Supplier Selection Study under the Respective of Low-Carbon Supply Chain : A Hybrid Evaluation Model Based on FA-DEA-AHP

With the development of global environment and social economy, it is an indispensable choice for enterprises to achieve sustainable growth through developing low-carbon economy and constructing low-carbon supply chain. Supplier is the source of chain, thus selecting excellent low-carbon supplier is the foundation of establishing efficient low-carbon supply chain. This paper presents a novel hybrid model for supplier selection integrated factor analysis (FA), data envelopment analysis (DEA), with analytic hierarchy process (AHP), namely FA-DEA-AHP. First, an evaluation index system is built, incorporating product level, qualification, cooperation ability, and environmental competitiveness. FA is utilized to extract common factors from the 18 pre-selected indicators. Then, DEA is applied to establish the pairwise comparison matrix and AHP is employed to rank these low-carbon suppliers comprehensively and calculate the validity of the decision-making units. Finally, an experiment study with seven cement suppliers in a large industrial enterprise is carried out in this paper. The results reveal that the proposed technique can not only select effective suppliers, but also realize a comprehensive ranking. This research has enriched the methodology of low-carbon supplier evaluation and selection, as well as owns theoretical value in exploring the coordinated development of low-carbon supply chain to some extent.


Introduction
In recent years, with the burgeoning development of economic society, increasing energy consumption and serious environmental pollution have ensued, in particular, the dramatic growth in carbon dioxide has led to global warming and the rise of sea level [1].Governments are dedicated to "Low-Carbon Revolution and Circular Economy" around the world through promulgation of policy and encouragement to enterprises on taking both economic and environmental benefits into account [2,3].Accordingly, enterprises, especially production-oriented ones, are bound to change their traditional operation modes to reduce carbon emissions as well as costs [4].Centobelli et al. [5,6] conducts a structured review on the topic of energy efficiency, environmental sustainability, and taxonomy of green initiatives in the supply chain management context.Simultaneously, improvement of the public's awareness on low-carbon environmental protection makes it remarkably intense for the demand of related products [7].Thus, it is imperative for suppliers to fulfill the customer's low-carbon requirements during the supply chain management.
A research implemented by TRUCOST shows only 19% greenhouse gases in the supply chain directly come from business operation, while the indirect sources contributes the other 81% [8], such as Tier One Suppliers, power suppliers, and other members.Indeed, the selection of suitable suppliers is adopted by Sadeghieh [30], while reference [31] combined SVM with hierarchical system of feature to address the problem of supplier selection.
In general, based on the aforementioned studies, it can be found that the issue of supplier selection has attracted wide attention for decades.The corresponding evaluation index system and models tend to be more and more scientific.Nevertheless, the development of information and low-carbon economy bring about changes in assessing suppliers, namely enterprise compatibility, deliver ability, environmental protection capability should be taken into consideration.Accordingly, the evaluation and selection technique should also be better adapted to the variety of index system so as to make the results more accurate and intuitive.
Therefore, a new index system is built in this paper that covers product quality, enterprise qualification, cooperation ability, and environmental competitiveness.Moreover, a hybrid model that integrates factor analysis (FA) and data envelopment analysis (DEA) with AHP is put forward to make a research on low-carbon supplier option.FA is exploited to reduce the dimension of pre-selected factors through extracting several comprehensive indicators to reflect the characteristics of original data [32].In view of multi-input and multi-output elements, as well as non-linearity in low-carbon supplier selection, in coincidence with the multi-objective decision-making method DEA, the paper applied this technique to cope with the problem.However, it is noted that the consequences of DEA can merely be parted as effectiveness, weak effectiveness and ineffectiveness, which still can't identify the best one.Thus, AHP is introduced to compensate the shortcomings by establishment of a hierarchical structure and quantization of the influence of each factor on the final results with weight.The rest of the paper is organized as follows: Section 2 builds the evaluation index system of low-carbon suppliers.Section 3 shows the framework of the proposed evaluation technique FA-DEA-AHP, while Section 4 illustrates the case study with seven low-carbon cement suppliers in a Chinese industrial enterprise.Section 5 makes a discussion on the results derived from the model.In the end, Section 6 concludes the paper.

