Green supplier development programmes selection: a hybrid fuzzy multi-criteria decision-making approach

ABSTRACT

This study aims to evaluate the Green Supplier Development Programs (GSDPs) for greening a supply chain. However, this problem is threatened by restricted quantitative information, the specific context of the organisation, lack of prior experience and varying supplier backgrounds. In this paper, we propose a fuzzy integrated Multi-Criteria Decision-Making approach for investigating and prioritising GSDPs. The approach is developed by integrating fuzzy Decision-Making Trial and Evaluation Laboratory (DEMATEL), fuzzy Analytic Hierarchy Process (AHP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) methods. First, fuzzy DEMATEL is applied to determine the main green factors, then the fuzzy AHP method is used to acquire the local weights of criteria, and finally, the GSDPs are prioritised based on the green factors by fuzzy TOPSIS. The proposed approach is employed to estimate GSDPs of the painting companies. The outcomes indicate that ‘requiring ISO 14,000 certification for suppliers? and ‘building top management commitment for suppliers for green supply practices’ have the highest and lowest impact on improving the environmental performance of suppliers, respectively. It is also concluded that ‘green procurement’ measure has the highest effect on prioritising the GSDPs.

KEYWORDS:

• Environmental performance
• green supplier development programs
• green criteria
• fuzzy DEMATEL
• fuzzy AHP-TOPSIS

1. Introduction

With the advent of a new era of business where change is regarded as one of its main features, nowadays the success and survival of organisations cannot be easily guaranteed, particularly regarding demanding environmental protection and green manufacturing issues (Pourjavad and Shahin 2018b). Green Supply Chain Management (GSCM) as an organisational philosophy aims to increase the market share and financial capability of companies with minimising environmental negative impacts and increasing ecological efficiency (Govindan, Soleimani, and Kannan 2015). Hence, most companies are looking for solutions approaches to improve the performance of GSCM. In this regard, suppliers play a significant role in developing GSCM (Hussain and Al-Aomar 2018). The performance of GSCM is highly improved by improving the environmental performance of suppliers (Fu, Zhu, and Sarkis 2012). Hence, companies improve the performance of GSCM through the selection of existing green suppliers. Regarding this matter, scholars have proposed various approaches for selecting green and sustainable suppliers, evaluating the environmental performance of suppliers, and assessing the green suppliers.

However, it is undeniable fact that all suppliers are not initially green and able to create better their environmental or sustainability performance, effectively. Therefore, companies have focused on aiding suppliers to improve their environmental performance by ‘introducing’ Green Supplier Development Programs (GSDPs). Competitive advantages can be accrued from GSDPs, but significant organisational resources are required to implement these programs. Also, all GSDPs cannot equally provide environmental improvement and supplier operational performance. The investigation and selection of the appropriate and efficient GSDPs are required by companies due to the heterogeneous performance of GSDPs and limited available resources for implementation (Dou, Zhu, and Sarkis 2014).

Several criteria and their inter-relationships with uncertain information should be implemented to evaluate GSDPs (Bai and Sarkis 2010). Multi-Criteria Decision-Making (MCDM) approaches (Sangaiah et al. 2017) have been commonly employed to evaluate the supplier environmental performance (Shaik and Abdul-Kader 2011), for instance, Analytic Hierarchy Process (AHP), Analytic Network Process (ANP), and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). These methods have been applied to evaluate the relationships between supplier development program involvement attributes and performance outcomes, to analyse the influence relationships amongst GSDPs, and to assess the effects of green programs on supplier performance (Pourjavad and Shahin 2018a).

The defined criteria for evaluating green supplier development programs are divided into two categories; quantitative and vague or imprecisely defined qualitative. The vagueness intrinsic to the evaluation of qualitative criteria and vague weighing of these criteria by several decision-makers increases the uncertainty of GSDPs evaluation. Hence, the importance of a good approach which handles both quantitative and qualitative criteria is highlighted to reach the appropriate results of GSDPs evaluation. In addition, the MCDM approaches are accompanied by human judgements and preferences which are vague because of uncertainty and imprecision in the human decision-making process (Goyal, Kaushal, and Sangaiah 2018). Hence, these approaches are coped with subjective human preferences for most problems in real-world applications (Sangaiah et al. 2018). The decision-makers prefer to use linguistic terms instead of exact scales for evaluation (Pourjavad and Mayorga 2019). The fuzzy set theory facilitates decision-making by approximate reasoning and linguistic terms (Pourjavad and Mayorga 2018c), hence it is recognised as a solution to solve such uncertainty problems of MCDM models.

