Multi-Criteria Group Decision Making for Green Supply Chain Management under Uncertainty

This paper presents a multi-criteria group decision making model for effectively evaluating the performance of green supply chain management (GSCM) practices under uncertainty in an organization. The subjective assessments of individual decision makers are appropriately represented with the use of intuitionistic fuzzy numbers for better tackling the uncertainty existent. An algorithm is developed to assist individual decision makers in evaluating the performance of alternative GSCM practices across all the evaluation criteria. An example is presented for demonstrating the applicability of the proposed model in solving similar problems in the real-world setting.


Introduction
The importance of sustainability development is being recognized increasingly across the world in individual organizations [1].This is due to the rapid development of the world economy for consuming non-renewable resources and the increasingly deteriorating world environment [2,3].With this increasing recognition, organizations have started to adopt various sustainability development practices including green supply chain management (GSCM) in their operations to strengthen the green image of their organizations and to protect the environment along the whole supply chain while actively seeking the improvement of the competitiveness of the organization [4][5][6].
GSCM is about the effective consideration of sustainability development along the whole supply chain in an organization [7].This involves redesigning the business processes in an organization for satisfying the customer of the supply chain while considering the issue of sustainability development [8,9].GSCM focuses on minimizing the wastage in the operations of an organization along the supply chain through specific activities such as product design, material resourcing, product delivery, and management of the end-of-life of products [10].It involves coordinating the activities along the supply chain for improving the sustainability development of an organization [11,12].Effective GSCM helps organizations improve their competitiveness through: (a) reducing pollution and waste; (b) working with environmental-friendly suppliers; (c) developing green products and services; and (d) reducing emissions related to the transportation and delivery of products and services [13].
Evaluating the performance of GSCM practices is challenging.Multiple decision makers are often involved.Often, multiple and conflicting evaluation criteria exist.Furthermore, uncertainty is always present due to the use of subjective assessments in the evaluation process.To adequately solve this problem, the development of structured models capable of comprehensively evaluating the performance of individual GSCM practices is, therefore, desirable.
Much research has been done, and various models have been developed for solving the problem of evaluating the performance of GSCM practices from different perspectives [14][15][16].Such models can be classified usually from two perspectives: multi-criteria evaluation and multi-objective optimization [17,18].They have shown their respective merits in addressing this problem in organizations in various circumstances.
Multi-criteria evaluation models formulate the performance evaluation process as a discrete optimization problem with the development of specific algorithms for facilitating the performance evaluation process while adequately considering multiple, usually conflicting evaluation criteria.Kannan et al. [15], for example, combined interpretive structural modeling and analytic hierarchy process [19] for evaluating GSCM practices.Interpretive structural modeling is used for studying the interaction between criteria, leading to the determination of the weights of the evaluation criteria.The analytical hierarchy process is then applied for determining the suitable GSCM practice in organizations.Awasthi et al. [14] developed a fuzzy model for assessing GSCM practices in organizations.Linguistic assessments are used for better modeling the uncertainty in the evaluation process.The technique for order preference by similarity to ideal solutions (TOPSIS) is adopted for aggregating these linguistic assessments in determining the performance index value for all the alternatives across the evaluation criteria [20].Shen et al. [16] extended the TOPSIS model for evaluating GSCM practices in the Taiwanese electronic industry.Linguistic variables are used for assessing the weights of the evaluation criteria and the performance rating of each alternative with respect to each criterion.A weighted decision matrix is constructed on which a closeness coefficient is calculated for ranking all the GSCM practices across all the evaluation criteria.
Multi-objective optimization models treat the performance evaluation process as a continuous optimization problem with the focus on the tangible benefits and costs in the decision process.Roghanian et al. [21], for example, proposed a multi-objective optimization model for planning green supply chains in organizations.Torabi and Hassini [22] presented a multi-objective model for designing multi-echelon supply chains.Pinto-Varela et al. [23] developed a mixed-integer programming model for designing green supply chains with respect to the economic and environmental consideration of an organization.Liu and Papageorgiou [24] constructed a linear programming model for evaluating green supply chains.
In summary, these models have shown their merits in evaluating GSCM practices from different perspectives.They are, however, not completely satisfactory for effectively addressing this problem due to: (a) the need for adequately considering the interest of multiple decision makers; (b) the presence of uncertainty; and (c) the demand on decision makers in the evaluation process.
This paper presents a group decision making model for evaluating GSCM practices in an organization.To adequately model the uncertainty in decision-making, intuitionistic fuzzy numbers are used for representing the assessment of the decision maker.To effectively aggregate the subjective assessment, an algorithm is developed for determining the overall performance of GSCM practices with respect to the sustainability criteria.An example is presented that shows the proposed model is effective in solving similar problems in the real world setting.
In what follows, the problem of evaluating GSCM practices are first formulated as a multi-criteria group decision making problem.An algorithm is then developed for effectively solving this problem, followed by an example.

