Research on Green Supplier Selection Method Based on Improved AHP-FMEA

Abstract

The increasing demand for sustainable business practices has highlighted the need for a robust and risk-aware green supplier selection framework. Traditional supplier evaluation methods primarily focus on cost, quality, and delivery performance but often fail to incorporate sustainability and risk factors effectively. This study proposes an improved AHP-FMEA method that integrates the Analytic Hierarchy Process (AHP), entropy weight method, and Failure Mode and Effects Analysis (FMEA) to enhance decision-making in green supplier selection. The AHP method determines subjective criteria weights, while the entropy method adjusts these weights objectively to reduce bias. The FMEA approach incorporates risk assessment by identifying and quantifying potential supplier failures, ensuring a more comprehensive evaluation. A case study is conducted to validate the proposed model, comparing it with classical AHP and AHP-Entropy methods. The results show that incorporating risk factors significantly influences supplier ranking, demonstrating the model’s ability to provide a more scientific, objective, and risk-conscious evaluation. The proposed approach enhances the accuracy and reliability of green supplier selection, making it a valuable tool for sustainable supply chain management.

1. Introduction

The growing importance of sustainable practices and environmental responsibility in modern business operations has led companies to rethink their supplier selection processes. Green suppliers, who prioritize eco-friendly products, sustainable practices, and environmental stewardship, are increasingly becoming integral to corporate supply chains [1]. The shift toward greener supply chains has been driven by rising consumer demand for sustainable products, stricter environmental regulations, and the need for companies to reduce their carbon footprint. As sustainability becomes a key competitive factor, selecting the right green suppliers has become an essential aspect of corporate strategy.

Supplier selection is a critical decision that directly impacts an organization’s efficiency, cost-effectiveness, and environmental sustainability. A successful supplier selection process ensures that a company’s supply chain is not only cost-effective and efficient but also aligned with its sustainability goals [2]. Traditional supplier selection methods often focus on factors such as price, quality, and delivery time. However, with the increasing emphasis on sustainability, it has become necessary to incorporate environmental and risk-related factors into supplier evaluations. This shift requires a comprehensive approach that balances financial and environmental considerations while accounting for potential risks.

In this context, multi-criteria decision-making (MCDM) techniques, such as the Analytic Hierarchy Process (AHP) and Failure Modes and Effects Analysis (FMEA), have proven to be valuable tools for selecting suppliers in an environmentally conscious manner. AHP helps decision-makers prioritize criteria based on their relative importance [3], while FMEA allows for the identification and evaluation of potential risks associated with each supplier [4]. Although both methods have been widely used in various fields, they have not been fully integrated in the context of green supplier selection, particularly in addressing the challenges posed by risk management and objective decision-making.

This paper proposes an improved AHP-FMEA method for green supplier selection, combining the strengths of both AHP and FMEA to create a more robust and comprehensive evaluation framework [5]. The primary objective of this approach is to integrate subjective judgments (such as expert opinions) and objective assessments (such as entropy-based weight calculations) with risk assessment techniques to provide a more accurate and holistic supplier ranking. By combining these methods, this study aims to offer a novel decision-making framework that helps organizations identify the most suitable green suppliers, while considering both sustainability and operational risks.

The research presented here highlights the importance of risk factors in the supplier selection process. While many traditional methods focus on price and performance, the failure to account for risks, such as potential disruptions in supply chains, environmental violations, or a supplier’s inability to meet sustainability targets, can lead to long-term consequences for organizations. By integrating FMEA into the green supplier selection process, this study addresses these concerns by evaluating the likelihood and impact of various failure modes, such as non-compliance with environmental regulations or failure to achieve carbon reduction targets. The result is a more comprehensive, risk-aware evaluation process that goes beyond traditional supplier selection criteria.

The paper also explores the application of the entropy weight method as a means to objectively determine the importance of different selection criteria. While AHP has been widely used to assign subjective weights based on expert judgment, the entropy method provides an objective approach to weight determination, reducing the subjectivity inherent in the decision-making process. By using both methods, this research ensures that the supplier selection process is both scientifically sound and aligned with the goals of sustainability.

To achieve these objectives, this study addresses the following research questions:

• How can green supplier selection methods be improved to effectively integrate sustainability and risk assessment?
• What are the limitations of traditional AHP and AHP-Entropy methods in handling supplier-related risks, and how can FMEA enhance the evaluation process?
• How does the proposed improved AHP-FMEA method compare with traditional approaches in terms of supplier ranking, risk mitigation, and environmental outcomes?

The main contributions of this paper are threefold: First, while green supplier selection has been extensively studied, existing research often lacks a comprehensive integration of objective weighting, risk assessment, and subjective evaluation into a unified decision-making framework. Most traditional methods focus on either subjective assessments (e.g., AHP), objective weighting (e.g., entropy method), or risk analysis (e.g., FMEA) in isolation. This paper bridges this gap by proposing an improved AHP-FMEA method, which systematically combines AHP for subjective weighting, the entropy method for objective weight adjustments, and FMEA for risk evaluation. Through this integration, we provide a more balanced, scientifically sound, and risk-aware approach to green supplier selection, enriching the literature on MCDM and sustainable supply chain management. Second, this paper makes theoretical contributions to the MCDM field by advancing the integration of risk assessment into multi-criteria decision frameworks. While traditional MCDM methods primarily focus on optimizing performance criteria, they often neglect dynamic risk evaluation in supplier selection. Our proposed approach enhances classical MCDM techniques by incorporating risk impact quantification using FMEA, offering a hybrid decision-making model that is more applicable to real-world uncertainties in sustainable supply chains. This contributes to the theory of MCDM by demonstrating how risk factors can be systematically embedded into the weighting process, ensuring a more holistic evaluation framework. Third, this paper contributes to managerial practice by offering a structured and practical decision-making framework for green supplier evaluation. Using a case study of Company T, we validate the effectiveness of our model by comparing it with traditional methods, demonstrating its superior ability to mitigate supplier-related risks while ensuring sustainability and operational efficiency. The inclusion of numerical simulations and comparative analysis provides actionable insights for supply chain managers, helping them make more informed and strategic supplier selection decisions. This study thus offers practical guidance for businesses seeking to enhance sustainability while minimizing risks in their supply chains. By addressing both theoretical and practical dimensions, this paper extends the academic discourse on green supplier selection within MCDM research and equips decision-makers with a scientifically robust evaluation framework for sustainable supply chains.

The remainder of this paper is organized as follows: Section 2 reviews the relevant literature on supplier selection methods, including traditional techniques like AHP and FMEA, as well as their applications in green supplier selection. Section 3 presents the methodology, including the improved AHP-FMEA method and how it is applied to evaluate and select green suppliers. Section 4 describes the case study of Company T, demonstrating the application of the proposed method in real-world green supplier selection, and then compares the results obtained from the improved AHP-FMEA method with traditional methods like AHP and AHP-Entropy, evaluating the effectiveness and advantages of the proposed approach. Section 5 concludes with a discussion of the findings, the limitations of the study, and suggestions for future research.

In conclusion, this paper presents an innovative approach to green supplier selection, combining the strengths of AHP, FMEA, and entropy weight methods. By considering both sustainability and risk factors, this framework enables organizations to make more informed, risk-aware decisions when selecting green suppliers, thus contributing to more sustainable and resilient supply chains.

2. Literature Review

2.1. Literature Review of Green Supplier Selection Indicators

As sustainability becomes a focal point in global business practices, green supplier evaluation has gained significant attention. Evaluating green suppliers involves assessing their ability to meet sustainability standards and contribute to environmentally friendly practices throughout their operations. A comprehensive set of evaluation indicators is essential to effectively assess these suppliers.

Green supplier quality indicators are among the most commonly discussed in the literature. Key factors include eco-certifications, carbon footprint reduction, and waste management practices. Eco-certifications, such as ISO 14001 [6] and ISO 50001 [7], are important indicators for ensuring a supplier’s environmental responsibility. For example, Porter and van der Linde [8] emphasized that certification schemes signal a supplier’s commitment to sustainable operations, which can influence both supplier performance and reputation. Similarly, carbon footprint and energy efficiency metrics are often used to assess the environmental impact of suppliers’ operations. These indicators focus on the reduction of greenhouse gas emissions and energy consumption, with companies often setting specific goals to limit their carbon footprint.

Efficiency indicators are also critical in evaluating green suppliers. According to Linton et al. [9], resource utilization, including water and material usage, is crucial for assessing the sustainability of suppliers. Efficient resource management not only reduces operational costs but also aligns with environmental goals. Moreover, logistics cost is increasingly becoming a vital indicator in green supplier evaluations. McKinnon et al. [10] argued that optimizing logistics processes, particularly through greener transportation methods and reducing packaging waste, is a key area for suppliers to demonstrate sustainability.