As mentioned earlier, the problem of GSDPs evaluation is influenced by multiple criteria with various levels of importance. The process of GSDPs evaluation would be more difficult, time-consuming and inappropriate if green criteria with low importance are being considered. The Decision-Making Trial and Evaluation Laboratory (DEMATEL) is recognised as one of the best methods to analyse the cause-and-effect relationships of criteria and find the most important ones (Sangaiah, Subramaniam, and Zheng 2015). Hence, in this paper, we use a fuzzy DEMATEL to define key green criteria by avoiding low influences for evaluating GSDPs.

In this paper, an integrated fuzzy MCDM approach based on the fuzzy DEAMTEL, fuzzy AHP, and fuzzy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is proposed to evaluate GSDPs according to green criteria. The proposed approach is composed of three main steps. In the first step, the fuzzy DEMATEL is implemented to determine critical green factors that have a high effect on decision-making. Then, the fuzzy AHP method is applied to obtain the local weights of each criterion, and finally, the programs of green supplier development are assessed and ranked based on green criteria by fuzzy TOPSIS. The proposed fuzzy-integrated approach is applied to evaluate GSDPs for greening suppliers in painting industries. In addition, a sensitivity analysis is conducted to estimate the importance of green criteria to prioritise green supplier development suppliers.

We make the following research contributions in this study:

1. Determining critical green criteria to investigate green supplier development programs;

2. Developing an integrated fuzzy MCDM approach to prioritise GSDPs under restricted quantitative information;

3. Conducting a sensitivity analysis to evaluating the influence of green criteria in ranking GSDPs.

The rest of this paper is organised as follows: Section 2 presents a review of the literature related to GSDPs, Section 3 reveals the proposed fuzzy MCDM approach for GSDPs evaluation, Section 4 applies the proposed approach for prioritising GSDPs of painting industries, Section 5 discusses the achieved results from the proposed approach and presents a sensitivity analysis on the effect of green criteria for evaluating GSDPs and managerial implications, finally, Section 6 provides some concluding remarks.

2. Literature review

The conducted studies in the field of green supply chain management are divided into six main categories: sustainable supplier selection, green supplier selection, green supplier evaluation, green partner selection, supplier environmental performance evaluation, and green supplier development program evaluation (Table 1).

Table 1. A summary of GSCM approaches

Subject	Approach	Reference
Sustainable supplier selection	AHP-VIKOR	Luthra et al. (2017)
	Fuzzy TOPSIS	Memari et al. (2019)
	Grey-based MCDM	Bai et al. (2019)
	Full Consistency method	Durmić (2019)
Green supplier selection	DEA and ANP	Kuo and Lin (2012)
	ANN, MADA, DEA, ANP	Kuo, Wang, and Tien (2010)
	Grey methods	Bali, Kose, and Gumus (2013)
	Empirical studies and conceptual models	Genovese et al. (2013)
	Fuzzy AHP and Generalised Choquet Fuzzy Integral (GCFI)	Cakir (2017)
	Fuzzy TOPSIS-VIKOR	Banaeian et al. (2018)
	Fuzzy AHP-TOPSIS	Chatterjee and Stević (2019)
Green supplier evaluation	AHP	Büyüközkan et al.(2012)
	ANP and TOPSIS	Akman and Piskın (2013)
	Fuzzy DEMATEL, ANP and TOPSIS	Büyüközkan and Çifçi (2012)
	Fuzzy TOPSIS	Shen et al. (2013)
	VIKOR-based Sorting	Demir et al. (2018)
Green partner selection	AHP	Lee et al. (2012)
	Multi-objective genetic algorithms (MOGA)	Yeh and Chuang (2011)
	AHP and fuzzy TOPSIS	Hamdan and Cheaitou (2017)
Supplier environmental performance evaluation	AHP	Handfield et al. (2002)
	Empirical studies and conceptual models	Yang et al. (2010)
	Fuzzy TOPSIS	Awasthi, Chauhan, and Goyal (2010)
	Fuzzy AHP-TOPSIS	Stević et al. (2016)
	Entropy-TOPSIS	Dos Santos, Godoy, and Campos (2019)
Green Supplier development program evaluation	Grey system and rough set theory	Bai and Sarkis (2010)
	Grey based DEMATEL	Fu, Zhu, and Sarkis (2012)
	Empirical studies and conceptual models	Blome, Hollos, and Paulraj (2014)
	Grey based ANP	Dou, Zhu, and Sarkis (2014)
	Fuzzy DEMATEL-AHP-TOPSIS	Our approach

