaluation dimensionsSortingPrimary evaluation indexSecondary evaluation indexEnvironment3Low-carbon greenGrowth rate of carbon dioxide emissionConsumption per unit output value of carbon dioxideGrowth rate of environmental Protection investmentRecycling resource utilizationClean energy utilization rateFinance4Financial valueAsset liability ratioProfit growth rateAsset turnoverService5Customer serviceDelivery timeCustomer satisfactionProcess1Internal processOperating costsRate of sale of marketed goodsGrowth rate of information Equipment investmentScientific research2Innovation and learningAccuracy of market forecastRatio of scientific researchersFinally, from the five dimensions of low-carbon green, financial value, customer service, internal process, and innovation learning, this paper constructs an evaluation index system model of key elements of green supply chain optimization and regulation, which covers 15 secondary indicators. There is a causal relationship between these five evaluation angles. Due to the addition of environmental performance, it puts forward new requirements for the operation of the whole supply chain and promotes the performance of learning and growth. The improvement of learning and growth promotes the improvement and optimization of internal business processes and can provide customers with better services. Due to the particularity of green supply chain, in order to meet the needs of customers, it will promote the performance of logistics capacity, improve the product quality of the supply chain, and finally increase the financial performance of the supply chain.


## 3.1. Acquisition and Selection of Evaluation Indicators

The selection of index system is directly related to the scientific nature, objectivity, and accuracy of the research conclusion and is the core step of the evaluation of key elements. Figure1 is the relationship between indicator selection principles.Figure 1
Relationship between indicator selection principles.There are many methods of index screening, such as principal component analysis, factor analysis, AHP, K-L information method, peak valley correspondence method, TDOA correlation analysis method, cluster analysis method, and comprehensive induction method. Based on the theoretical research on supply chain optimization and regulation, the key indicators are selected through analysis and evaluation, and then the comprehensive induction method is adopted to further optimize the selection of indicators. Comprehensive induction can combine objective statistical analysis data with subjective scientific description data and ensure the scientific nature and effectiveness of index selection to a certain extent. Figure2 shows specific process for determining the index system.Figure 2
Specific process for determining the index system.


## 3.2. Construction of Evaluation Index for Key Elements of Supply Chain Optimization

Based on the existing theoretical research on supply chain optimization and regulation, further analyze and sort out the influencing factors and constituent elements of supply chain optimization and build the evaluation model of key elements of supply chain optimization, as shown in Table2:Table 2
Model of main elements of supply chain optimization.
Evaluation dimensionsSortingPrimary evaluation indexSecondary evaluation indexEnvironment3Low-carbon greenGrowth rate of carbon dioxide emissionConsumption per unit output value of carbon dioxideGrowth rate of environmental protection investmentRecycling resource utilizationFinance4Financial valueClean energy utilization rateAsset liability ratioProfit growth rateAsset turnoverService5Customer serviceDelivery timeCustomer satisfactionProcess1Internal processOperating costsRate of sale of marketed goodsGrowth rate of information Equipment investmentScientific research2Innovation and learningAccuracy of market forecastRatio of scientific researchers