Capability indicators such as technological innovation, workforce knowledge, and management systems are also discussed in the literature. Wu and Pagell [11] pointed out that the technological capability of suppliers, especially in areas such as renewable energy usage and waste recycling, is a critical factor in their sustainability performance. Additionally, workforce knowledge of sustainability practices plays a significant role in ensuring that green practices are implemented effectively within the supply chain. Suppliers with robust environmental management systems (EMSs), such as those certified under ISO 14001, are more likely to be successful in managing their environmental impact.

In addition, Abuzaid et al. [12] argued that integrating traditional supplier selection criteria with green factors, such as eco-friendliness, flexibility, price, and delivery performance, significantly enhances a firm’s overall performance. Their study demonstrated that companies prioritizing environmentally responsible suppliers tend to achieve better operational outcomes, reinforcing the importance of green performance indicators in supplier evaluation. Similarly, Anvarjonov et al. [13] emphasized that green supplier selection plays a crucial role in improving firms’ environmental performance, particularly when combined with strong internal governance mechanisms. Their research suggests that outcome and process controls can amplify the benefits of selecting environmentally responsible suppliers, highlighting the importance of monitoring mechanisms in green supplier evaluation frameworks. Li et al. [14] explored the relevance of ESG (environmental, social, and governance) considerations in supplier selection, noting that companies often prioritize environmental criteria over social and governance aspects. They also found that traditional evaluation methods focus on past environmental performance rather than forward-looking sustainability innovations. This study contributes to the discourse by proposing an updated set of sustainability indicators that align with emerging ESG mandates, ensuring a comprehensive and future-oriented approach to green supplier selection.

The literature emphasizes that a holistic approach to selecting green suppliers requires the integration of these various indicators to provide a comprehensive evaluation. By combining multiple dimensions of supplier performance, businesses can ensure that their suppliers are not only efficient but also resilient in managing sustainability challenges.

2.2. Literature Review of Green Supplier Selection Methods

Several methodologies have been proposed to evaluate green suppliers, each offering unique advantages and limitations. Among the most common methods are MCDM techniques such as AHP, the entropy weight method, and Fuzzy AHP, which help prioritize the multiple indicators used in green supplier selection.

The AHP method has been widely used in supplier evaluation. Albayrak et al. [15] introduced AHP as a structured technique for organizing and analyzing complex decision-making problems. In green supplier evaluation, AHP is used to rank suppliers based on subjective criteria, such as environmental performance, quality, and cost. It allows decision-makers to assign weights to each criterion and aggregate the results. Handfield et al. [16] applied AHP to select green suppliers, arguing that it helps balance both qualitative and quantitative factors in the decision-making process. However, AHP relies heavily on expert opinions, which can introduce subjectivity into the evaluation process.

Tavana et al. [17] applied the entropy method to green supplier selection, highlighting its ability to reduce subjectivity by calculating weights based on data variability. The entropy method is particularly useful when decision-makers have access to quantitative data but lack comprehensive expert knowledge. However, its main limitation is that it may not fully capture the qualitative aspects of supplier performance, such as a supplier’s commitment to sustainability.

Fuzzy AHP combines the AHP method with fuzzy logic to handle uncertainty and imprecision in decision-making. Zadeh [18] introduced fuzzy logic, which allows for the modeling of subjective judgments using linguistic variables. Nirmal et al. [19] applied fuzzy logic to evaluate green suppliers, arguing that it is more suitable for uncertain or ambiguous data, such as the perception of a supplier’s sustainability efforts. The fuzzy method provides more flexibility, but its complexity increases with the number of criteria and sub-criteria being considered.

In recent years, hybrid approaches that combine multiple methods, such as AHP-FMEA or AHP-Entropy, have gained popularity. Mangla et al. [20] proposed the use of FMEA to assess the risks associated with green chain. This methodology identifies potential risks in the supplier selection process and helps businesses avoid choosing suppliers that pose significant operational or environmental risks. Additionally, the combination of entropy weights with AHP helps to objectively adjust the weights assigned to different evaluation criteria, reducing the influence of personal biases.

Ograh et al. [21] conducted a systematic review of green supplier selection (GSS) methods, categorizing them into multi-criteria decision-making (MCDM), mathematical programming, and AI-based approaches. Their findings indicate that AHP, DEA, and TOPSIS remain the dominant techniques in green supplier evaluation, demonstrating their effectiveness in handling multiple sustainability criteria. Khattak et al. [22] introduced a novel multi-objective decision model integrating Quality Function Deployment (QFD) with fuzzy programming to enhance supplier selection. Their results showed that this hybrid approach balances economic and environmental objectives, proving particularly useful for industries where sustainability must be weighed alongside cost and delivery constraints. Akin Bas [23] proposed a hybrid fuzzy MCDM approach, combining interval type-2 fuzzy AHP and TOPSIS to improve decision- making under uncertainty. Their case study in the automotive industry highlighted the robustness of this method, particularly in structuring complex green supplier evaluation frameworks with multi-level sub-criteria.

While the literature on green supplier selection provides a wide range of methodologies, there is a gap in integrating objective weighting, risk analysis, and subjective evaluation into a single, comprehensive decision-making model. Most existing methods either focus solely on subjective assessment (e.g., AHP), objective weighting (e.g., entropy method), or risk analysis (e.g., FMEA), but few studies integrate all three components effectively.

Our improved AHP-FMEA method addresses this gap by combining subjective judgment (AHP), objective weighting (entropy method), and risk analysis (FMEA) into one coherent framework. This method offers a more comprehensive, accurate, and risk-aware approach to green supplier selection. By incorporating both qualitative and quantitative indicators, along with risk factors, it allows businesses to make better-informed decisions when choosing green suppliers, ultimately enhancing sustainability and operational resilience in the supply chain.

3. Green Supplier Selection Model Based on Improved AHP-FMEA

3.1. Related Concepts and Definitions

3.1.1. Basic Concepts of Entropy Weight Method

The German mathematician and physicist Rudolf Clausius introduced the concept of entropy in 1856 in his work The Mechanical Theory of Heat [24], as part of the second law of thermodynamics, aiming to formalize the principles of classical thermodynamics. In 1923, physicist Josiah Willard Gibbs was the first to formally name the term “entropy” in physics. Later, Claude Shannon introduced the concept of entropy into information theory in 1948, marking a significant milestone in the field [24]. In information theory, entropy represents the uncertainty of an information source, and the degree to which uncertainty is eliminated is defined as information. Entropy is inversely proportional to the amount of information, meaning it increases with uncertainty and unavailability [25].

If a system can exhibit multiple different states, and the probability of each state occurring is denoted as $p_{\mathrm{i}}(i=1,2,\cdots ,m)$, then the entropy of the system is defined as follows [25]:

$$e=-\sum _{i=1}^m{p}_i\cdot \ln p_i.$$

(1)

It can be derived that when $p_{\mathrm{i}}=1/m$ for $i=1,2,\cdots ,m$, meaning all states occur with equal probability, the entropy reaches its maximum value, given by the following:

$$e_{\max }=\ln m.$$

(2)

In other words, when a criterion exhibits a low entropy value, it implies that the variation of this criterion is more significant, providing more distinct information. Consequently, it holds a greater weight in the evaluation system. Conversely, when a criterion has a high entropy value, it suggests that the variation of this criterion is relatively small, offering less distinct information, and thus, its weight in the overall evaluation is correspondingly lower.

In summary, the entropy weight method applies information entropy to determine the weight of each criterion based on its degree of variation. The entropy value is then used to adjust the weighted sum of the criteria, ultimately yielding the objective weight.

3.1.2. Basic Concepts of FMEA

Failure Modes and Effects Analysis (FMEA) is a quality management technique designed to continuously improve products and process designs [26]. FMEA is a proactive failure prediction method, employing specialized technical expertise and experience to identify potential failure types and develop corresponding technical solutions to mitigate risks.

Currently, this technique has been widely applied across various production processes and is gradually being extended to other technical domains. By employing FMEA, organizations can systematically assess the severity, likelihood, and detectability of potential failures, which is essential for risk evaluation and prioritization.

Typically, the FMEA process can be broken down into the following steps, as illustrated in

Table 1. FMEA analysis steps.

Step No.	Analysis Steps	Analysis Content
1	Step 1	Identify the target system for analysis
2	Step 2	Analyze failure modes and their causes
3	Step 3	Examine the consequences of different failure types
4	Step 4	Fill in the failure modes and effects analysis table
5	Step 5	Perform risk assessment calculations

:

Failure Modes and Effects Analysis (FMEA) utilizes the Risk Priority Number (RPN) to assess the risk level associated with a component or process. The RPN is determined by three key factors:

O (Occurrence Probability): The likelihood of failure occurrence.