Evaluating the Performance of GSCM Practices
Conserving resources and protecting environments are becoming increasingly important nowadays, thereby exerting pressures on organizations worldwide.These pressures have forced individual organizations to improve their environmental performance while maintaining their competitiveness in the marketplace [25].As a result, organizations are looking for the adoption of specific GSCM practices [5].To ensure that the best GSCM practice is implemented, evaluating individual GSCM practices across various evaluation criteria by different stakeholders is necessary.
There are numerous studies on investigating the criteria for affecting the performance of GSCM practices in organizations [25][26][27][28][29][30].These criteria can usually be classified into four perspectives: (a) green design; (b) green purchasing; (c) green manufacturing; and (d) green marketing.
Green design is about the active consideration of the impact of products and services on the environment while designing these products and services [9,10].In designing a specific product or service, it is critical for organizations to adequately consider the impact of the whole lifecycle of that product.Such a practice is often referred to as eco-design.It can improve the environmental outcome and reduce the costs of the operations in an organization [31].
The role of green design in effective GSCM has been explored in the literature.Diabat and Govindan [10], for example, stated that green design must be considered when evaluating GSCM practices in organizations.This is because green design emphasizes on sustainable practices of reusing and recycling materials in the daily operations of an organization.Arena et al. [32] showed that green design should consider the impact of products and services along their life cycles [33].Zhu et al. [25] believed that organizations need to adequately consider the design of products for possible reuse.This is because green design not only allows the product and its components to be easily reused, but also helps to replace products with greener substitutes in specific circumstances.
Green design is important for evaluating GSCM practices.It is equally critical to balance the consideration between green design and the practicality of the product function.Rao and Holt [34] and Azevedo et al. [35], for example, showed that it is critical for organizations to adopt a balanced view between green design and product functions.Hu and Hsu [36] and Barari et al. [26] found that it is necessary to consider various factors in designing a product or service in an environmentally sustainable manner including: (a) avoiding utilizing toxic substances; (b) reducing the use of energy; (c) meeting the requirement for disassembly, reuse, and recycling; and (d) increasing innovation capabilities of an organization.Sarkis [37] and Shen et al. [16] proved that green design can help organizations to minimize waste and improve the environmental performance by designing the functionality of products and minimizing the environmental impact.Mangla et al. [38] believed that green design can minimize the ecological effect of a new product throughout the entire lifecycle of the product without compromising on the functionality.Overall green design can be approached from several perspectives including: (a) environmental risk management; (b) pollution prevention; (c) resource conservation; (d) product safety; and (e) waste management.
Green purchasing is related to the ability of an organization to procure products and services that minimize the negative environmental impact over the lifecycle of the product and services [16].It involves identifying, selecting and purchasing products and services with less adverse environmental impacts than competing products and services.Green purchasing considers the environmental characteristics of a product in all stages of the life-cycle [34].It enables organizations to establish environmental standards in their purchasing policies for improving GSCM.
