5.1. Implementation
Our simulated Company C.C., is a leading manufacturer of high-tech premium polymers, in which sustainability is regarded as one of the most important driving forces behind the continuous development of its products, processes, and facilities. In order to safeguard its global competitiveness and the supply of materials and services, it operates responsibly in collaboration with its suppliers, aiming to mitigate risks and create stable, long-term business relationships with its partners. It follows a four-step process, including supplier awareness, supplier nomination, supplier sustainability performance evaluation, and supplier development, in order to improve sustainability practices within a supply chain. When choosing new suppliers or continuing its relationships with existing ones, the company applies not only economic standards, but also environmental, social, and corporate governance standards. These standards are divided into four themes which include environment (EVN), labor practices (LAB), fair business practices (FBP), and sustainable procurement (SUP), and these standards are used as the criteria for evaluating the sustainability performance of its selected suppliers.
Suppose that after pre-assessment, Company C.C. nominates a list of potential suppliers
for further evaluation and selection. These nominated suppliers are evaluated with respect to four evaluation criteria
, which are EVN, LAB, FBP, and SUP. In order to choose the best supplier, a committee of three decision makers,
is formed. These experts are from different departments including a full-time auditor, a sourcing manager, and head of the sustainable development department. Note that the proposed approach is applicable to any number of team members and the three experts selected in this case are for demonstration purposes only. The weights for the three decision makers are given as
,
and
. Specifically, the crisp values and the interval numbers with the same zero to 10 qualitative scale are used to express the assessments provided by decision makers on each supplier with respect to the evaluation criteria EVN and LAB, respectively. While, the TFNs (
Table 1) are applied to express the risk assessments provide by decision makers on each supplier with respect to both of the evaluation criteria FBP and SUP. The computational procedures conducted in this case are explained according to each step of the proposed sustainable supplier selection method.
The assessments of the five suppliers given by the three decision makers are provided in
Table 2.
Stage 1: Aggregating decision information into IVIFNs.
Step 1 Since the assessment values are given according to the ten-mark system, the smallest grade, the middle grade, and the largest grade of the assessment vector is determined as follows:
If the assessment value is given as the crisp number, then , and ; if the assessment value is given as the interval numbers, then , and ; if the assessment value is given as the TFNs, then , and .
Step 2 By using Equations (18) to (20), the Qsd, Qdd, and Qud of each assessment value is derived and shown in
Table 3.
Step 3 Using Equations (21) to (23), the Qsi, Qdi, and Qui can be computed and presented in
Table 4.
Step 4 By Equation (24), the induced IVIFNs of assessment vectors can be obtained and displayed in
Table 4.
Stage 2: Ranking alternative sustainable suppliers.
Step 1 The evaluation vector of the decision criteria is shown in
Table 5. By Equation (25), the weights of the four decision criteria are derived as
,
,
and
.
Step 2 By Equations (26) and (27), the relative weight of each criterion is computed as , , and .
Step 3 The parameter
is taken as 1. By Equation (28), the dominance of alternative
over alternative
under each criterion is derived and presented below:
Step 4 By Equation (29), the overall dominance of alternative
over alternative
is obtained and displayed as follows:
Step 5 Finally, by using Equation (30), the global value of each alternative is derived as , , , , . Therefore, is the optimal permutation of the alternative sustainable suppliers and the optimal ranking order of the suppliers is A1 > A2 > A3 > A5 > A4. Thus, A1 is selected as the most sustainable supplier for the simulated Company C.C.
5.2. Comparative Analysis
To further demonstrate the efficiency of the proposed sustainable supplier selection method, a comparative study was performed with several existing methods to solve the same supplier evaluation problem. As the proposed approach is designed to overcome the shortcomings of the simple weighted average algorithm applied in the ECO system, the weighted average method was selected for the comparison [
32]. In addition, the TOPSIS method is among the most widely used MCDM methods for solving supplier section problems. Therefore, we also compare the proposed method with the fuzzy TOPSIS method [
4] to show its merits. The ranking orders of the five alternative suppliers produced by these three methods are shown in
Table 6.
As depicted in
Table 6,
A1 is the optimal sustainable supplier and
A4 is the least favorable supplier by the proposed approach and the two comparative approaches, which shows the validity of the proposed model. In addition, there are some differences between the ranking orders determined by the proposed method and the two comparative methods. First, the differences between the proposed method and the weighted average method can be seen in the alternative suppliers
A2,
A3,
A4, and
A5. These differences are mainly due to the deficiencies in the simple weighted average method. As can be seen in
Table 6, the alternatives,
A2 and
A3, are given the same rank by the weighted average method. However, the sustainability performance of the two suppliers is different. In contrast, the proposed method can distinguish the sustainability performance of these two suppliers by ranking
A2 before
A3. The same case can be seen in the suppliers
A4 and
A5, which also have the same rank when using the weighted method. Whereas by the proposed method,
A5 is given a higher rank than
A4.
Secondly, apart from A2 and A3, the ranking order for the other alternatives acquired by the proposed method is the same as those of the fuzzy TOPSIS method. The fuzzy TOPSIS method ranked A3 before A2. However, the results determined by the proposed method ranked A2 higher than A3. The inconsistency in the ranking results can be explained by the following reasons: (1) Intuitionistic fuzzy numbers are used by the fuzzy TOPSIS method to evaluate the sustainability performance of the suppliers, while the heterogeneous information is adopted in the proposed method and then aggregated into IVIFN. With the membership function and non-membership function degrees assigned in the form of intervals, the proposed method has better agility for expressing the uncertainty and ambiguity of decision makers’ assessment information as it can be used to describe the characteristics of affirmation, negation, and hesitation simultaneously. (2) The ranking procedures of the fuzzy TOPSIS method are based on the assumption that the decision makers are completely rational. In contrast, based on the TODIM method, the proposed heterogeneous MCDM method has bounded rationality and takes the psychological characteristics of the team members into account, and therefore is able to derive a ranking result that is closer to the real situation.