S (Severity): The impact of the failure if it occurs.

D (Detection): The probability that the failure cannot be detected before it causes harm.

The RPN is calculated as the product of these three factors, using the following mathematical formula [27]:

$$R=S\times O\times D.$$

(3)

FMEA classifies risks into five levels: R, L, M, H, VH, representing extremely low, low, moderate, high, and very high probabilities of failure occurrence. The risk scores range from 1 to 10, serving as a metric to evaluate the probability, severity, and undetectability of potential failures [28]. The detailed severity rating criteria are presented in

Table 2. FMEA severity rating scale.

Score Range	Verbal Rating	Failure Severity (S)	Failure Occurrence Probability (O)	Failure Detection Probability (D)
1–2	Extremely Low (R)	Consequences of failure are negligible	Failure is extremely rare (e.g., occurs once)	Failure is highly unlikely to go undetected
3–4	Low (L)	Consequences of failure are minor	Failure is unlikely to occur	Failure is less likely to go undetected
5–6	Moderate (M)	Consequences of failure are moderately severe	Failure is likely to occur	Failure has a moderate probability of going undetected
7–8	High (H)	Consequences of failure are severe	Failure may occur multiple times	Failure has a high probability of going undetected
9–10	Very High (VH)	Consequences of failure are catastrophic	Failure occurs frequently	Failure has an extremely high probability of going undetected

.

3.2. Selection Model Establishment

This section focuses on the selection of green suppliers and constructs an evaluation model from a risk perspective. The model is developed through the following five steps:

(1)

First, the AHP method is employed to determine the subjective weights of the evaluation criteria.

(2)

Next, the entropy weight method is applied to obtain the objective weights of the criteria.

(3)

The subjective and objective weights are then integrated to derive an optimized combined weight ${\lambda }_j$.

(4)

Subsequently, the improved FMEA (Failure Modes and Effects Analysis) method is used to calculate the risk scores $K_{ij}$ for each supplier under different criteria.

(5)

Finally, the combined weight ${\lambda }_j$, risk score $K_{ij}$, and baseline score $I_{ij}$ are multiplied to compute the comprehensive score $F_{ij}$ for each secondary criterion. The suppliers are then ranked based on their aggregated secondary criteria scores, with higher scores indicating better-performing green suppliers, Figure 1 shows the relevant steps of modeling:

When using the improved AHP, the problem is first broken down into several evaluation criteria. These criteria are then grouped into different levels based on their relationships and characteristics, forming a structured analytical model [29]. Below are the sets and variables used in this study.

(a)

The set of alternatives is denoted as $A_i=\left\{A_1,A_2,\cdots ,A_m\right\}$, representing the set of green suppliers, where $A_i$ refers to the $i\text{-}\mathrm{th}$ supplier, with $i=1,2,\dots ,m$.

(b)

The set of first-level criteria is denoted as $B_c=\left\{B_1,B_2,\cdots ,B_d\right\}$, representing the first-level evaluation criteria for green suppliers. Here, $B_c$ denotes the $c\text{-}\mathrm{th}$ criterion, where $c=1,2,\dots ,d$.

(c)

The set of second-level criteria is denoted as $C_j=\left\{C_1,C_2,\cdots ,C_n\right\}$, representing the second-level evaluation criteria for green suppliers. Here, $C_j$ refers to the $j\text{-}\mathrm{th}$ criterion, where $j=1,2,\dots ,n$.

(d)

The set of evaluation experts is denoted as $D_h=\left\{D_1,D_2,\cdots ,D_t\right\}$, representing the set of experts evaluating green suppliers. Here, $D_h$ refers to the $h\text{-}\mathrm{th}$ expert, where $h=1,2,\dots ,t$.

3.2.1. Module 1: Determining Subjective Weights

• Step 1: Constructing the Hierarchical Judgment Matrix and Calculating the Weights of Each Criterion

In the hierarchical model, different criteria have different levels of importance. To determine their weights, it is essential to compare their relative significance. The judgment matrix is built based on higher-level criteria, and experts evaluate the importance of the lower-level criteria to create a comparison matrix.

In this study, the “0–2 scale method” is adopted for pairwise comparisons, which minimizes potential inconsistencies in expert judgments [30]. As a result, there is no need to conduct a consistency test for the judgment matrix. The detailed calculation process is as follows:

(i) According to the “0–2 scale method”, the initial judgment matrix $a_{pq}$ is first constructed for each hierarchical level, where $p,q=1,2,\cdots ,k$ and $k$ represents the number of factors being compared. The matrix is defined as follows:

$$a_{pq}=\left\{\begin{array}{c}2, \mathrm{if} \mathrm{element} p \mathrm{is} \mathrm{more} \mathrm{important} \mathrm{than} \mathrm{element} q\hfill \\ 1, \mathrm{if} \mathrm{element} p \mathrm{and} \mathrm{element} q \mathrm{are} \mathrm{equally} \mathrm{important}\hfill \\ 0, \mathrm{if} \mathrm{element} p \mathrm{is} \mathrm{not} \mathrm{compared} \mathrm{with} \mathrm{element} q\hfill \end{array}\right..$$

(4)

Next, the sum of the elements in each row of the initial judgment matrix is calculated to obtain the relative importance weight value $r_p$. The calculation formula is given as follows:

$$r_p=\sum _{q=1}^k{a}_{pq}.$$

(5)

Here, $r_{\max }$ represents the maximum importance weight value, while $r_{\min }$ represents the minimum importance weight value. The corresponding criteria for these values are referred to as benchmark comparison elements.

(ii) Based on Equation (6), the judgment matrix is constructed as follows:

$$b_{pq}=\left\{\begin{array}{cc}{\displaystyle \frac{r_p-r_q}{r_{\max }-r_{\min }}}\left(v-1\right)+1,& r_p\ge r_q\\ 1/\left[{\displaystyle \frac{r_q-r_p}{r_{\max }-r_{\min }}}\left(v-1\right)+1\right],& r_p<r_q\\ 1,& r_{\max }=r_{\min }\end{array}\right..$$

(6)

Here, $v$ represents the relative importance degree between two benchmark comparison elements, which is assigned based on a predefined scale (such as the “1–9 scale”).

(iii) The square root method [31] is used to obtain the initial weight $\overline{W_p}$, which is then normalized to derive the single-level hierarchical weight.

$$\overline{W_p}=\sqrt[k]{\prod _{q=1}^k{b}_{pq}},p=1,2,\cdots ,k.$$

(7)

$$W_p^{\prime }={\displaystyle \frac{\overline{W_p}}{{\displaystyle \sum _{p=1}^k}\overline{W_p}}}.$$

(8)

• Step 2: Calculation of Subjective Weights

The weights at each hierarchical level are transmitted downward, and the weights of factors with affiliation relationships are multiplied to determine the relative importance of the lowest-level indicators with respect to the overall objective. The calculated hierarchical weight values $W_p^{\prime }$ are then classified into different levels, including the first-level criterion weight $W_c^{\prime }$ and the second-level criterion weight $W_{cj}^{\prime }$ under the corresponding first-level criterion.

Thus, the final weight of each second-level criterion, i.e., the subjective weight, is calculated as follows:

$$W_j=W_c^{\prime }\times W_{cj}^{\prime }.$$

(9)

where $W_c^{\prime }$ represents the weight of a factor at the higher level, and $W_{cj}^{\prime }$ represents the weight of a factor at the lower level that belongs to the higher level.