## 3.3. Key Elements of Supply Chain Optimization Model Evaluation Index Screening Technology Processing

The comprehensive optimization method is based on scientific calculation methods, expert dialectical decision-making, and typical data calculation. The whole screening process combines qualitative and quantitative. Firstly, six methods are used to screen the indicators in order, and then the established index system is modified and improved. One or more methods can be selected or reused until it meets the needs. The index system established by this method has high scientific nature and rationality. The specific process is shown in Figure3.Figure 3
Specific process of comprehensive optimization method.According to the screening principles of the above index system, the initial index set is determined by consulting data, and then a number of valuable index systems with unanimous expert opinions are selected by inviting senior experts of relevant enterprises according to the above principlesZ=Z1,Z2,Z3⋯Zn.Step 1.
Set filtering method.
The unnecessary indicators are filtered out through the collection method, leaving the selected indicators. Set the initial index systemZ=Z1,Z2,Z3⋯Zn. Suppose K experts are invited to screen n indicators, respectively, leaving more important and indispensable indicators.
Suppose the first expert selectst1 indicators Z=Z21,Z22,Z23⋯Z2t1, the second expert selected t2 indicators Z1=Z21,Z22,Z23⋯Z2t2, the K expert selected tK indicators Zi=Zk1,Zk2,Zk3⋯Zktk, so UiK=1Zi is the index system recognized by all experts;
UiK=1Ziis a complete index system accepted by experts;
−UiK=1Ziis the filtered indicator set, which may also be an empty set;
Z0=UiK=1ZK=Z10,Z20,Z30⋯ZK0is the selected index system.Step 2.
Weight filtering method.
According to the weight coefficient of the indicator, the indicator with smaller weight coefficient is filtered out, and the selected indicator is left.
Set index systemZ=Z1,Z2,Z3⋯Zn, the corresponding weight coefficient isai=a1,a2,⋯,an.
For a givena∈0,1.
(1)Z∗=Za=Zi∣ai≥a,i=1,2,⋯,n=X1∗,X2∗,⋯,Xn∗.
Z∗ here is the filter index system relative to a. Where a is a very small positive number, and its value should be determined by experts according to specific principles and actual conditions.Step 3.
Purify the validity of the index set.
This step can improve the rationality of the index system, which is recorded asβ.
Set index systemZ=Z1,Z2,Z3⋯Zn, the evaluation object is S, the score set for indicator Zi is F1i,F2i,F3i⋯,FSi, they were divided into three groups according to the size of score F1i,F2i,F3i⋯FSi, the number of high group and low group should account for about 1/4 of the total number S.
SetF¯1i as the average score of the high group of index, Zi, F¯2i is the average score of the low group of index, and Zi, Fi is the full score of indicatorZi.
Then, the validity of indicatorZi is βi=F1i¯/Fi−F2i¯/Fi, i=1,2,⋯,n, the average validity of indicator system Z is βi¯=1/n∑i=1nβi in general:
When the evaluation result ofβi or β¯ is better than that of Zi, it shall be retained;
Whenβi is between 0.2 and 0.4, the evaluation result is general, and Zi should be corrected at this time;
Whenβi is less than 0.2, the evaluation result is poor, and Zi should be modified or eliminated.Step 4.
Purify the reliability of the index set.
This method is a purification of the stability and reliability of the index set. SupposeY¯ is the average of the first evaluation of indicator Zi, and X¯ is the average of the second evaluation of indicatorZi.
(2)Y¯=1n∑i=1nYi.(3)X¯=1n∑i=1nXi.
Then, the reliability of index systemZ=Z1,Z2,Z3⋯Zn is
(4)ρ=∑i=1nYi−Y¯−Xi−X¯∑i=1nYi−Y¯2·∑i=1nXi−X¯2
If the evaluation objects involved in the evaluation are all carried out under stable normal conditions and there is no significant change in the evaluation objects during the two evaluations, then(i)
whenρ is between 0.90 and 0.95, the index system has excellent stability and reliability(ii)
whenρ is between 0.80 and 0.90, the index system has good stability and reliability(iii)
whenρ is between 0.65 and 0.80, the index system has general stability and reliability(iv)
whenρ is below 0.65, the index system has poor stability and reliability; At this time, it means that there are significant differences in some indicators in the index system in the two evaluations. The following methods can be adopted to find out these indicators
SupposeRi1=Yi11,Yi21,Yi31⋯Yim1,Ri2=Yi12,Yi22,Yi32⋯Yim2 are the evaluation vectors of the evaluation object corresponding to Zi, respectively, i=1,2,⋯,n, clusters setR11,R21⋯Rn1,R12,R22⋯Rn2.
If the designed stored valuesRi1andRi2 are divided into different categories, take out Zi for qualitative analysis. If the difference between the two evaluation results is really the cause of Zi itself, modify or eliminate index Zi.Step 5.