For the first category, sustainable supplier selection, scholars developed different approaches such as Full Consistency method (Durmić 2019) to evaluate suppliers based on the aspects of sustainability; environmental, social, and economy. In this regard, Zarbakhshnia et al. (2020) also integrated fuzzy AHP and grey multi-objective optimisation by ratio analysis (MOORA-G) to evaluate third-party reverse logistics providers based on sustainability criteria. For the categories of green supplier selection and green partner selection, the deterministic and fuzzy MCDM methods such as ANP and DEA (Kuo and Lin 2012), fuzzy AHP-TOPSIS (Chatterjee and Stević 2019), AHP and fuzzy TOPSIS (Hamdan and Cheaitou 2017) have been also used for selecting suppliers based on green factors. Lo et al. (2018) proposed a novel model to select green suppliers by integrating best–worst method (BWM), TOPSIS, and fuzzy multi-objective linear programming (FMOLP). Chang, Liou, and Lo (2019) developed an integrated BWM and the fuzzy TOPSIS technique framework to evaluate the performance and priority rankings of strategic alliance partners. The review of conducted studies for the category of green supplier evaluation shows the MCDM methods have been applied for assessing the suppliers based on green criteria. The environmental performance of suppliers has been evaluated by the fuzzy MCDM approach such as fuzzy TOPSIS (Awasthi, Chauhan, and Goyal 2010), and fuzzy AHP-TOPSIS (Stević et al. 2016).

For all conducted studies in the first five categories, it is assumed that all suppliers are green or follow the sustainability criteria in their performance. However, as mentioned above, all suppliers are not green or improve sustainability performance. Hence, in the last category, green supplier development programmes evaluation, scholars focus on finding ways to green and improve the environmental performance of suppliers in order to improve the green supply chain management. Despite the importance of development programs to green suppliers, there are a few studies in this area. For example, Bai and Sarkis (2010) presented a formal method based on rough set theory to explore the relationships between GSDPs attributes and performance outcomes. A formalised grey-based DEMATEL methodology was suggested to investigate the GSDPs by Fu, Zhu, and Sarkis (2012) within a telecommunication systems provider. Blome, Hollos, and Paulraj (2014) extracted the opposing theoretical views of legitimacy in exploring company performance and top management commitment as results in green supplier development. In addition, they evaluated the effects of two criteria on supplier performance, green procurement and green supplier development. Dou, Zhu, and Sarkis (2014) introduced a grey Analytical Network Process-based (grey ANP-based) model to determine GSDPs that improved the performance of suppliers, effectively. They also investigated green supplier development programs, comprehensively with explicit consideration of supplier involvement propensity levels. The review of conducted studies in field of Green Supplier Development Programs evaluation show there is not a procedure to find the important green criteria for evaluating GSDPs. Hence, the above approaches are time-consuming and inappropriate when green criteria with low significance are being considered. In addition, the uncertainty issue in the process of GSDPs evaluation has been neglected by other scholars. The uncertainty is addressed by fuzzy logic in the proposed approach of this study.

3. The proposed approach

In this section, we develop an integrated fuzzy MCDM approach to investigate GSDPs. The main steps of the proposed approach are highlighted in Figure 1. This approach comprises three main steps, (i) recognising the evaluation dimensions and related criteria of GSDPs using the fuzzy DEMATEL method, (ii) obtaining the local weights of green criterion by fuzzy AHP, (iii) prioritising the green supplier development programs using fuzzy TOPSIS. The main steps of approach are detailed as below:

3.1. Green criteria selection by fuzzy DEMATEL

The GSDPs evaluation is complicated by the fact that various criteria should be considered in the assessment process. These factors are generally categorised into supplier operational performance and supplier environmental performance (Table 2). The supplier operational performance metrics include cost (C1), quality (C2), time (C3), flexibility (C4), innovativeness (C5) and process management (C6) (Sarkis and Talluri 2002). Ho, Xu, and Dey (2010) identified quality as the most popular factor, followed by delivery, cost, manufacturing capability, and service. Cost, quality, on-time delivery, and flexibility were recognised as the most common supplier performance criteria by Chuu (2011). Innovativeness and process management have also been considered as important operational performance criteria for supplier performance assessment.