The importance of green purchasing is well recognized in existing literature.Sarkis [37], for example, believed that green purchasing is about waste reduction, environmental material substitution, and hazardous material minimization.Vachon and Klassen [12] stated that the performance of green supply chains is dependent on the ability of an organization to adopt green design and green purchasing.Shen et al. [16] indicated that green purchasing significantly eliminates waste, therefore improving the performance of GSCM. Lee et al. [39] pointed out that organizations need to improve green purchasing initiatives for better achieving the economic and operational goals.Luthra et al. [40] emphasized the importance of green purchasing for achieving a positive outcome of GSCM practices.An investigation of the related literature shows that green purchasing is usually measured by: (a) green competencies; (b) green image; and (c) green management abilities of individual suppliers.
Green manufacturing is the production of products that can minimize the natural resources use and improve recycling and reusing [9].It focuses on utilizing greener sources of energy via the adoption of latest technologies in the daily operations of an organization.Furthermore, green manufacturing is about reducing pollution and wastes while improving the efficiency of the operations of an organization [25].Azevedo et al. [35] and Barari et al. [26], for example, showed that green manufacturing should consider the willingness of an organization to develop green products while reducing the negative environmental impact of the manufacturing process.Chen et al. [41] pointed out that green manufacturing is directly related to the selection and use of the right materials in an organization.Thanki et al. [17] believed that green manufacturing can enhance the market share, the competitive advantage and the green image of an organization.Govindan et al. [8] stated that effective green manufacturing helps to improve business performance of an organization in a dynamic global market.In general, green manufacturing is reflected by: (a) the green energy utilization; (b) the degree of green energy; (c) the reduction of hazardous waste; and (d) the reuse of hazardous waste.
Green marketing is about the initiative that an organization takes for promoting the green characteristics of its products and services for reducing the negative environmental impact [25].It is a strategic activity in an organization that involves in green logistics and green alliances through manipulating segmenting, targeting, and positioning in addition to the traditional marking principles such as product, price, place, and promotion [26].Ginsberg and Bloom [42], for example, pointed out that it is important for organizations to implement green marketing strategies by continuously: (a) interacting with customers; and (b) increasing the credibility of products and services.Carter and Ellram [43] believed that organizations need to continuously interact with government, suppliers, customers, and even competitors for improving the sustainability development of the supply chain.Zhu et al. [25] claimed that the cooperation with suppliers and customers is critical for organizations to close the supply chain loop towards sustainability development.Linton et al. [44] and Zhu et al. [45] stated that GSCM practices should be evaluated based on the effective communication of an organization with suppliers and customers on sustainability development in the delivery of products and services.Fang and Zhang [46] believed that organizations need to collaborate with customers to reduce the total cost, decrease the lead time and improve the satisfaction of customers.In general, green marketing is measured by: (a) the use of information and communication technologies; (b) the transparency of the disclose of environmental information of products and services; (c) the willingness of extending producers' responsibility; and (d) the provision of education and training on the benefits of green products and services.A summary of the critical criteria for determining the performance of GSCM practices in an organization is shown in Table 1.
Table 1.Criteria for Determining the Performance of GSCM Practices.