The Construction of Low-Carbon Supplier Evaluation and Selection Index System
There is still not a unified standard for establishment of index system for supplier selection in terms of preceding studies in the Introduction.Moreover, different levels of cooperation between suppliers and enterprises and types of business provided by suppliers also lead to great difference in evaluation indicators.
The construction of supplier evaluation and selection index system in low-carbon supply chain aims at revealing the characteristics of supplier assessment under the fire-new environment and competition conditions.Based on previous studies at home and abroad [13,14,18,19], the evaluation index system of supplier selection proposed in this paper is built from four aspects: product level, qualification, cooperation ability, and environmental competitiveness, as shown in Table 1.The definitions of the above indexes are given here so as to make them understood clearly.
(1).Production qualification rate is equal to the percentage of qualified products in the total procurement within a period of time.(2).Quality management system is imperative for quality assurance.Total quality management (TQM) and ISO standard series are employed here to carry out this appraisal.(3).Quality improvement plan refers to assessment of supplier's future quality administration, particularly the strategic partners.( 4).Relative price level can be obtained through the comparison of supplier's product price with that of the industry on the average.(5).The rate of return on total assets is equal to the whole amount of remuneration acquired by the enterprise divided by average total assets, which reflects the profitability of all the assets.( 6).Quick ratio is equal to quick assets divided by current liabilities, which shows the ability of suppliers in immediate wealth realization and repayment of current liabilities.(7).Profit growth rate is equal to the difference of profits between the previous period and the current one divided by the profit in the prior period.This index represents supplier's development ability in finance.(8).Per employee training time is necessary to enhance staffs' energy saving and environmental protection awareness as well as master new technologies, besides the encouragement of policy-making and technological innovation and application.The index is equal to training days divided by the number of trained employees.(9).Equipment directly affects the formulation of product techniques and further has an effect on production capacity, which reflects whether advanced technology is adopted.(10).Input rate of research funding equals research funds divided by sales revenue over a period of time as a symbol of R&D capability.(11).On-time delivery rate examines suppliers' delivery capacity, represented by the total number of delivery on time divided by whole times of delivery.(12).Order completion rate is expressed as completed orders divided by total ones, which reflects suppliers' satisfaction to customers' purchasing needs.(13).Enterprise reputation can be acquired through the credit rating given by banks and customers.(14).Information level stands for the ability of suppliers and enterprise to exchange and share information, as well as represents the technical basis of suppliers' quick response to urgent orders.(15).Strategic objective compatibility reflects whether the supply chain is coordinated.This paper will particularly focuses on the low-carbon strategic target in supplier selection.(16).Carbon dioxide emission is calculated by the method of carbon emission factor, which indicates the amount of greenhouse gas emitting during production.(17)."Three-wastes" recycling rate refers to the recycling proportion of waste gas, waste water and waste residues generated during production and operation.(18).Environmental amelioration cost equals the expenses that the enterprise invests on environmental improvement and pollution control in a period of time.

FA
FA refers to a species of statistical method that extracts information and simplifies data by dimension reduction.The main steps are shown as follows [32]: (1) Test whether FA can be implemented on the variables.FA picks up common factors from a group of relevant variables.This technique will be invalid if variables are independent of each other or the overlap of information is small.Thus, it is imperative to carry out correlation analysis, mainly the Kaiser-Meyer-Olkin (KMO) test and Barylett test of sphericity.
(2) Identify common factors and determine the number by means of maximum likelihood estimate, least square method or principal component analysis (PCA), and so on.PCA, selected in this paper, is a technique that transforms normalized variables into irrelevant ones by coordinate alternation.Through calculating the eigenvalue λ i and corresponding standard orthogonal eigenvector l i , the factor loading matrix A can be derived from Equations ( 1) and ( 2).
Variance contribution rate, namely square sum of elements of the j-th column in matrix A, describes the total information extracted by common factors F j .The higher the variance contribution rate is, the more significant the common factor is. Generally, in order to enhance the interpretability of the factors, loading matrix A needs to be rotated so that elements in each row are divided into 0 and 1.
For the determination of the number of common factors, there ordinarily exists two approaches, choosing the factors of which eigenvalues are more than 1 or accumulative explained variation that accounts for the proportion of information in original indexes is over 0.85.
(3) Name the common factors.The nomenclature is customarily based on the rotated factor loading matrix.The common factor with large load illustrates the pre-selected variables have a strong correlation, thus it can be name after the mutual meaning of the bracketed variables.
(4) Calculate factor scores.The regression technique can be expressed as Equation (3). where In this way, the samples can be distinctly compared according to the scores of common factors in all aspects.