Table 2. GSDP Criteria

Category	Criteria	Reference
Supplier Operational Performance	Cost (C1)	Jabbour and Jabbour (2009); Govindan, Khodaverdi, and Jafarian (2013)
	Quality (C2)	Amin and Zhang (2012); Govindan, Khodaverdi, and Jafarian (2013)
	Time (C3)	Govindan, Khodaverdi, and Jafarian (2013)
	Flexibility (C4)	Amin and Zhang (2012)
	Innovativeness (C5)	Sarkis and Talluri (2002)
	Labour (C6)	Bai and Sarkis (2010)
	Process Management (C7)	Sarkis and Talluri (2002)
Supplier Environmental Performance	Green Packaging (C8)	Handfield et al. (2002)
	Green Product Design (C9)	Govindan, Khodaverdi, and Jafarian (2013); Bai and Sarkis (2010)
	Green Transportation (C10)	Handfield et al. (2002)
	Green Warehousing (C11)	Jabbour and Jabbour (2009)
	Green Procurement (C12)	Handfield et al. (2002)
	Reverse Logistics (C13)	Jabbour and Jabbour (2009)
	Solid Waste (C14)	Bai and Sarkis (2010); Amin and Zhang (2012)
	Chemical Waste (C15)	Jabbour and Jabbour (2009)
	Water Recovery (C16)	Govindan, Khodaverdi, and Jafarian (2013)
	Energy Usage (C17)	Jabbour and Jabbour (2009)
	Noise (C18)	Govindan, Khodaverdi, and Jafarian (2013)
	Emissions (C19)	Handfield et al. (2002)

The environmental criteria are another significant player in supplier performance evaluation (Tang and Zhou 2012). Humphreys, Wong, and Chan (2003) used environmental factors such as green design, environmental management systems, and environmental competencies to evaluate suppliers. Handfield et al. (2002) introduced 10 environmental criteria such as emissions, noise, waste, green packaging, green manufacturing, green procurement and reverse logistics to evaluate supplier performance. Jabbour and Jabbour (2009) identified qualitative and quantitative environmental criteria to investigate and select suppliers for Brazilian companies. They applied green warehousing, reverse logistics, waste, water recovery and energy usage criteria in their assessment.

As mentioned above, all these green criteria do not have the same level of importance for evaluating GSDPs. Hence, we use the fuzzy DEMATEL method to determine the important green criteria. A set of 10 academic experts who are working in fields of sustainability, green supply chain management, and environmental issues from Business schools and Industrial Engineering departments participated to complete pair-wise of green criteria. In this study, we used the developed fuzzy DEMATEL by Dalalah, Hayajneh, and Batieha (2011) to determine the green criteria with high importance. The main steps of this approach are detailed as below:

Step one: the matrix $\tilde{Z}$ with $n$ dimension is built up with the linguistic assessment terms (Table 4) based on the experts’ opinions. The dimension $n$ denotes the number of green criteria. Each element of this matrix is represented with Triangular Fuzzy Numbers (TFNs) as ${\tilde{Z}}_{ij}$ = ($z_{ijl}$, $z_{ijm}$, $z_{iju}$). The ${\tilde{Z}}_{ij}$ represents the degree to which the criterion $C_i$ affects criterion $C_j$.

(1) $\tilde{Z}=\begin{array}{c}\\ \left[\begin{array}{cccc}1& {\tilde{Z}}_{12}& \cdots & {\tilde{Z}}_{1n}\\ {\tilde{Z}}_{21}& 1& \cdots & {\tilde{Z}}_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ {\tilde{Z}}_{n1}& {\tilde{Z}}_{n2}& \cdots & 1\end{array}\right]\end{array}$(1)

Table 3. Total relation matrix of green criteria

Category	Criteria	${\tilde{D}}_i^{def}$	${\tilde{R}}_i^{def}$	${\tilde{D}}_i^{def}+{\tilde{R}}_i^{def}$	${\tilde{D}}_i^{def}-{\tilde{R}}_i^{def}$	$W_i$	Rank	Selected criteria
Supplier Operational Performance	C1	8.5	7.1	15.6	1.3	0.0661	2	Cr1
	C2	7.6	7.1	14.7	0.5	0.0621	3	Cr2
	C3	6.5	5.3	11.8	1.2	0.0501	4
	C4	8.8	7.5	16.3	1.3	0.0691	1	Cr3
	C5	4.3	5.6	9.9	−1.3	0.0422	5
	C6	7.5	3.6	11.1	3.9	0.0497	6
	C7	6.1	4.8	10.9	1.3	0.0464	7
Supplier Environmental Performance	C8	4.8	4.1	8.9	0.7	0.0377	9
	C9	8.6	6.9	15.5	1.7	0.0659	3	Cr4
	C10	6.3	8.1	14.4	−1.8	0.0613	4	Cr5
	C11	5.8	4.6	10.4	1.2	0.0442	7
	C12	7.5	6.9	14.4	0.6	0.0609	5	Cr6
	C13	3.3	5.2	8.5	−1.9	0.0368	11
	C14	4.9	3.8	8.7	1.1	0.0370	10
	C15	8.7	3.9	12.6	4.8	0.0570	6
	C16	5.6	4.2	9.8	1.4	0.0418	8
	C17	8.7	7.9	16.6	0.8	0.0702	1	Cr7
	C18	4.4	3.8	8.2	0.6	0.0347	12
	C19	7.6	8.2	15.8	−0.6	0.0668	2	Cr8