Criteria References
Green design [9,10,14,16,25,26,31,[34][35][36][37][38]44] Green purchasing [10,12,16,34,37,39,40] Green manufacturing [8,9,14,17,25,26,41] Green marketing [25,26,42,43,[45][46][47] In selecting the most appropriate GSCM practice in an organization, every available GSCM practice has to be comprehensively evaluated with respect to the criteria and their associated sub-criteria in a holistic manner for determining their overall performance across all the evaluation criteria in a specific situation.Furthermore, various stakeholders are presented in such an evaluation process due to the nature of the GSCM process and the existence of uncertainty.To effectively solve this problem, the next section presents an interactive fuzzy multi-criteria group decision making model for evaluating the performance of GSCM practices in an organization.

A Fuzzy Multi-Criteria Group Decision Making Model
Multi-criteria group decision making involves several decision makers in prioritizing and ranking available alternatives with respect to multiple, often conflicting criteria [17,[48][49][50][51]. Evaluating and selecting specific GSCM practices in an organization usually consists of several activities.First, all the alternatives and the evaluation criteria have to be identified.The performance rating of the GSCM practice alternatives and the weight of the evaluation criteria and their associated sub-criteria if existent then have to be determined.Finally, the alternative rating and the criteria weight have to be aggregated for determining the overall performance index value for each alternative across all the criteria, on which the best alternative can be selected.
Uncertainty is always present in human decision making.It is usually existent due to the presence of subjectiveness and imprecision [1].To better model the uncertainty, intuitionistic fuzzy numbers [52,53] are used for representing the assessments of the decision maker.This is due to: (a) the appropriateness of intuitionistic fuzzy numbers in tackling the uncertainty in decision-making; and (b) the simplicity of representing subjective assessments with the use of membership degree and non-membership degree [54,55].
The proposed model starts with assessing the performance rating of each GSCM practice alternative A i (i = 1, 2, . . ., n) with respect to each criterion C j (j = 1, 2, . . ., m).To facilitate the subjective assessment process, intuitionistic preference relations y k ij = (µ k ij , v k ij ) are used to represent the assessment of the decision maker D k (k = 1, 2, . . ., s) with respect to criterion C j in which 0 In this situation, µ k ij indicates the degree that alternative A i satisfies criterion C j , while v k ij describes the degree that alternative A i does not satisfy criterion C j .As a result, the decision matrix for each decision maker in this problem can be determined as follows With the determination of the subjective assessments as above, the consensus among the decision makers needs to be assessed [56].In this situation, a distance-based similarity measure is proposed [1,56].It is used to describe the closeness between the fuzzy assessments of a decision maker and the group fuzzy assessments for all the alternatives.This leads to the determination of the degree of consensus between a decision maker' assessments r k ij and the group assessments m ij for alternative performance ratings on each criterion as follows where To determine whether a decision maker has reached the group consensus, a consensus threshold value δ can be used.If S k i ≥ δ, this means that the decision maker must change the assessments.Through such interactive changes and modifications, the consensus value of individual decision makers can be lower than the specified consensus threshold, and therefore the consensus development process can stop.
The relative importance of the criteria can be determined subjectively by the decision maker using intuitionistic fuzzy numbers represented as w k j = (µ k j , v k j ) .µ k j indicates the degree to which criterion C j is considered as important.v k j describes the degree to which criterion C j is deemed to be unimportant.To facilitate the decision-making process, the criteria weight w j can be normalized as follows where To prioritize and rank all the alternatives, the subjective assessments should be aggregated.To facilitate the aggregation process, the intuitionistic fuzzy hybrid geometric averaging (IFHGA) operator [56] is introduced for determining the overall intuitionistic fuzzy performance r i of the alternative A i , shown as in Equation ( 5).
With the use of the score function [57], the performance index value of each alternative with respect to all the criteria can be determined as where . The larger the S(r i ) is, the more preferred the alternative is.
The procedure for the proposed model as above can be summarized as follows.
Step 1 Obtain the decision matrix from each decision maker as expressed in Equation (1).
Step 2 Assess the consensus among the decision makers by Equation (2).
Step 3 Determine the relative importance of the criteria as expressed in Equations ( 3) and (4).
Step 4 Calculate the performance of each alternative from all decision makers as in Equation (5).
Step 5 Compute the performance index value for each alternative across criteria by Equation ( 6).
Step 6 Rank the alternatives in descending order of their performance index values.