Fuzzy clustering purification method.
This method is a purification of the compatibility between indicators. Through this method, the indicators with greater compatibility between indicators can be combined into one item or modified, or the compatibility between indicators can be reduced, so as to make the index system more independent, scientific, and concise.
Assuming that all the data involved are obtained in a steady state, the index system is set asZ=Z1,Z2,Z3⋯Zn,
Fuzzy relation matrix:(5)Q=q11⋯q1n⋮⋱⋮qm1⋯qnn,
in which,Q1i represents the similarity coefficient of Z1 and Zi, which can be calculated by the following formula:
(6)qij=∑k=1mrik−ri¯−rjk−rj¯∑k=1mrik−ri¯2·∑k=1mrjk−rj¯2,
in which,rik is the evaluation vector corresponding to Z for the evaluation object Pt (representative typical evaluation object). And
(7)ri¯=1m∑k=1mrik,(8)rj¯=1m∑k=1mrjk.
According to the relevant fuzzy theory, we assume(9)qii=1,∀i∈0,1,qij=qjk,∀i,j,qij∈0,1,qij≤qjk≤qik,∀i,j,k=1,2,3⋯n.
Operation symbol⊲ indicates a⊲b=mina,b.
At this time, matrixQ=qijn×n is called fuzzy equivalent matrix Q=qijλm×n, among qijλ=0,qij<λ1,qij≥λ.Obviously, there are different Qλ for different λ. For a given λ, it is a matrix consisting of 0 and 1. If the elements in column i and column j are completely equal, we think that indicator Zi and indicator Zj are of the same class. In this way, the classification of different λ is also different. We should select such λ, which makes the index difference in the same category very small, but the difference between classes is significant. Such λ is the best, and the selection of the best λ is not introduced. The cluster corresponding to the best λ is called the best cluster. And recorded as
(10)Zpt=Z1c,Z2c,Z3c⋯Zncc⋯Zpt1⋯ZptcZ11,Z21,Z31⋯Zn11,Z12,Z22,Z32⋯Zn22⋯,
Zpti=Z1i,Z2i,Z3i⋯Zniiis called a subclass of Zpt.
Set the evaluation objectS, set Zpt∣t=1,2,3⋯s, where Zpt is the best clustering relative to the evaluation object. Obviously, Zi must belong to a subclass of Zpt. If Zi1,Zi2,Zi3⋯Zib belongs to subclass, Zi1,Zi2,Zi3⋯Zib is said to be relative to the same kind. Suppose Zi1,Zi2,Zi3⋯Zib is the same as k elements in Zpt∣t=1,2,3⋯s, then φ=k/s,1≤k≤s, Zi1 is the degree of clustering between Zi1,Zi2,Zi3⋯Zib, obviously 0≤φ≤1. If φ≥0.8, Zi1,Zi2,Zi3⋯Zib can be merged into one item. If φ<0.8, it will not be merged and shall be retained. For indicators that can be incorporated into two or more items at the same time, they should be adjusted so that they can be incorporated into only one item.
There are many factors affecting supply chain optimization, such as government policies and regional political stability. because many factors are not quantifiable and lack of statistical data, they are not included in the research scope. Therefore, this chapter constructs the comprehensive regression method system of key elements of supply chain optimization and regulation and finally establishes the evaluation index system model of key elements of supply chain optimization and regulation as shown in Table3.Table 3
Evaluation model of key elements of supply chain optimization.
Evaluation dimensionsSortingPrimary evaluation indexSecondary evaluation indexEnvironment3Low-carbon greenGrowth rate of carbon dioxide emissionConsumption per unit output value of carbon dioxideGrowth rate of environmental Protection investmentRecycling resource utilizationClean energy utilization rateFinance4Financial valueAsset liability ratioProfit growth rateAsset turnoverService5Customer serviceDelivery timeCustomer satisfactionProcess1Internal processOperating costsRate of sale of marketed goodsGrowth rate of information Equipment investmentScientific research2Innovation and learningAccuracy of market forecastRatio of scientific researchersFinally, from the five dimensions of low-carbon green, financial value, customer service, internal process, and innovation learning, this paper constructs an evaluation index system model of key elements of green supply chain optimization and regulation, which covers 15 secondary indicators. There is a causal relationship between these five evaluation angles. Due to the addition of environmental performance, it puts forward new requirements for the operation of the whole supply chain and promotes the performance of learning and growth. The improvement of learning and growth promotes the improvement and optimization of internal business processes and can provide customers with better services. Due to the particularity of green supply chain, in order to meet the needs of customers, it will promote the performance of logistics capacity, improve the product quality of the supply chain, and finally increase the financial performance of the supply chain.