DEA
DEA is an approach based on the concept of relative efficiency and employs convex analysis and linear programming as techniques.The main steps are explained as follows [33]: Suppose that there are n low-carbon suppliers, called n decision making units (DMUs).Each DMU owns m inputs and p outputs expressed by different evaluation indicators.
The linear programming model of DEA can be mathematically presented as Equation ( 4). (P) where x ij is input i of DMU j , x ij > 0, y rj is output r of DMU j , y rj ≥ 0; v i represents the weight assigned to input i, v i ≥ 0, u r equals the weight assigned to output r, u r ≥ To make DEA more practical, non-Archimedean infinitesimal ε is introduced, as shown in Equation ( 5).
where êT and e T are the m and p dimension unit vectors, respectively.
The dual programming of (P ε ) is written as Equation ( 6): where T are slack variables.

AHP
AHP is a decision-making method combining qualitative and quantitative analysis based on the multiple hierarchy structure incorporating objectives, criteria, and projects.The priorities of elements in every hierarchy can be obtained as follows [34]: (1) Establish the pairwise comparison matrix.Suppose there are n elements, b ij stands for the relative importance of element i in contrast with element j.
where B is the pairwise comparison matrix and b ij = 1/b ji .
(2) Derive the priorities.Calculate the largest eigenvalue λ max and the corresponding eigenvector W of matrix B, that is, BW = λ max W and (w 1 , w 2 , • • • , w n ) equals the importance ranking of the elements.
(3) Test the consistency of the judgements.If the judgement is completely consistent, λ max = n, otherwise λ max > n.Thus, λ max − n can be used as a measure of the deviation from the coherence.
where CI and RI are the consistency indicator and random index, respectively.CR refers to the random consistency ratio.The comparison matrix is coincident if CR ≤ 0.01, otherwise the comparison matrix needs to be modified until the test is satisfied.The values of RI obtained from random 500 samples are listed in Table 2 [34].FA-DEA-AHP proposed in this paper can be constructed according to the following steps: (1) Division of input and output indicators.According to the index system recorded in Table 1, the indexes can be decomposed into two parts: input indexes required to be consumed and output indexes attached to effects in management, as shown in Table 3. (2) Refinement and simplification of the pre-selected indexes by FA.
(3) Establishment of comparison matrixes by DEA.Randomly choose two low-carbon suppliers M as well as N, then calculate the relative efficiency values θ MN and θ N M according to Equation (6).
The relative efficiency of low-carbon suppliers M and N, namely b MN or b N M can be derived from Equations ( 12) and (13).
b MN < 1 means supplier M is superior to supplier N; b MN = 1 represents supplier M is equivalent to supplier N; b MN > 1 indicates supplier M is inferior to supplier N. Thus, the comparison matrix can be achieved on the foundation of Equation ( 7).
(4) Sequence and selection of low-carbon suppliers using AHP.The validity of DEA for each supplier can also be judged.
Low-carbon supplier selection technique incorporating FA, DEA, and AHP is built, as illustrated in Figure 1.indicates supplier M is inferior to supplier N .Thus, the comparison matrix can be achieved on the foundation of Equation (7).
(4) Sequence and selection of low-carbon suppliers using AHP.The validity of DEA for each supplier can also be judged.
Low-carbon supplier selection technique incorporating FA, DEA, and AHP is built, as illustrated in Figure 1.

Case study
A large steel enterprise in China, integrating mining, smelting, processing, and building construction as a whole, is chosen as an example in this paper.This company positively responds to low-carbon policy, but pays no special attention to the choice of low-carbon supplier.In order to demonstrate the efficiency of the proposed model, seven available cement suppliers are selected as samples.Through the historical information of the suppliers, the qualitative indicators are scored by relevant leaders (the criteria are shown in the Appendix).
FA is firstly exploited to extract common factors from the seven inputs and eleven outputs listed in Table 1.The results of KMO and Bartlett's sphericity test can be attained from the following Table 4.The statistic value of KMO is generally between 0 and 1, the closer to 1 KMO is, the more appropriate