3.2.2. Module 2: Determining Objective Weights

• Step 3: Calculating Objective Weights Using the Entropy Method

(i) Constructing the Normalized Matrix

Given $t$ evaluation objects, denoted as the evaluation object set $D_h$, and $n$ second-level evaluation criteria, denoted as the second-level criterion set $C_j$, a data matrix $S={\left(s_{hj}\right)}_{t\times n}$ is constructed for the evaluation process. Here, $s_{hj}$ represents the evaluation value of the $j\text{-}\mathrm{th}$ criterion for the $j\text{-}\mathrm{th}$ evaluation object.

$$s_{hj}={\left[\begin{array}{cccc}{s}_{11}& s_{12}& \dots & s_{1n}\\ s_{21}& s_{22}& \dots & s_{2n}\\ \dots & \dots & \dots & \dots \\ s_{t1}& s_{t2}& \dots & s_{tn}\end{array}\right]}_{t\times n}.$$

(10)

(ii) Calculate the proportion $p_{hj}$ of the evaluation value of the $h\text{-}\mathrm{th}$ evaluation object under the $j\text{-}\mathrm{th}$ evaluation criterion:

$$p_{hj}={\displaystyle \frac{s_{hj}}{{\displaystyle \sum _{h=1}^t}{s}_{hj}}}.$$

(11)

(iii) Compute the entropy value $e_j$ of the $j\text{-}\mathrm{th}$ criterion [25]:

$$e_j=-{\displaystyle \frac{1}{\ln t}}\sum _{h=1}^t{p}_{hj}\cdot \ln p_{hj}.$$

(12)

(iv) Compute the entropy weight $u_j$ of the $j\text{-}\mathrm{th}$ criterion:

$$u_j={\displaystyle \frac{1-e_j}{{\displaystyle \sum _{j=1}^n}\left(1-e_j\right)}}.$$

(13)

3.2.3. Module 3: Determining the Combined Weights

• Step 4: Optimizing the Combined Weights

In this study, the improved AHP and the entropy method are first applied to obtain the subjective weight $W_j$ and the objective weight $u_j$, respectively. Then, a preference coefficient $\theta$ is introduced to integrate the subjective and objective weights, resulting in the combined weight ${\lambda }_j$.

$${\lambda }_j=\theta W_j+(1-\theta )u_j,(0<\theta <1).$$

(14)

To minimize the deviation between the combined weight and the two individual weights, $\theta$ is set to 0.5, indicating that subjective and objective weights each contribute 50% to the final weight.

3.2.4. Module 4: Determining Risk Scores

The traditional RPN calculation method simply multiplies Severity ($S$), Occurrence ($O$), and Detection ($D$). In this study, a new calculation approach is proposed [32].

First, the possible failure modes are identified. Then, an evaluation matrix is created for the candidate green suppliers using the FMEA. Experts rate each supplier based on Severity (S), Occurrence (O), and Detection (D). Finally, the risk scores are calculated following the steps below.

• Step 5: Calculating the Risk Score

The risk score $R$ represents a comprehensive measure of both risk severity and occurrence. Therefore, for different green suppliers, the risk score for each secondary criterion is calculated as follows:

$$R_{ij}=S_{ij}\times O_{ij}.$$

(15)

where $S$ denotes the severity of the risk, with $S\in \left[1, 10\right]$; $O$ represents the occurrence of the risk, with $O\in \left[1, 10\right]$; $R\in \left[1, 10\right]$, indicating that the risk score ranges from a minimum of 1 to a maximum of 100.

• Step 6: Calculating the Risk Ratio

The detection level $D$ represents the existing detection and control technologies that can be applied to mitigate risk. If the current detection and control measures are effective [32] (i.e., $D$ has a lower value), the associated risks can be better managed.

Since $R=1$ and $R=100$ represent the best and worst risk conditions, respectively, the control technology does not affect these two extreme cases. By fixing these endpoints, the risk ratio for each secondary criterion of different green suppliers (denoted as $x_{ij}$) is calculated as follows:

$$x_{ij}={\left({\displaystyle \frac{R_{ij}-1}{99}}\right)}^{-r{D}_{ij}+c}.$$

(16)

where $D$ represents the detection level of the risk, with $D\in \left[1, 10\right]$; $r$ is the scaling factor, and $c$ ensures that when the detection level is at its optimal value $D=1$, the exponent equals 1.

These two parameters $r$ and $c$ can be adjusted based on specific practical conditions [32].

• Step 7: Calculating the Risk Score

Finally, the risk score for each secondary criterion of different green suppliers is calculated as follows:

$$K_{ij}=1-x_{ij}.$$

(17)

3.2.5. Module 5: Ranking of Suppliers

• Step 8: Calculating the Comprehensive Score for Each Supplier

Based on the optimization weights ${\lambda }_j$ and the risk ratio $K_{ij}$ obtained in Module 3, and integrating the initial evaluation scores $I_{ij}$ of the green suppliers, the comprehensive scores $F_{ij}$ for each green supplier under each secondary criterion are calculated as follows:

$$F_{ij}=I_{ij}\times {\lambda }_j\times K_{ij}.$$

(18)

• Step 9: Calculating the Final Score for Each Supplier

The final score $Z_i$ for each green supplier is obtained by summing the comprehensive scores $F_{ij}$ of all the secondary criteria under each supplier as follows:

$$Z_i=\sum _{j=1}^n{F}_{ij}.$$

(19)

Finally, the green suppliers are ranked according to their final scores $Z_i$ with the highest score indicating the most optimal choice.

4. Case Analysis

4.1. Company T Background and Issues in Green Supplier Selection

Company T was founded in 2014 and specializes in the innovative wearable medical electronics industry. Its main customer base includes startups and large OEMs from Europe and the United States. The company aims to become a global leader in wearable medical electronics product design and manufacturing, providing a one-stop service that integrates advanced product development with cutting-edge production capabilities.

The core team consists of industry veterans with nearly 20 years of product design experience and Electronic Manufacturing Services (EMS) industry management expertise. These professionals have previously worked for leading brands in the advanced electronics sector in Europe and the U.S., giving them a deep understanding of global industry standards and technological innovations. Company T has over 1300 square meters of office space and has established partnerships with numerous advanced manufacturers, further strengthening its competitive edge.

However, despite its strong technological innovation and lean production capabilities, Company T faces critical challenges in green supply chain management, particularly in green supplier selection. As the company expands its market presence, the increasing pressure from regulatory bodies, consumers, and international sustainability standards makes it imperative for Company T to integrate green procurement practices into its supply chain. The current inefficiencies in green supplier selection hinder the company’s ability to align with global sustainability initiatives, reduce environmental impact, and enhance operational cost-efficiency.

4.1.1. Lack of a Comprehensive Green Supplier Evaluation System

Company T does not have a structured evaluation system that effectively integrates theoretical frameworks with practical applications in green supplier selection. The company currently assesses suppliers based on their ability to fulfill basic contract requirements, without considering critical environmental and sustainability metrics. As a result, suppliers with poor sustainability performance may still be classified as qualified, leading to suboptimal supplier choices, inefficient resource utilization, and high logistics costs. This lack of a scientific and systematic approach prevents Company T from achieving a truly sustainable and cost-effective supply chain.

4.1.2. Over-Reliance on Qualitative Indicators and Lack of Standardization

The existing supplier evaluation criteria rely heavily on qualitative assessments, with limited use of quantitative metrics. The inconsistency in measurement standards makes the evaluation highly subjective and less data-driven, reducing the credibility and reliability of supplier assessments. Without a structured approach to quantifying environmental performance, the company struggles to differentiate between high-performing and low-performing green suppliers, making supplier selection a highly uncertain and inefficient process.

4.1.3. Subjective, Oversimplified, and Reactive Supplier Selection Approach

Company T’s supplier selection process lacks a strategic, forward-looking approach. Decisions are often made based on immediate operational needs rather than long-term sustainability and risk mitigation. Furthermore, the company frequently changes suppliers after short-term partnerships, leading to disruptions in supply chain operations and decreased service consistency. This issue is exacerbated by inadequate risk assessment mechanisms, which fail to predict and mitigate supplier-related sustainability risks. Without a robust evaluation framework, the company remains vulnerable to supply chain instability and sustainability compliance challenges.

In sum, Company T urgently needs to build a scientifically structured green supplier evaluation system, combining theoretical and practical aspects. The company should leverage the expertise of top-level managers and industry experts to evaluate the indicators of potential suppliers, using mathematical modeling techniques to obtain more rational and comprehensive evaluation results. Furthermore, Company T should adopt strategic thinking in the selection and development of green suppliers, actively identifying high-quality suppliers and fostering long-term strategic partnerships. This approach will be essential for the long-term and stable development of the company.

4.2. Indicator System and Evaluation Criteria for Green Supplier Selection

Combined with the characteristics of green supplier selection, this study follows the principles of being comprehensive, systematic, rigorous, scientific, simple, and practical, integrating both subjective and objective factors. The evaluation is conducted in three main aspects: “Green Supplier Quality”, “Green Supplier Efficiency”, and “Green Supplier Capability”.

“Green Supplier Quality” refers to the ability of the green supplier to fulfill sustainability-related tasks, such as product quality, eco-friendliness, and adherence to environmental regulations [33].

“Green Supplier Efficiency” refers to the resources consumed by the green supplier to meet sustainable production and logistics needs, including costs, energy use, and waste management [34].

“Green Supplier Capability” refers to the green supplier’s capacity to complete sustainability-related tasks, encompassing infrastructure, human resources, and technological systems [35].