## 4. Simulation Calculation

At present, the calculation methods of weight mainly include subjective weighting method and objective weighting method. The subjective method includes the expert scoring method, Delphi method, expert ranking method, and analytic hierarchy process. The objective method includes entropy weight method, principal component method, factor analysis method, coefficient of variation method, standard deviation method, and multiobjective programming method. Because the subjective weighting method is based on personal experience and knowledge, the subjective assumption is strong, the simple objective weighting method has strong mathematical theory, and the calculation method is cumbersome. Sometimes the determined weight is contrary to the actual result.Therefore, in this paper, the expert ranking method and the comprehensive weighting method of subjective and objective combination of coefficient of variation are used for weighting.


### 4.1. Expert Arranges Method

We invited several authoritative experts, scholars, and their own practitioners in the field of green supply chain to determine the weight of the evaluation index system of key elements of green supply chain optimization proposed in this paper. Ask experts to rank each index according to its own importance. The most important index is recorded as 1, ranking first, then the second important index is recorded as 2, ranking second, and so on. Assuming that there aren indicators in total, ask m experts to sort them and arrange them into a number table of n×m, whose numbers are 1, 2, 3…n. The serial number of each index is the rank of the index. The rank determined by m experts is added together to obtain the rank sum, which is expressed by R. The rank sum of the j index is represented by Rj, and dj represents the weight of the j index. Table 4 presents weight of each index calculated by expert ranking method.Table 4
Weight of each index calculated by expert ranking method.
IndicatorsExpert 1Expert 2Expert 3Expert 4Expert 5Rank sumdjDelivery time32214120.113Growth rate of carbon dioxide emission551086340.077Growth rate of environmental protection investment13121497550.042Clean energy utilization rate65274240.093Customer satisfaction71481212530.045Asset liability ratio36342180.103Growth rate of information equipment investment210786330.078Operating costs10115810440.06Asset turnover756710350.075Rate of sale of marketed goods9710810440.06Profit growth rate14915109570.038Accuracy of market forecast81171413530.045Consumption per unit output value of carbon dioxide310785330.078Recycling resource utilization791044340.077Ratio of scientific researchers725108310.082The calculation formula is(11)dj=2m1+n−Rj/mn1+n,j=1,2,⋯n.Since the calculation result of the weight is related to the evaluation of experts, if the opinions are consistent, the evaluation result has practical significance; otherwise it is invalid. Therefore, before determining the weight, it is necessary to test the significance of the evaluation results of experts. If the results are consistent, calculate the weight.The significance test method is as follows:Suppose that the opinions ofm experts on the importance of n indicators are inconsistent.
(1)
Calculation statisticsX2=mn−1w, which(12)W=12S/m2n3−n,(13)S=R12+R22+⋯+Rn2−R1+R2+⋯+Rn/n.RJj=1,2,⋯,nis the rank sum of index j.
(2)
According to the significance level and degree of freedomdf=n−1, check the x2 value to find the critical value X2dfConclusion: Ifx2≥x2df negates H0, it is considered that the views of m experts are significantly consistent.Ifx2≤x2df, accept H0 and consider it compatible, that is, the views of m experts have not been significantly consistent. It is suggested that the experts should be sorted again, and then conduct consistency test again in the same way until significant consistency is S=15230−390=14918 reached.The calculation process is as follows:(14)S=15230−390=14918,(15)W=12×14918÷25×153−15=2.13,(16)X2=mn−1w=5×15−1×2.13=149.1.At the significance level of∂=0.5, the chi-square test table shows that
(17)X2=14=13.339≤149.1.Therefore, it denies the original hypothesis and believes that the views of the five experts are significantly consistent. Weight calculation can be performed.