Case Study
A large steel enterprise in China, integrating mining, smelting, processing, and building construction as a whole, is chosen as an example in this paper.This company positively responds to low-carbon policy, but pays no special attention to the choice of low-carbon supplier.In order to demonstrate the efficiency of the proposed model, seven available cement suppliers are selected as samples.Through the historical information of the suppliers, the qualitative indicators are scored by relevant leaders (the criteria are shown in the Appendix A).
FA is firstly exploited to extract common factors from the seven inputs and eleven outputs listed in Table 1.The results of KMO and Bartlett's sphericity test can be attained from the following Table 4.The statistic value of KMO is generally between 0 and 1, the closer to 1 KMO is, the more appropriate for FA the variable is.The value of KMO in Table 4 equals 0.814, which proves that FA can be applied.Additionally, the significant probability of Bartlett's sphericity test is 0.000, denying the correlation matrix is a unit one.The common factors whose eigenvalues are over 1 are obtained by PCA in accordance with Equations ( 1) and (2).As we can see, the accumulative contribution rate of the four extracted common factors for outputs in Table 5 can be 96.965%,which indicates a large majority of information in original variables is summarized.Tables 6 and 7 presents the factor loading matrix and the deformation rotated by Varimax, respectively.As can be seen in Table 7, the first common factor has high load on information level (0.959), strategic objective compatibility (0.913), and enterprise reputation (0.885), nominated as credit cooperation factor.Similarly, the second factor is defined as low-carbon environmental factor, with high load on carbon dioxide emission (0.932) and "three wastes" recycling rate (0.721).The third common factor owing high load on the rate of return on total assets (0.939), quick ratio (0.733), and profit growth rate (0.967), as well as the fourth common factor with high load on product qualification rate (0.793), on-time delivery rate (0.906), and order completion rate (0.676) are respectively designated as economic level factor and supply capacity factor.Table 8 shows common factor scores derived from Equation (3).
Since there exists negative numbers in the original data, normalization is imperative as shown in Table 9.
Analogously, FA is implemented on input indicators and two common factors are obtained for original seven input indexes whose accumulative contribution rate reaches 86.34%.There, into the quality management system, quality improvement plan, and relative price level present a high load on the first common factor, named as product level factor, while per employee training time, equipment, input rate of research funding, and environmental amelioration cost have a high load on the second common factor designated as business security factor.The final score of input indexes are listed in Table 10.According to the DEA model, seven suppliers can be regarded as seven DMUs.Each factor has two input indicators and four output indicators for each DMU, as shown in Table 11.Calculate the pairwise relative efficiency of DMUs.Here, DMU 1 and DMU 2 are taken as an example, according to Equations ( 10) and (11).
where θ 12 and θ 21 are relative efficiency belonging to DMU 1 and DMU 2 .
The comparison matrix of AHP is expressed as follows: The validity of each DMU is further attained as illustrated in Tables 12 and 13.

Discussion
In Tables 12 and 13, it can be seen that the third low-carbon supplier ranks the first in AHP results, thus it is the optimal choice in supplier selection.
From the perspective of overall scale effectiveness and technical validity, DMU 3 = 1, s 0− = 0 and s 0+ = 0, DMU 3 is effective, indicating that for the third supplier, the resources are fully utilized and input elements have reached the best combination, as well as the maximum output has been achieved.The relative efficiency values of other DMUs are less than 1, thus these DMUs are invalid.In terms of scale profits, the values of k of other six low-carbon suppliers are all more than 1, except the third supplier, namely returns to scale have descended.The results reveal that these low-carbon enterprises have not fully utilize resources and the output has not achieved the desired effect.Therefore, these suppliers should further strengthen management and make full use of resources so as to obtain more output and improve the decreasing trend of economic benefits.
It is noteworthy that there exit redundancies in slack variables, which doesn't mean suppliers invest too much in product quality and business assurance.Whether the investment in product quality management, per employee training time or in environmental amelioration costs should be encouraged.The key to this problem is to make the investment really work, for example, it needs to be judged whether the expenses on equipment and environmental management are helpful for improvement of product quality and environment.
The part over 0 in slack variables of output responds to output deficit, mainly reflecting in low-carbon environmental factor.It can be seen that suppliers have not attached importance to environmental protection or received clear effects in the early stage of low-carbon economy.
In addition, in order to justify the effectiveness of the proposed model, the comparison model of factor analysis and analytic hierarchy process (FA-AHP) is introduced to solve the same problem of low carbon supplier selection.The operation steps of factor analysis and analytic hierarchy process are consistent with the proposed model.It is worth pointing out that the judgement matrix of FA-AHP is obtained through the enterprise relevant leaders scoring.The comparison results are shown in Table 14.