Based on the above principles and concepts, a green supplier evaluation index system is constructed, as shown in

Table 3. Green supplier evaluation and selection index system.

Primary Indicator	Secondary Indicator	Type	Unit
Green Supplier Quality (Environmental Impact) C1	Eco-Certifications (C11)	Quantitative	%
	Sustainability in Product Materials (C12)	Quantitative	%
	Customer Satisfaction with Green Practices (C13)	Quantitative	%
	Special Sustainability Projects Completion Rate (C14)	Quantitative	%
Green Supplier Efficiency (Cost and Resource Consumption) C2	Operational Cost for Green Practices (C21)	Quantitative	RMB
	Cost of Eco-Friendly Materials (C22)	Quantitative	RMB
	Energy Efficiency in Operations (C23)	Quantitative	kWh/unit
Green Supplier Capability (Infrastructure and Technology) C3	Green Technology Integration (C31)	Qualitative	Level
	Workforce Knowledge in Sustainability (C32)	Qualitative	Level
	Supplier’s Environmental Management System (C33)	Qualitative	Level
	Use of Renewable Energy (C34)	Qualitative	Level

:

4.3. Case Application

Based on the 11 secondary indicator evaluation criteria, a multi-criteria evaluation is conducted for three candidate green suppliers. In this study, 10 industry experts were selected to provide qualitative assessments for the corresponding indicators. The results were then scored, where a score of 10 represents the best capability for that indicator, and 0 represents the worst capability. For the quantitative indicators, the initial scores were assigned based on the evaluation standards. The initial scores for the three suppliers are shown in

Table 4. Initial scores for green supplier selection.

Primary Indicator	Secondary Indicator	Supplier A	Supplier B	Supplier C
Green Supplier Quality (Environmental Impact) C1	C11	8	8	8
	C12	7	8	8
	C13	8	7	9
	C14	8	8	8
Green Supplier Efficiency (Cost and Resource Consumption) C2	C21	9	8	9
	C22	7	8	8
	C23	8	9	7
Green Supplier Capability (Infrastructure and Technology) C3	C31	8	7	7
	C32	9	8	7
	C33	7	8	8
	C34	8	8	7

:

4.3.1. Module 1: Determining Subjective Weights

• Step 1: Constructing the Judgment Matrix for Each Hierarchical Level and Calculating the Weights of Each Indicator

(i) Establishing the Initial Judgment Matrix and Calculating Relative Importance Weights

In this study, 10 experts with extensive experience in the fields of supply chain management, procurement, and logistics were invited to participate. The experts were engaged through surveys and interviews, and the results were statistically adjusted to determine the relative importance of the various dimensions involved in the selection of green suppliers. Based on this, the initial judgment matrix for the first-level indicators was established.

$$a_{pq}=\left[\begin{array}{ccc}1& 2& 2\\ 0& 1& 0\\ 0& 2& 1\end{array}\right].$$

(20)

Relative importance weights of the indicators are calculated according to Equation (5). The results are shown in

Table 5. Initial judgment matrix for first-level indicators.

C	C1	C2	C3	${\mathit{r}}_{\mathit{p}}$
C1	1	2	2	5
C2	0	1	2	3
C3	0	0	1	1

:

(ii) Constructing the Judgment Matrix

Based on the “1–9 scale” [36], and combining expert opinions, the indicator C1, which is assigned the largest importance weight, is compared with C3, the indicator with the smallest importance weight, and is assigned a relative importance degree of $v=5$. Based on Equation (6), the first-level judgment matrix is constructed as follows:

$$b_{pq}=\left[\begin{array}{ccc}1.000& 3.000& 5.000\\ 0.333& 1.000& 3.000\\ 0.200& 0.333& 1.000\end{array}\right].$$

The first-level indicator judgment matrix is shown in

Table 6. First-level indicator judgment matrix.

C	C1	C2	C3
C1	1.000	3.000	5.000
C2	0.333	1.000	3.000
C3	0.200	0.333	1.000

:

(iii) Calculating the Weights from the Judgment Matrix

According to Equation (7), the elements of the judgment matrix are then processed sequentially:

$$\overline{W_1}=\sqrt[3]{1\times 3\times 5}=2.466,$$

calculated as:

$$\overline{W_2}=\sqrt[3]{0.333\times 1\times 3}=1.000, \overline{W_3}=\sqrt[3]{0.2\times 0.333\times 1}=0.405.$$

According to Equation (8), the weights are calculated as follows:

$$W_1^{\prime }={\displaystyle \frac{\overline{W_1}}{{\displaystyle \sum _{p=1}^3}\overline{W_p}}}={\displaystyle \frac{2.466}{2.466+1+0.405}}=0.637,$$

calculated as:

$$W_2^{\prime }={\displaystyle \frac{\overline{W_2}}{{\displaystyle \sum _{p=1}^3}\overline{W_p}}}={\displaystyle \frac{1}{2.466+1+0.405}}=0.258;$$

$$W_3^{\prime }={\displaystyle \frac{\overline{W_3}}{{\displaystyle \sum _{p=1}^3}\overline{W_p}}}={\displaystyle \frac{0.405}{2.466+1+0.405}}=0.105.$$

Based on the above steps, the initial judgment matrix and judgment matrices for the secondary criteria relative to the first-level criteria can be obtained, and the weights are further calculated as shown in

Table 7. Initial judgment matrix and weights of C1 secondary indicators.

C1	C11	C12	C13	C14	Weights ($\mathit{v} = 5$)
C11	1	0	0	2	0.197
C12	2	1	0	2	0.257
C13	2	2	1	2	0.403
C14	0	0	0	1	0.143

,

Table 8. Initial judgment matrix and weights of C2 secondary indicators.

C2	C21	C22	C23	Weights ($\mathit{v} =5$)
C21	1	0	2	0.356
C22	2	1	2	0.527
C23	0	0	1	0.117

and

Table 9. Initial judgment matrix and weights of C3 secondary indicators.

C3	C31	C32	C33	C34	Weights ($\mathit{v} =5$)
C31	1	0	0	0	0.135
C32	2	1	0	2	0.278
C33	2	2	1	2	0.382
C34	2	0	0	1	0.205

:

• Step 2: Calculating Subjective Weights

Based on the weights of the first-level and second-level criteria and Equation (9), the overall weights for each second-level criterion relative to the first-level criteria can be calculated. The calculation process for the overall weights under the first-level criterion C1 is as follows:

$$W_1=W_1^{\prime }\times W_{11}^{\prime }=0.637\times 0.197=0.125;$$

$$W_2=W_1^{\prime }\times W_{12}^{\prime }=0.637\times 0.257=0.164;$$

$$W_3=W_1^{\prime }\times W_{13}^{\prime }=0.637\times 0.403=0.256;$$

$$W_4=W_1^{\prime }\times W_{14}^{\prime }=0.637\times 0.143=0.091.$$

Similarly, the overall weight calculation results for each second-level criterion under the other first-level criteria are shown in

Table 10. Weights of second-level criteria relative to the objective layer under the improved AHP.

Primary Indicator	Secondary Indicator	Overall Weight
Green Supplier Quality (Environmental Impact) C1	Eco-Certifications (C11)	0.125
	Sustainability in Product Materials (C12)	0.164
	Customer Satisfaction with Green Practices (C13)	0.256
	Special Sustainability Projects Completion Rate (C14)	0.091
Green Supplier Efficiency (Cost and Resource Consumption) C2	Operational Cost for Green Practices (C21)	0.092
	Cost of Eco-Friendly Materials (C22)	0.136
	Energy Efficiency in Operations (C23)	0.030
Green Supplier Capability (Infrastructure and Technology) C3	Green Technology Integration (C31)	0.014
	Workforce Knowledge in Sustainability (C32)	0.029
	Supplier’s Environmental Management System (C33)	0.040
	Use of Renewable Energy (C34)	0.022

.

4.3.2. Module 2: Determining Objective Weights

• Step 3: Calculating Objective Weights Using the Entropy Method

(i) Constructing the Normalized Matrix

The entropy method is used to determine the objective weights of the indicators. The 10 experts who participated in scoring the subjective weights were invited to assess the importance of the second-level indicators based on the Likert six-point scale and the scoring criteria from the subjective weight evaluation. The results are shown in

Table 11. Original data table for the entropy weight method.