### 4.2. Coefficient of Variation Method

According to the operation steps of the coefficient of variation method, firstly, according to the time series data of each index, calculate the mean and standard deviation of each index by using SPSS software and then calculate the coefficient of variationVar (the ratio of mean to standard deviation). According to the proportion of the coefficient of variation of each index, determine the weight ωi of each index. The formula is as follows:
(18)Vi=σixi,in which,Vi is the coefficient of variation of index i, also known as the coefficient of standard deviation; σi is the standard deviation of index i, xi is the average value of index i, i=1,2,3⋯n. Table 5 is the simulation data of each evaluation index. Table 6 is the average value and standard deviation of each index. Table 7 is the weight of each index calculated by coefficient of variation method.Table 5
Simulation data of each evaluation index.
IndicatorsA1A2A3A4A5A6A7Delivery time51057080293098110501170Growth rate of carbon dioxide emission2.32.52.73.23.89.510Growth rate of environmental protection investment4178.00120140205260341Clean energy utilization rate2.94.87.48.311.513.517.9Customer satisfaction1113.001414141521Asset liability ratio81105231399539727.65982.33Growth rate of information equipment investment8.19.411.212.3512.7413.4113.40Operating costs15343183462423929565368244588357170Asset turnover0.350.380.390.400.410.440.47Rate of sale of marketed goods77798385899296Profit growth rate7780848895102108Accuracy of market forecast57.1359.6260.8961.6869.1773.1177.28Consumption per unit output value of carbon dioxide1434318147242392950538244578357007Recycling resource utilization223451015Ratio of scientific researchers15.318.416.819.716.511.317.2Table 6
Average value and standard deviation of each index.
IndicatorsAverage valueStandard deviationDelivery time859245.53Growth rate of carbon dioxide emission4.863.38Growth rate of environmental protection investment169.29105.73Clean energy utilization rate9.475.20Customer satisfaction14.573.10Asset liability ratio437.85334.94Growth rate of information equipment investment11.512.06Operating costs32481.4315154.56Asset turnover0.410.04Rate of sale of marketed goods85.866.89Profit growth rate90.5711.54Accuracy of market forecast65.557.64Consumption per unit output value of carbon dioxide27549.7118442.28Recycling resource utilization5.864.88Ratio of scientific researchers16.462.67Table 7
Weight of each index calculated by coefficient of variation method.
IndicatorsViWiDelivery time0.290.05Growth rate of carbon dioxide emission0.700.11Growth rate of environmental protection investment0.620.10Clean energy utilization rate0.550.09Customer satisfaction0.210.03Asset liability ratio0.760.12Growth rate of information equipment investment0.180.03Operating costs0.470.08Asset turnover0.100.02Rate of sale of marketed goods0.080.01Profit growth rate0.130.02Accuracy of market forecast0.120.02Consumption per unit output value of carbon dioxide0.670.11Recycling resource utilization0.830.13Ratio of scientific researchers0.160.03The calculation formula of each index weight is(19)Wi=Vi∑i=1nVi.