Model Selection Evaluation Results Sorted in Descending Order
FA-DEA-AHP Supplier 3, Supplier 2, Supplier 6, Supplier 4, Supplier 5, Supplier 7, Supplier 1 FA-AHP Supplier 6, Supplier 3, Supplier 2, Supplier 4, Supplier 5, Supplier 1, Supplier 7 As can be seen from Table 14, the selection evaluation results of these two models are slightly different.In the FA-AHP model, supplier 6 ranks first, which means that the enterprise should first select supplier 6 as its own low carbon supplier.The reason for the difference between this and the proposed model was that supplier 6 had been a raw material supplier to the enterprise and left a good impression on the leadership of the enterprise in terms of delivery efficiency and corporate reputation.Therefore, in the process of constructing judgment matrix, it is influenced by the strong subjectivity of AHP itself, and the supplier ranks relatively high.However, in addition to the good cooperation ability, the supplier 6 performs generally in terms of product level, enterprise qualification, environmental competitiveness and other aspects, inferior to supplier 3 and supplier 2. From this perspective, the FA-DEA-AHP mentioned in this paper can effectively remedy the defects of FA-AHP.In addition, if there are two suppliers with DMU = 1, the validity of DEA cannot be judged.Therefore, the proposed model FA-DEA-AHP can make further differentiation.
As mentioned in the Section 2, there is no unified standard for supplier selection and evaluation index system.To the suppliers of different product types, choose the evaluation index are influenced by the characteristics of the product type changes, especially the environmental competitiveness evaluation index, it needs to pay special attention to in the study of supplier selection problem in the future.

Conclusions
Environmental sustainability in supply chain depends on supplier selection of all the members.Excellent suppliers are important guarantee of enterprise profit and consumer satisfaction, thus the option of low-carbon supplier is a vital strategy for long-term development of enterprise.In light of this complex task, a novel model FA-DEA-AHP is put forward in this paper.First of all, an evaluation index system is constructed, incorporating product level, qualification, cooperation ability, and environmental competitiveness.FA is applied to effectively refine and synthesize the 18 pre-selected indicators.Then, this paper employs DEA to establish pairwise comparison matrix and adopts AHP to rank low-carbon suppliers comprehensively as well as calculate the validity of decision-making units.Finally, seven cement suppliers in a large industrial enterprise are taken as an example.The experiment results indicate that the integrated model can not only choose effective suppliers, but also realize the ranking, which is more reasonable and effective than FA-AHP.To sum up, the research methods on supplier evaluation and selection have been enriched and the theoretical value in exploring low-carbon coordinated development has been presented on the basis of this paper.Simultaneously, the research is of practical significance in selecting suppliers in green environment and constructing a competitive low-carbon supply chain.Nevertheless, according to the different product types of supplier, the evaluation index selection, especially the environmental competitiveness evaluation index, are influenced by the characteristics of the product, which needs to pay special attention to in the study of supplier selection problem in the future.

Figure1.
Figure1.The framework of low-carbon supplier selection.

Figure 1 .
Figure 1.The framework of low-carbon supplier selection.

Table 1 .
Evaluation index system of low-carbon supplier selection.

Table 2 .
The values of RI obtained from random 500 samples.

Table 3 .
Inputs and Outputs in low-carbon supplier selection.Inputs quality management system, quality improvement plan, relative price level, per employee training time, equipment, environmental amelioration cost, input rate of research funding Outputs product qualification rate, the rate of return on total assets, quick ratio, profit growth rate, on-time delivery rate, order completion rate, enterprise reputation, information level, strategic objective compatibility, carbon dioxide emission, "three wastes" recycling rate

Table 5 .
The total explained variance of output indicators.

Table 6 .
Factor loading matrix of output indicators.

Table 8 .
Factor scores of output indicators.

Table 9 .
Normalized factor scores of output indexes.

Table 10 .
Normalized factor scores of output indexes.

Table 11 .
Low carbon supplier input and output data.

Table 12 .
Validity evaluation results of each DMU.

Table 13 .
Validity evaluation results of each DMU.