An Example
This section presents an example of evaluating the available GSCM practices for ensuring that the best GSCM practice can be selected in an organization.
Due to the intense competition and the presence of the networked market, a reputable company in Taiwan is considering a green supply chain initiative for improving its performance [10].The company is one of the largest professional printed circuit board manufacturers in Taiwan.It is developing the next generation of technology for enhancing its competitiveness.Due to the increasing market pressure, the company needs to develop green products for satisfying the changing market situation.This leads to the consideration of the implementation of a proper GSCM practice in the organization.
Three top managers from three functional departments within the organization are involved in assessing the GSCM practices represented as D 1 , D 2 , and D 3 .A series of meetings have been held.This leads to the identification of four criteria for evaluating the four GSCM practices in an organization.These criteria include the Green Design (C 1 ), Green Manufacturing (C 2 ), Green Purchasing (C 3 ), and Green Marketing (C 4 ).The hierarchical structure of GSCM practice evaluation is shown in Figure 1.
Green Design (C 1 ) is related to the capability of an organization to reduce the negative impact on the environment through product designs [4,57].This is often measured by the ability of the organization to minimize using toxic substances, meet sustainability principles, increase innovation capabilities, and reduce energy use in the operations of the organization.
Green manufacturing (C 2 ) considers the enhancement of the production processes for reducing the generation of toxic matter [58].It requires an organization to produce products with less waste and less pollution.This is often measured by the amount of resources used, the greenness of the energy, and the reduction of hazardous waste [11,59].
Sustainability 2018, 10, x FOR PEER REVIEW 7 of 13 Green manufacturing (C2) considers the enhancement of the production processes for reducing the generation of toxic matter [57].It requires an organization to produce products with less waste and less pollution.This is often measured by the amount of resources used, the greenness of the energy, and the reduction of hazardous waste [11,58].Green Purchasing (C3) is about the practice of sourcing and purchasing products and services that are less damaging to the environment than their substitutes [6].Several factors including the green image, the green competency, and the green management ability are usually considered in this regard [12,26].
Green Marketing (C4) is about promoting the green characteristics of products and services that are safe for individuals and environments [59].This is often measured through the adoption of information and communication technologies in marketing and the provision of education and training on the benefits of green products and services [10,59].
With the determination of the alternatives and the criteria as above, the performance rating of all available alternatives with respect to each criterion from decision makers D 1 , D 2 , and D 3 can be determined as in Table 2. Green Purchasing (C 3 ) is about the practice of sourcing and purchasing products and services that are less damaging to the environment than their substitutes [6].Several factors including the green image, the green competency, and the green management ability are usually considered in this regard [12,26].
Green Marketing (C 4 ) is about promoting the green characteristics of products and services that are safe for individuals and environments [60].This is often measured through the adoption of information and communication technologies in marketing and the provision of education and training on the benefits of green products and services [10,60].
With the determination of the alternatives and the criteria as above, the performance rating of all available alternatives with respect to each criterion from decision makers D 1 , D 2 , and D 3 can be determined as in Table 2.In this situation, the consensus threshold is set at 0.65.Based on all the information provided, the similarity between individual decision makers' assessments and the group assessments can be calculated by Equation (2).The results are shown in Table 3. Table 3 shows that the familiarity values of individual decision makers are lower than the threshold value of 0.65.As a result, there is no need for developing consensus further.With the achievement of the consensus, the weights of the criteria need to be determined by the decision maker.Table 4 shows the results.Based on this information, the criteria weight vector w j can be calculated using Equations ( 3) and ( 4).The resulted criteria weights are determined as W j = (0.2451, 0.2563, 0.2422, 0.2564).
With the use of Equations ( 5) and ( 6), the performance index value of each alternative with respect to all the criteria and its corresponding ranking can be determined.Table 5 shows the results.It shows that alternative A 2 has the best performance with the highest performance index value of 0.675.To demonstrate the merits of the proposed model, a comparative study is conducted.Five other models [47,[61][62][63][64][65][66] are used.The results shown in Table 6 reveal that the proposed model produces consistent ranking results as compared to other comparable models.This demonstrates that the proposed model is effective due to its simplicity in concept and its efficiency in computation.

Conclusions
Evaluating the performance of available GSCM practices in an organization is not an easy task.This is because such an evaluation involves several decision makers and multiple criteria with the presence of uncertainty in the group decision making process.This paper has presented a multi-criteria group decision making model for effectively evaluating the performance of GSCM practices in an organization.The uncertainty of the evaluation process is adequately modeled by using intuitionistic fuzzy numbers.A fuzzy multi-criteria group decision making model is developed for evaluating the performance of GSCM practices in an organization.The example presented shows that this developed model is capable of effectively and efficiently solving the multi-criteria group decision making problem.It can help organizations to better understand the performance of GSCM practices for improving their overall sustainability development performance.
There are several limitations in this study.One is to do with the dependency of the decision outcome on the inputs of the decision maker.This is to do with the way that this problem is formulated.Another is about the need for considering tangible and intangible benefits and costs together in evaluating the available GSCM practices.Future research can be carried out to better deal with these two issues through the proper use of organizational data and knowledge in the evaluation and the development of continuous optimization models for addressing the performance evaluation problem.

Figure 1 .
Figure 1.The Hierarchical Structure of GSCM Practice Evaluation.

Figure 1 .
Figure 1.The Hierarchical Structure of GSCM Practice Evaluation.

Table 2 .
Performance Assessments of GSCM Practices.

Table 3 .
The Degree of Similarity of Individual Decision Makers.

Table 5 .
The Performance Index Value and the Ranking of GSCM Practices Alternatives.

Table 6 .
An Overview of the Comparative Study.