Experts	C11	C12	C13	C14	C21	C22	C23	C31	C32	C33	C34
1	2	4	5	3	3	3	2	2	4	5	3
2	3	2	4	2	5	4	1	5	2	3	4
3	4	3	3	1	4	3	2	4	3	5	3
4	2	4	4	1	3	6	3	3	2	4	4
5	4	4	3	1	4	5	4	3	4	5	3
6	2	4	3	3	5	4	2	4	3	6	5
7	3	3	5	2	3	5	4	3	2	4	2
8	4	2	3	3	2	6	1	3	5	5	3
9	3	5	6	2	3	5	3	2	4	4	5
10	4	3	4	2	4	4	2	3	4	5	4

:

Based on the original data matrix, the initial matrix $s_{hj}$ is constructed, as shown below:

$$s_{hj}=\left[\begin{array}{ccccc}2& 4& 5& \dots & 3\\ 3& 2& 4& \dots & 4\\ 4& 3& 3& \dots & 3\\ ⋮& ⋮& ⋮& \dots & ⋮\\ 4& 2& 3& \dots & 3\\ 3& 5& 6& \dots & 5\\ 4& 3& 4& \dots & 4\end{array}\right].$$

(ii) Calculate the proportion $p_{hj}$ of the evaluation value of the $h\text{-}th$ evaluation object under the $j\text{-}th$ evaluation index

Based on Equation (11), the initial matrix is processed, and the normalized matrix $p_{hj}$ is constructed. The calculation process for $p_{11}$ is shown below:

$$p_{11}={\displaystyle \frac{2}{{\displaystyle \sum _{i=1}^{10}}{s}_{h1}}}={\displaystyle \frac{2}{2+3+4+2+4+2+3+4+3+4}}=0.065.$$

Thus, the normalized matrix $p_{hj}$ is calculated as follows:

$$p_{hj}=\left[\begin{array}{ccccc}0.065& 0.1176& 0.125& \dots & 0.083\\ 0.097& 0.059& 0.100& \dots & 0.111\\ 0.129& 0.088& 0.075& \dots & 0.083\\ ⋮& ⋮& ⋮& \dots & ⋮\\ 0.129& 0.059& 0.075& \dots & 0.083\\ 0.097& 0.147& 0.150& \dots & 0.139\\ 0.129& 0.088& 0.100& \dots & 0.111\end{array}\right].$$

(iii) Calculating the Entropy Value for Each Indicator

Based on Equation (12), the calculation process for $e_1$ is as follows:

$$e_1=-{\displaystyle \frac{1}{\ln 10}}\sum _{h=1}^{10}{p}_{h1}\cdot \ln p_{h1}=-2.265\times -0.434=0.984.$$

Thus, the entropy values for the other indicators can be calculated, and the results are as follows:

$$e_j=[0.984,0.984,0.987,0.966,0.986,0.989,0.960,0.984,0.979,0.993,0.986].$$

(iv) Calculating the Weights for Each Indicator

Based on Equation (13), the calculation process for $u_1$ is as follows:

$$u_1={\displaystyle \frac{1-e_1}{{\displaystyle \sum _{j=1}^{11}}\left(1-e_j\right)}}={\displaystyle \frac{1-0.984}{(1-0.984)+(1-0.984)+\cdots +(1-0.986)}}=0.079,$$

Similarly, the entropy weights of the remaining evaluation indicators are calculated, as shown in

Table 12. Weights of secondary indicators relative to the target layer under the entropy weight.

Primary Indicator	Secondary Indicator	Overall Weight
Green Supplier Quality (Environmental Impact) C1	Eco-Certifications (C11)	0.079
	Sustainability in Product Materials (C12)	0.080
	Customer Satisfaction with Green Practices (C13)	0.065
	Special Sustainability Projects Completion Rate (C14)	0.168
Green Supplier Efficiency (Cost and Resource Consumption) C2	Operational Cost for Green Practices (C21)	0.070
	Cost of Eco-Friendly Materials (C22)	0.056
	Energy Efficiency in Operations (C23)	0.197
Green Supplier Capability (Infrastructure and Technology) C3	Green Technology Integration (C31)	0.078
	Workforce Knowledge in Sustainability (C32)	0.102
	Supplier’s Environmental Management System (C33)	0.034
	Use of Renewable Energy (C34)	0.071

:

4.3.3. Module 3: Determining the Combined Weights

• Step 4: Optimizing the Combined Weights

Based on the results from Equation (14) and the method outlined above, the combined weights for each second-level indicator relative to the objective layer and each first-level criterion can be obtained. The calculation process for the combined weights under first-level criterion C1 is shown below:

$${\lambda }_1=0.5\times 0.079+0.5\times 0.125=0.102; {\lambda }_2=0.5\times 0.080+0.5\times 0.164=0.122;$$

$${\lambda }_3=0.5\times 0.065+0.5\times 0.256=0.161; {\lambda }_4=0.5\times 0.168+0.5\times 0.191=0.130;$$

Similarly, the combined weights for each second-level indicator under the other first-level criteria are calculated and organized. The results are shown in

Table 13. Combined weights of indicators at all levels under the improved AHP-Entropy weight.

Primary Indicator	Weights	Secondary Indicator	Overall Weight
Green Supplier Quality (Environmental Impact) C1	0.637	Eco-Certifications (C11)	0.102
		Sustainability in Product Materials (C12)	0.122
		Customer Satisfaction with Green Practices (C13)	0.161
		Special Sustainability Projects Completion Rate (C14)	0.130
Green Supplier Efficiency (Cost and Resource Consumption) C2	0.258	Operational Cost for Green Practices (C21)	0.081
		Cost of Eco-Friendly Materials (C22)	0.095
		Energy Efficiency in Operations (C23)	0.113
Green Supplier Capability (Infrastructure and Technology) C3	0.105	Green Technology Integration (C31)	0.046
		Workforce Knowledge in Sustainability (C32)	0.066
		Supplier’s Environmental Management System (C33)	0.037
		Use of Renewable Energy (C34)	0.047

:

4.3.4. Module 4: Determining Risk Scores

First, based on the 11 evaluation criteria, FMEA is used to identify failure modes. The failure modes reflect the potential risks associated with each criterion, as well as their impact, causes, and methods of detection and control.

FMEA adopts five levels—R (Rare), L (Low), M (Moderate), H (High), and VH (Very High)—to represent the probability of risk occurrence. The risk scores range from 1 to 10, measuring the likelihood of failure or risk occurrence, severity of the impact, and detectability of the risk.

The FMEA dimension evaluation for green suppliers in this study is shown in

Table 14. FMEA dimension evaluation table.

Score	Qualitative Rating	Risk Severity (S)	Risk Occurrence Frequency (O)	Risk Detection Probability (D)
1–2	Rare (R)	Consequences of risk occurrence are negligible	Extremely unlikely to occur	Very low probability of being undetected
3–4	Low (L)	Consequences of risk occurrence are minor	Unlikely to occur	Relatively low probability of being undetected
5–6	Moderate (M)	Consequences of risk occurrence are moderate	Possible occurrence	Moderate probability of being undetected
7–8	High (H)	Consequences of risk occurrence are severe	Likely to occur more than once	High probability of being undetected
9–10	Very High (VH)	Consequences of risk occurrence are catastrophic	Frequent occurrence	Very high probability of being undetected

.

Experts were invited to assess the Severity (S), Occurrence (O), and Detection (D) scores based on the actual performance and operational capabilities of the suppliers.

Taking supplier A as an example, its FMEA evaluation scheme is shown in

Table 15. FMEA evaluation table of supplier A.

Criterion	Failure Mode	Severity (S)	Occurrence (O)	Detection (D)
Green Supplier Quality (Environmental Impact)	Insufficient Eco-Certifications	8	3	2
	Low Sustainability in Product Materials	8	6	4
	Low Customer Satisfaction with Green Practices	9	5	3
	Low Completion Rate of Special Sustainability Projects	8	3	2
Green Supplier Efficiency (Cost and Resource Consumption)	High Operational Cost for Green Practices	9	6	4
	High Cost of Eco-Friendly Materials	8	4	3
	Low Energy Efficiency in Operations	7	3	2
Green Supplier Capability (Infrastructure and Technology)	Insufficient Green Technology Integration	7	3	2
	Inadequate Workforce Knowledge in Sustainability	7	2	1
	Poor Supplier’s Environmental Management System	8	3	3
	Low Use of Renewable Energy	7	2	2

.

Similarly, the FMEA evaluation plans for supplier B and supplier C are formulated according to the same scoring criteria, as shown in

Table 16. FMEA evaluation table of supplier B.