### 4.3. Comprehensive Weight Calculation

After the above two assignments, the weights of each index aredj and wi, respectively. Due to the influence on the reliability allocation and the fuzziness of its weight, the reliability allocation problem is an uncertain problem. According to the principle of minimum identification information, in order to make the combined weight as close as possible to the two, the target function is established as follows:
(20)minF=∑i=1mαilnαidi+∑i=1mαilnαiωi,(21)s.t.∑i=1mαi=1,αi>0.The above objective function is solved by the Lagrange multiplication:(22)Lαi,λ=Fαi−λ∑i=1mαi=∑i=1mαilnαidi+∑i=1mαilnαiωi−λ∑i=1mαi−1.The conditions for the existence of the extreme points of the Lagrange function are as follows:(23)∂L∂αi=0,∂L∂λ=0,i=1,2,⋯,m.By solving this simultaneous equation, the combined weight of key factors can be obtained:(24)αi=diωi0.5∑i=1ndiωi0.5.Based on the evaluation index system of key elements of supply chain optimization regulation, firstly, a scientific and effective evaluation index system model is selected through a five-step comprehensive optimization method. Then, the index system of key elements of supply chain optimization is finally established through expert ranking method, secondary ranking and screening of each index, and significance test. The evaluation index system of key elements of supply chain optimization is technically processed, that is, the weight of each index is simulated and calculated with the help of expert ranking method and variation coefficient method. Finally, the comprehensive weight of each index is calculated twice with the comprehensive method, and the comprehensive weight of 15 key element evaluation indexes is calculated, as shown in Figure4.Figure 4
Comprehensive weight of each indicator.It can be seen from the table that the top five evaluation indicators of key elements of supply chain optimization are asset liability ratio, utilization rate of circular resources,CO2 emission growth rate, CO2 unit output value consumption, and clean energy utilization rate. Therefore, it can be seen that the indicators related to low carbon and green in the key elements of supply chain optimization and regulation play a key role in modern supply chain operation. Paying attention to low-carbon development is conducive to establishing a good social image for enterprises, reducing enterprise costs and improving economic benefits. Therefore, the green supply chain should be planned and designed based on the low-carbon concept in the planning, procurement, manufacturing, delivery and recycling processes, so as to optimize and regulate the supply chain.


## 4.1. Expert Arranges Method

We invited several authoritative experts, scholars, and their own practitioners in the field of green supply chain to determine the weight of the evaluation index system of key elements of green supply chain optimization proposed in this paper. Ask experts to rank each index according to its own importance. The most important index is recorded as 1, ranking first, then the second important index is recorded as 2, ranking second, and so on. Assuming that there aren indicators in total, ask m experts to sort them and arrange them into a number table of n×m, whose numbers are 1, 2, 3…n. The serial number of each index is the rank of the index. The rank determined by m experts is added together to obtain the rank sum, which is expressed by R. The rank sum of the j index is represented by Rj, and dj represents the weight of the j index. Table 4 presents weight of each index calculated by expert ranking method.Table 4
Weight of each index calculated by expert ranking method.
IndicatorsExpert 1Expert 2Expert 3Expert 4Expert 5Rank sumdjDelivery time32214120.113Growth rate of carbon dioxide emission551086340.077Growth rate of environmental protection investment13121497550.042Clean energy utilization rate65274240.093Customer satisfaction71481212530.045Asset liability ratio36342180.103Growth rate of information equipment investment210786330.078Operating costs10115810440.06Asset turnover756710350.075Rate of sale of marketed goods9710810440.06Profit growth rate14915109570.038Accuracy of market forecast81171413530.045Consumption per unit output value of carbon dioxide310785330.078Recycling resource utilization791044340.077Ratio of scientific researchers725108310.082The calculation formula is(11)dj=2m1+n−Rj/mn1+n,j=1,2,⋯n.Since the calculation result of the weight is related to the evaluation of experts, if the opinions are consistent, the evaluation result has practical significance; otherwise it is invalid. Therefore, before determining the weight, it is necessary to test the significance of the evaluation results of experts. If the results are consistent, calculate the weight.The significance test method is as follows:Suppose that the opinions ofm experts on the importance of n indicators are inconsistent.
(1)
Calculation statisticsX2=mn−1w, which(12)W=12S/m2n3−n,(13)S=R12+R22+⋯+Rn2−R1+R2+⋯+Rn/n.RJj=1,2,⋯,nis the rank sum of index j.
(2)
According to the significance level and degree of freedomdf=n−1, check the x2 value to find the critical value X2dfConclusion: Ifx2≥x2df negates H0, it is considered that the views of m experts are significantly consistent.Ifx2≤x2df, accept H0 and consider it compatible, that is, the views of m experts have not been significantly consistent. It is suggested that the experts should be sorted again, and then conduct consistency test again in the same way until significant consistency is S=15230−390=14918 reached.The calculation process is as follows:(14)S=15230−390=14918,(15)W=12×14918÷25×153−15=2.13,(16)X2=mn−1w=5×15−1×2.13=149.1.At the significance level of∂=0.5, the chi-square test table shows that
(17)X2=14=13.339≤149.1.Therefore, it denies the original hypothesis and believes that the views of the five experts are significantly consistent. Weight calculation can be performed.


