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

Economic globalization competition leads to rapid replacement of green products, large demand ﬂ uctuations, 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 ﬁ ve dimensions of ﬁ nancial 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 coe ﬃ cient of variation are used to simulate the weight of indicators.


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 farreaching 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 "Rclustering" 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].Amaladha-san 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][22][23][24][25]. Few scholars consider optimizing the regulation of green supply chain through the analysis of key elements [26][27][28][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.

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

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based on value triangle logic.The elements of the supply chain are classified in Table 1.

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.Figure 1 is the 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.Figure 2 shows specific process for determining the index system.

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 Table 2:

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 scien-tific nature and rationality.The specific process is shown in Figure 3.
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 = fZ 1 , Z 2 , Z 3 ⋯ Z n g.
The unnecessary indicators are filtered out through the collection method, leaving the selected indicators.Set the initial index system Z = fZ 1 , Z 2 , Z 3 ⋯ Z n g.Suppose K experts are invited to screen n indicators, respectively, leaving more important and indispensable indicators.
Suppose the first expert selects

the index system recognized by all experts;
U K i = 1 Z i is a complete index system accepted by experts; −U K i = 1 Z i is the filtered indicator set, which may also be an empty set; 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.
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 as β.Set F 1i as the average score of the high group of index, Z i , F 2i is the average score of the low group of index, and Z i , F i is the full score of indicatorZ i .

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Then, the validity of indicator Z i is When the evaluation result of β i or β is better than that of Z i , it shall be retained; When β i is between 0.2 and 0.4, the evaluation result is general, and Z i should be corrected at this time; When β i is less than 0.2, the evaluation result is poor, and Z i 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.Suppose Y is the average of the first evaluation of indicator Z i , and X is the average of the second evaluation of indicatorZ i .

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Then, the reliability of index system 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) when ρ is between 0.90 and 0.95, the index system has excellent stability and reliability (ii) when ρ is between 0.80 and 0.90, the index system has good stability and reliability (iii) when ρ is between 0.65 and 0.80, the index system has general stability and reliability (iv) when ρ 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 Suppose R  are divided into different categories, take out Z i for qualitative analysis.If the difference between the two evaluation results is really the cause of Z i itself, modify or eliminate index Z i .
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

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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 as Z = fZ 1 , Z 2 , Z 3 ⋯ Z n g, Fuzzy relation matrix: in which, Q 1i represents the similarity coefficient of Z 1 and Z i , which can be calculated by the following formula: in which, r ik is the evaluation vector corresponding to Z for the evaluation object P t (representative typical evaluation object).And According to the relevant fuzzy theory, we assume q ij = q jk ,∀i, j, q ij ∈ 0, 1 ½ , Operation symbol ⊲ indicates a⊲b = min fa, bg.At this time, matrix 1,q ij ≥λ 0,q ij <λ .Obviously, there are different Q λ 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 Z i and indicator Z j 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 where Z pt is the best clustering relative to the evaluation object.Obviously, Z i must belong to a subclass of Z pt .If Z i1 , Z i2 , Z i3 ⋯ Z ib belongs to subclass, Z i1 , Z i2 , Z i3 ⋯ Z ib is said to be relative to the same kind.Suppose Z i1 , Z i2 , Z i3 ⋯ Z ib is the same as k elements in 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 Table 3.
Finally, 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.

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.

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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 are n 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 R j , and d j represents the weight of the j index.Table 4 presents weight of each index calculated by expert ranking method.The calculation formula is 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 of m experts on the importance of n indicators are inconsistent.
(1) Calculation statistics X 2 = mðn − 1Þw, which (2) According to the significance level and degree of freedom it is considered that the views of m experts are significantly consistent.
If x 2 ≤ x 2 ðd f Þ, accept H 0 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: At the significance level of ∂ = 0:5, the chi-square test table shows that Therefore, it denies the original hypothesis and believes that the views of the five experts are significantly consistent.Weight calculation can be performed.

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 variation

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Var (the ratio of mean to standard deviation).According to the proportion of the coefficient of variation of each index, determine the weight ω i of each index.The formula is as follows: in which, V i is the coefficient of variation of index i, also known as the coefficient of standard deviation; σ i is the standard deviation of index i, x i 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.
The calculation formula of each index weight is 4.3.Comprehensive Weight Calculation.After the above two assignments, the weights of each index are d j and w i , 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:

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The above objective function is solved by the Lagrange multiplication: The conditions for the existence of the extreme points of the Lagrange function are as follows: By solving this simultaneous equation, the combined weight of key factors can be obtained: 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 Figure 4.
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, CO 2 emission growth rate, CO 2 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

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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.

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 dimen-sions: financial value, internal process of supply chain, customer service level, innovation and learning, and lowcarbon 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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S
the evaluation object is S, the score set for indicator Z i is fF ðiÞ ðiÞ S g, they were divided into three groups according to the size of score F ðiÞ , the number of high group and low group should account for about 1/4 of the total number S.
the evaluation vectors of the evaluation object corresponding to Z i, respectively, i = 1, 2, ⋯, n, clusters setfR

2
⋯ R ð2Þ n g.If the designed stored values R ð1Þ i and R ð2Þ i

Figure 3 :
Figure 3: Specific process of comprehensive optimization method.

Figure 4 :
Figure 4: Comprehensive weight of each indicator.

Table 1 :
Composition of supply chain elements.

Table 2 :
Model of main elements of supply chain optimization.

Table 3 :
Evaluation model of key elements of supply chain optimization.

Table 4 :
Weight of each index calculated by expert ranking method.

Table 5 :
Simulation data of each evaluation index.

Table 6 :
Average value and standard deviation of each index.

Table 7 :
Weight of each index calculated by coefficient of variation method.