Criterion	Failure Mode	Severity (S)	Occurrence (O)	Detection (D)
Green Supplier Quality (Environmental Impact)	Insufficient Eco-Certifications	8	2	2
	Low Sustainability in Product Materials	8	4	3
	Low Customer Satisfaction with Green Practices	9	3	3
	Low Completion Rate of Special Sustainability Projects	8	2	2
Green Supplier Efficiency (Cost and Resource Consumption)	High Operational Cost for Green Practices	8	3	3
	High Cost of Eco-Friendly Materials	8	4	3
	Low Energy Efficiency in Operations	7	3	2
Green Supplier Capability (Infrastructure and Technology)	Insufficient Green Technology Integration	8	6	4
	Inadequate Workforce Knowledge in Sustainability	7	2	1
	Poor Supplier’s Environmental Management System	8	3	3
	Low Use of Renewable Energy	7	1	1

and

Table 17. FMEA evaluation table of supplier C.

Criterion	Failure Mode	Severity (S)	Occurrence (O)	Detection (D)
Green Supplier Quality (Environmental Impact)	Insufficient Eco-Certifications	8	2	2
	Low Sustainability in Product Materials	8	2	2
	Low Customer Satisfaction with Green Practices	7	1	1
	Low Completion Rate of Special Sustainability Projects	8	2	2
Green Supplier Efficiency (Cost and Resource Consumption)	High Operational Cost for Green Practices	8	3	3
	High Cost of Eco-Friendly Materials	7	2	1
	Low Energy Efficiency in Operations	8	4	3
Green Supplier Capability (Infrastructure and Technology)	Insufficient Green Technology Integration	9	6	5
	Inadequate Workforce Knowledge in Sustainability	7	2	1
	Poor Supplier’s Environmental Management System	8	3	3
	Low Use of Renewable Energy	8	6	4

:

• Step 5: Calculate the risk number

The risk number reflects the occurrence degree of the risk and the severity after it occurs. According to Formula (15), taking the various failure modes under the quality of green supplier A as an example, the risk number of the failure mode is calculated:

$$R_{11}=S_{11}\times O_{11}=8\times 3=24; R_{12}=S_{12}\times O_{12}=8\times 6=48;$$

$$R_{13}=S_{13}\times O_{13}=9\times 5=45; R_{14}=S_{14}\times O_{14}=8\times 3=24.$$

Similarly, calculate the remaining risk numbers of green supplier A and the risk numbers of green supplier B and C (

Table 18. Risk number of supplier A, B, and C.

Criterion	Failure Mode	Supplier A’s Risk Number	Supplier B’s Risk Number	Supplier C’s Risk Number
Green Supplier Quality (Environmental Impact)	Insufficient Eco-Certifications	24	16	16
	Low Sustainability in Product Materials	48	32	16
	Low Customer Satisfaction with Green Practices	45	27	7
	Low Completion Rate of Special Sustainability Projects	24	16	16
Green Supplier Efficiency (Cost and Resource Consumption)	High Operational Cost for Green Practices	54	24	24
	High Cost of Eco-Friendly Materials	32	32	14
	Low Energy Efficiency in Operations	21	21	32
Green Supplier Capability (Infrastructure and Technology)	Insufficient Green Technology Integration	21	48	54
	Inadequate Workforce Knowledge in Sustainability	14	14	14
	Poor Supplier’s Environmental Management System	24	24	24
	Low Use of Renewable Energy	14	7	48

):

• Step 6: Calculating the Risk Ratio

The risk ratio represents the probability of a given risk occurring. First, the scaling factor $r$ is set to 0.1, and the constant $c$ is set to 1.1, ensuring that when the detection level is at its optimal state ($D=1$), the index equals 1.

Next, based on Equation (16), the risk ratios for each failure mode under green suppliers’ failure modes are calculated. Supplier A’s performance in the Green Supplier Quality dimension is taken as an example to compute the corresponding risk ratios.

$$x_{11}={\left({\displaystyle \frac{R_{11}-1}{99}}\right)}^{-0.1D_{11}+1.1}={\left({\displaystyle \frac{24-1}{99}}\right)}^{-0.1\times 2+1.1}=0.269;$$

$$x_{12}={\left({\displaystyle \frac{R_{12}-1}{99}}\right)}^{-0.1D_{12}+1.1}={\left({\displaystyle \frac{48-1}{99}}\right)}^{-0.1\times 4+1.1}=0.594;$$

$$x_{13}={\left({\displaystyle \frac{R_{13}-1}{99}}\right)}^{-0.1D_{13}+1.1}={\left({\displaystyle \frac{45-1}{99}}\right)}^{-0.1\times 3+1.1}=0.523;$$

$$x_{14}={\left({\displaystyle \frac{R_{14}-1}{99}}\right)}^{-0.1D_{14}+1.1}={\left({\displaystyle \frac{24-1}{99}}\right)}^{-0.1\times 2+1.1}=0.232.$$

Similarly, the risk ratios of the remaining failure modes of green supplier A and the risk ratios of the failure modes of green suppliers B and C are calculated (

Table 19. Risk ratio of supplier A, B, and C.

Criterion	Failure Mode	Supplier A’s Risk Ratio	Supplier B’s Risk Ratio	Supplier C’s Risk Ratio
Green Supplier Quality (Environmental Impact)	Insufficient Eco-Certifications	0.269	0.183	0.183
	Low Sustainability in Product Materials	0.594	0.395	0.183
	Low Customer Satisfaction with Green Practices	0.523	0.343	0.061
	Low Completion Rate of Special Sustainability Projects	0.269	0.183	0.183
Green Supplier Efficiency (Cost and Resource Consumption)	High Operational Cost for Green Practices	0.646	0.311	0.311
	High Cost of Eco-Friendly Materials	0.395	0.395	0.131
	Low Energy Efficiency in Operations	0.237	0.237	0.395
Green Supplier Capability (Infrastructure and Technology)	Insufficient Green Technology Integration	0.237	0.594	0.687
	Inadequate Workforce Knowledge in Sustainability	0.131	0.131	0.131
	Poor Supplier’s Environmental Management System	0.311	0.311	0.311
	Low Use of Renewable Energy	0.161	0.061	0.594

):

• Step 7: Calculating the Risk Score

The risk score represents the probability that a given risk will not occur. Based on Equation (17), the risk scores for each supplier’s failure modes are calculated.

Taking supplier A’s Green Supplier Quality dimension as an example, the calculation process is as follows:

$$K_{11}=1-x_{11}=1-0.269=0.731; K_{12}=1-x_{12}=1-0.594=0.406;$$

$$K_{13}=1-x_{13}=1-0.523=0.477; K_{14}=1-x_{14}=1-0.269=0.731.$$

Similarly, calculate the risk scores of the remaining failure modes of green supplier A and the risk scores of green suppliers B and C (

Table 20. Risk scores of supplier A, B, and C.

Criterion	Failure Mode	Supplier A’s Risk Scores	Supplier B’s Risk Scores	Supplier C’s Risk Scores
Green Supplier Quality (Environmental Impact)	Insufficient Eco-Certifications	0.731	0.817	0.817
	Low Sustainability in Product Materials	0.406	0.605	0.817
	Low Customer Satisfaction with Green Practices	0.477	0.657	0.939
	Low Completion Rate of Special Sustainability Projects	0.731	0.817	0.817
Green Supplier Efficiency (Cost and Resource Consumption)	High Operational Cost for Green Practices	0.354	0.689	0.689
	High Cost of Eco-Friendly Materials	0.605	0.605	0.869
	Low Energy Efficiency in Operations	0.763	0.763	0.605
Green Supplier Capability (Infrastructure and Technology)	Insufficient Green Technology Integration	0.763	0.406	0.313
	Inadequate Workforce Knowledge in Sustainability	0.869	0.869	0.869
	Poor Supplier’s Environmental Management System	0.689	0.689	0.689
	Low Use of Renewable Energy	0.839	0.939	0.406

):

4.3.5. Module 5: Supplier Ranking

• Step 8: Calculating the Comprehensive Scores for Each Supplier

Based on the baseline scores assigned by experts, along with the calculated combined weights and risk scores, the final scores for each second-level indicator relative to the objective layer can be determined for each supplier.

According to Equation (18), the calculation process for supplier A’s secondary Indicator under the Green Supplier Quality dimension is as follows:

$$F_{11}=I_{11}\times {\lambda }_1\times K_{11}=8\times 0.102\times 0.731=0.596;$$

$$F_{12}=I_{12}\times {\lambda }_2\times K_{12}=7\times 0.122\times 0.406=0.347;$$

$$F_{13}=I_{13}\times {\lambda }_3\times K_{13}=8\times 0.161\times 0.477=0.614;$$

$$F_{14}=I_{14}\times {\lambda }_4\times K_{14}=8\times 0.130\times 0.731=0.760.$$

Similarly, calculate the final scores of green supplier A under the remaining secondary indicators and the final scores of green suppliers B and C under each secondary indicator (

Table 21. Final scores of supplier A, B, and C.