## 4.2. Coefficient of Variation Method

According to the operation steps of the coefficient of variation method, firstly, according to the time series data of each index, calculate the mean and standard deviation of each index by using SPSS software and then calculate the coefficient of variationVar (the ratio of mean to standard deviation). According to the proportion of the coefficient of variation of each index, determine the weight ωi of each index. The formula is as follows:
(18)Vi=σixi,in which,Vi is the coefficient of variation of index i, also known as the coefficient of standard deviation; σi is the standard deviation of index i, xi is the average value of index i, i=1,2,3⋯n. Table 5 is the simulation data of each evaluation index. Table 6 is the average value and standard deviation of each index. Table 7 is the weight of each index calculated by coefficient of variation method.Table 5
Simulation data of each evaluation index.
IndicatorsA1A2A3A4A5A6A7Delivery time51057080293098110501170Growth rate of carbon dioxide emission2.32.52.73.23.89.510Growth rate of environmental protection investment4178.00120140205260341Clean energy utilization rate2.94.87.48.311.513.517.9Customer satisfaction1113.001414141521Asset liability ratio81105231399539727.65982.33Growth rate of information equipment investment8.19.411.212.3512.7413.4113.40Operating costs15343183462423929565368244588357170Asset turnover0.350.380.390.400.410.440.47Rate of sale of marketed goods77798385899296Profit growth rate7780848895102108Accuracy of market forecast57.1359.6260.8961.6869.1773.1177.28Consumption per unit output value of carbon dioxide1434318147242392950538244578357007Recycling resource utilization223451015Ratio of scientific researchers15.318.416.819.716.511.317.2Table 6
Average value and standard deviation of each index.
IndicatorsAverage valueStandard deviationDelivery time859245.53Growth rate of carbon dioxide emission4.863.38Growth rate of environmental protection investment169.29105.73Clean energy utilization rate9.475.20Customer satisfaction14.573.10Asset liability ratio437.85334.94Growth rate of information equipment investment11.512.06Operating costs32481.4315154.56Asset turnover0.410.04Rate of sale of marketed goods85.866.89Profit growth rate90.5711.54Accuracy of market forecast65.557.64Consumption per unit output value of carbon dioxide27549.7118442.28Recycling resource utilization5.864.88Ratio of scientific researchers16.462.67Table 7
Weight of each index calculated by coefficient of variation method.
IndicatorsViWiDelivery time0.290.05Growth rate of carbon dioxide emission0.700.11Growth rate of environmental protection investment0.620.10Clean energy utilization rate0.550.09Customer satisfaction0.210.03Asset liability ratio0.760.12Growth rate of information equipment investment0.180.03Operating costs0.470.08Asset turnover0.100.02Rate of sale of marketed goods0.080.01Profit growth rate0.130.02Accuracy of market forecast0.120.02Consumption per unit output value of carbon dioxide0.670.11Recycling resource utilization0.830.13Ratio of scientific researchers0.160.03The calculation formula of each index weight is(19)Wi=Vi∑i=1nVi.


## 4.3. Comprehensive Weight Calculation

After the above two assignments, the weights of each index aredj and wi, respectively. Due to the influence on the reliability allocation and the fuzziness of its weight, the reliability allocation problem is an uncertain problem. According to the principle of minimum identification information, in order to make the combined weight as close as possible to the two, the target function is established as follows:
(20)minF=∑i=1mαilnαidi+∑i=1mαilnαiωi,(21)s.t.∑i=1mαi=1,αi>0.The above objective function is solved by the Lagrange multiplication:(22)Lαi,λ=Fαi−λ∑i=1mαi=∑i=1mαilnαidi+∑i=1mαilnαiωi−λ∑i=1mαi−1.The conditions for the existence of the extreme points of the Lagrange function are as follows:(23)∂L∂αi=0,∂L∂λ=0,i=1,2,⋯,m.By solving this simultaneous equation, the combined weight of key factors can be obtained:(24)αi=diωi0.5∑i=1ndiωi0.5.Based on the evaluation index system of key elements of supply chain optimization regulation, firstly, a scientific and effective evaluation index system model is selected through a five-step comprehensive optimization method. Then, the index system of key elements of supply chain optimization is finally established through expert ranking method, secondary ranking and screening of each index, and significance test. The evaluation index system of key elements of supply chain optimization is technically processed, that is, the weight of each index is simulated and calculated with the help of expert ranking method and variation coefficient method. Finally, the comprehensive weight of each index is calculated twice with the comprehensive method, and the comprehensive weight of 15 key element evaluation indexes is calculated, as shown in Figure4.Figure 4
Comprehensive weight of each indicator.It can be seen from the table that the top five evaluation indicators of key elements of supply chain optimization are asset liability ratio, utilization rate of circular resources,CO2 emission growth rate, CO2 unit output value consumption, and clean energy utilization rate. Therefore, it can be seen that the indicators related to low carbon and green in the key elements of supply chain optimization and regulation play a key role in modern supply chain operation. Paying attention to low-carbon development is conducive to establishing a good social image for enterprises, reducing enterprise costs and improving economic benefits. Therefore, the green supply chain should be planned and designed based on the low-carbon concept in the planning, procurement, manufacturing, delivery and recycling processes, so as to optimize and regulate the supply chain.


## 5. Conclusion

Through comprehensive induction, subjective and objective analysis, this paper introduces the concept of low-carbon green environmental protection, establishes the evaluation index including the dimension of low-carbon green, and then establishes the evaluation index system of key elements of supply chain optimization by using set filtering method, weight filtering method, and fuzzy cluster purification method. The importance of each evaluation index for the evaluation of the whole supply chain is accurately located through simulation calculation. The research findings or conclusions are as follows:First, the evaluation of supply chain operation is the inevitable choice to realize supply chain optimization and improve supply chain competitiveness. The evaluation of key elements of supply chain optimization should not only pay attention to the operation status and economic benefits of the supply chain, but also pay attention to ecological environmental protection, resource utilization, and carbon emission. Low-carbon green index, the key element of supply chain optimization, is not only the inevitable product of low-carbon economic development, but also the common requirement of energy conservation and emission reduction, environmental protection, and the public.Secondly, an effective evaluation index system of key elements of supply chain optimization is established. Based on the traditional supply chain performance evaluation theory, combined with the actual situation of social development, this paper introduces low-carbon environmental protection factors and constructs an evaluation index system of key elements of supply chain optimization based on five dimensions: financial value, internal process of supply chain, customer service level, innovation and learning, and low-carbon green, which conforms to the development trend of low-carbon economy.Third, the supply chain is a huge network chain with many processes and complex cooperative relationships among node enterprises. When integrating the concept of low-carbon environmental protection into the evaluation of key elements of supply chain optimization, identifying the right for the key elements of low-carbon green will help support the green supply chain regulation mechanism from the perspective of carbon footprint and promote low-carbon environmental protection to become a new economic support point for enterprises, comprehensively enhance the core competitiveness of low-carbon supply chain.



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*Source: 8196756-2022-02-24.xml*