Secondary Indicator	Supplier A’s Final Scores	Supplier B’s Final Scores	Supplier C’s Final Scores
Eco-Certifications (C11)	0.596	0.667	0.667
Sustainability in Product Materials (C12)	0.347	0.590	0.797
Customer Satisfaction with Green Practices (C13)	0.614	0.740	1.361
Special Sustainability Projects Completion Rate (C14)	0.760	0.850	0.850
Operational Cost for Green Practices (C21)	0.258	0.446	0.502
Cost of Eco-Friendly Materials (C22)	0.402	0.460	0.660
Energy Efficiency in Operations (C23)	0.690	0.776	0.479
Green Technology Integration (C31)	0.281	0.131	0.101
Workforce Knowledge in Sustainability (C32)	0.516	0.459	0.401
Supplier’s Environmental Management System (C33)	0.178	0.204	0.204
Use of Renewable Energy (C34)	0.315	0.353	0.353

):

• Step 9: Calculate the total score of each green supplier

Based on the total score of each green supplier’s secondary indicator and combined with Formula (19), the final score of each green supplier can be obtained:

$$Z_1=\sum _{j=1}^n{F}_{1j}=0.596+0.347+\dots +0.178+0.315=4.959;$$

$$Z_2=\sum _{j=1}^n{F}_{2j}=0.667+0.590+\dots +0.204+0.353=5.676;$$

$$Z_3=\sum _{j=1}^n{F}_{3j}=0.667+0.797+\dots +0.204+0.134=6.155.$$

Clearly, $6.155>5.676>4.959$, indicating that $Z_3>Z_2>Z_1$. Thus, supplier C is the optimal choice, followed by supplier B, while supplier A ranks the lowest.

4.4. Comparative Analysis

This section presents a comparative analysis of several existing methods, including the classical AHP [37] and the AHP-Entropy method without considering risk factors [38], in order to demonstrate the effectiveness of the proposed improved AHP-FMEA method. The ranking results for green supplier selection obtained using these methods are shown in Figure 2:

From the figure, it is evident that all three methods identify supplier C as the optimal green supplier. Comparing the improved AHP-FMEA method with the classical AHP method, it can be observed that both yield the same ranking. However, the improved AHP method integrates objective weights by incorporating the entropy weight method, which adjusts the subjective weights accordingly. This combination reduces the impact of certain subjective biases and objective limitations in weight determination.

A comparison between improved AHP-FMEA and AHP-Entropy reveals that when risk factors are not considered, supplier A ranks higher than supplier B due to its relative advantages in “Efficiency” and “Capability”. However, after incorporating FMEA analysis, supplier B’s final score surpasses that of supplier A, as supplier A has a higher risk ratio in the “Customer Satisfaction with Green Practices” and “Operational Cost for Green Practices” indicators. This leads to a lower risk score, ultimately causing its ranking to drop, making it a less optimal choice as a green supplier. In contrast, supplier C maintains stability across “Quality”, “Efficiency”, and “Capability” in terms of risk assessment, securing its position as the top-ranked supplier.

The choice of FMEA over other risk assessment methods was driven by its structured approach to failure identification and risk quantification. Alternative methods such as Fault Tree Analysis (FTA) or Monte Carlo Simulation primarily focus on systemic failures or stochastic modeling, which are less suited for supplier-specific risk evaluations. In contrast, FMEA allows for a detailed, supplier-level risk assessment by evaluating specific failure modes related to environmental compliance, operational disruptions, and sustainability performance. Furthermore, compared to Bayesian Networks or Fuzzy Logic approaches, FMEA is more interpretable and does not require extensive probabilistic modeling, making it more applicable to real-world supplier evaluations. The integration of FMEA within the AHP framework ensures that risk is systematically incorporated into decision-making while maintaining methodological transparency and ease of implementation.

The inclusion of FMEA in supplier selection not only mitigates operational risks but also enhances environmental sustainability. The case study results demonstrate that supplier A, which initially ranked higher under AHP-Entropy, had a higher risk of non-compliance with sustainability standards. By incorporating risk assessment, supplier B moved ahead in ranking due to its stronger environmental performance. This adjustment reflects how risk-based selection methods prevent the inclusion of suppliers with unsustainable practices, ensuring that selected suppliers align with long-term sustainability goals. Furthermore, supplier C, which remained the top-ranked supplier across all methods, exhibited the lowest environmental impact in terms of carbon footprint and waste generation. This confirms that a risk-aware approach not only improves decision accuracy but also leads to better environmental outcomes. By prioritizing suppliers with lower sustainability risks, companies can proactively reduce regulatory violations, enhance resource efficiency, and improve compliance with green procurement policies.

Overall, this analysis demonstrates the effectiveness and superiority of the improved AHP-FMEA method. This approach minimizes subjectivity in weight determination, making the weights more scientifically sound and objective. Additionally, by incorporating risk factors, the evaluation results for green suppliers become more accurate, comprehensive, and well-rounded.

5. Conclusions

This study proposes an improved AHP-FMEA method for green supplier selection, integrating subjective and objective weighting techniques with a risk assessment framework. The AHP is used to determine subjective weights, while the entropy weight method objectively adjusts these weights, reducing the influence of personal biases. Additionally, Failure Modes and Effects Analysis (FMEA) is employed to quantify risk factors, enhancing the decision-making process by incorporating uncertainty and potential failures.

The results of this study demonstrate that the proposed method effectively evaluates green suppliers by considering three key dimensions: quality, efficiency, and capability. Through a comparative analysis of different methods, including classical AHP, AHP-Entropy, and the proposed AHP-FMEA, it is evident that the improved approach provides a more comprehensive and reliable ranking. The incorporation of risk assessment helps mitigate the potential impact of high-risk suppliers, ensuring that companies select sustainable, efficient, and resilient partners.

From the case study of Company T, the proposed model successfully identifies supplier C as the most optimal choice, followed by supplier B, while supplier A ranks the lowest due to its higher operational risk and customer dissatisfaction in green practices. This confirms that risk evaluation is a crucial component in green supplier selection, as traditional methods may overlook significant vulnerabilities.

Furthermore, the proposed method enhances decision-making transparency by balancing qualitative and quantitative factors, minimizing subjectivity, and ensuring a scientific and structured evaluation process. The integration of FMEA into supplier selection provides a more robust and risk-aware framework, which is critical in today’s sustainability-driven supply chains.

The findings of this study have important implications for both businesses and policymakers. For companies, the proposed AHP-FMEA approach offers a systematic way to incorporate sustainability and risk factors into supplier selection, ensuring a more resilient and responsible supply chain. By adopting this method, businesses can proactively identify suppliers with lower environmental risks, reducing regulatory violations and long-term operational disruptions. Additionally, this model can help organizations align their procurement strategies with ESG objectives, which is becoming increasingly important for investor relations and corporate reputation.

For policymakers, the integration of risk-based supplier evaluation can inform regulatory frameworks that promote sustainable supply chain management. Governments and industry associations can use similar methodologies to set procurement guidelines, ensuring that public and private sector organizations prioritize suppliers that comply with sustainability standards and minimize supply chain risks. This approach could also serve as a benchmark for green procurement policies, encouraging businesses to integrate structured risk assessment methods into their supplier selection processes.

While the improved AHP-FMEA method provides a more comprehensive evaluation framework, it also presents certain challenges. One of the primary limitations is its reliance on expert judgment for weight assignment in AHP and risk scoring in FMEA. This means that organizations adopting this method need access to domain experts who can accurately assess supplier risks and sustainability performance. Companies without sufficient expertise may find it difficult to implement the model effectively.

Additionally, the computational complexity of integrating AHP, entropy weighting, and FMEA may require advanced decision-support tools. Compared to simpler supplier selection methods, this approach demands more data processing and structured analysis, which could be a barrier for small and medium-sized enterprises (SMEs) with limited analytical capabilities. Future studies could explore ways to simplify the computational process, such as using automated decision-support systems or AI-driven risk assessment models to reduce manual effort while maintaining analytical rigor.

One promising direction for future research is the development of a dynamic risk assessment framework. The current model relies on predefined risk factors and static risk scores, which may not reflect the changing nature of real-world supply chains. As suppliers evolve, external factors such as market shifts, regulatory changes, and environmental crises can impact their performance and sustainability efforts. Future research could focus on integrating real-time data from suppliers, industry trends, and external environmental factors to continuously update risk evaluations. By leveraging data from IoT sensors, real-time performance tracking, and external environmental monitoring, dynamic risk assessment could offer a more accurate and responsive way to evaluate green suppliers. This approach would allow businesses to make more timely and informed decisions, adapting to risks as they emerge, rather than relying on static assessments.