Table 4. Linguistic terms of green criteria for GSDPs evaluation

Linguistic variables			Fuzzy Numbers	Linguistic Values
DEMATEL	AHP	TOPSIS
No influence	Equally important	Very low	$\tilde{1}$	(1, 1, 2)
Very low influence	Moderately more important	Low	$\tilde{3}$	(2, 3, 4)
Low influence	Strongly more important	Medium	$\tilde{5}$	(4, 5, 6)
High influence	Very strongly more important	High	$\tilde{7}$	(6, 7, 8)
Very high influence	Extremely more important	Very high	$\tilde{9}$	(8, 9, 10)

Step two: the normalised direct-relation fuzzy matrix ($\tilde{\mathrm{X}}$) is created as:

(2) $\tilde{X}=\begin{array}{c}\\ \left[\begin{array}{cccc}{\tilde{x}}_{11}& {\tilde{x}}_{12}& \cdots & {\tilde{x}}_{1n}\\ {\tilde{x}}_{21}& {\tilde{x}}_{22}& \cdots & {\tilde{x}}_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ {\tilde{x}}_{n1}& {\tilde{x}}_{n2}& \cdots & {\tilde{x}}_{nn}\end{array}\right]\end{array}$(2)

where:

${\tilde{x}}_{ij}=\frac{{\tilde{Z}}_{ij}}{\tilde{R}}=\left(\frac{Z_{ij,l}}{r_l},\frac{Z_{ij,l}}{r_m},\frac{Z_{ij,l}}{r_u}\right),$

$\tilde{R}$ = ($r_l$, $r_m$, $r_u$) and

$r_{s=max}\left(\sum _{j=1}^n{\tilde{Z}}_{ij,s}\right)\mathrm{\forall }s=l,m,u$

Step three: based on the following term the total-relation fuzzy matrix $\tilde{T}$ is provided.

(3) $\tilde{T}=\underset{w\to \mathrm{\infty }}{lim}\left(\tilde{X}+{\tilde{X}}^2+\dots +{\tilde{X}}^w\right)=\tilde{X}{\left(I-\tilde{X}\right)}^{-1}$(3)

Therefore, $\tilde{T}$ matrix could be displayed as:

(4) $\tilde{T}=\begin{array}{c}\\ \left[\begin{array}{cccc}{\tilde{t}}_{11}& {\tilde{t}}_{12}& \cdots & {\tilde{t}}_{1n}\\ {\tilde{t}}_{21}& {\tilde{t}}_{22}& \cdots & {\tilde{t}}_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ {\tilde{t}}_{n1}& {\tilde{t}}_{n2}& \cdots & {\tilde{t}}_{nn}\end{array}\right]\end{array}$(4)

where ${\tilde{t}}_{ij}$ = ($t_{ijl}$, $t_{ijm}$, $t_{iju}$) is identified as the overall influence rating of decision-maker for each criterion $i$ against criterion $j$.

Step four: the sum of rows (${\tilde{D}}_i$) and sum of columns (${\tilde{R}}_i$) of the sub-matrices $T_l$, $T_m$, $T_u$ are obtained by the following equations:

(5) ${\tilde{D}}_i=\sum _{j=1}^n{\tilde{t}}_{ij}\left(i=1,2,\dots ,n\right)$(5)

(6) ${\tilde{R}}_i=\sum _{j=1}^n{\tilde{t}}_{ij}\left(j=1,2,\dots ,n\right)$(6)

Step five: the casual diagram is provided by mapping the ordered pairs of (${\tilde{D}}_i^{def}$+ ${\tilde{R}}_i^{def}$) and (${\tilde{D}}_i^{def}$- ${\tilde{R}}_i^{def}$). Then, the following equation is used to calculate the importance of green criteria.

(7) ${\omega }_i={\left\{{\left({\tilde{D}}_i^{def}+{\tilde{R}}_i^{def}\right)}^2+{\left({\tilde{D}}_i^{def}-{\tilde{R}}_i^{def}\right)}^2\right\}}^{\frac{1}{2}}$(7)

Step six: the final weights of green criteria are provided by normalising values as follows:

(8) $W_i=\frac{{\omega }_i}{{\sum }_{i=1}^n{\omega }_i}$(8)

The prominence, relation and respective weights of green criteria are shown in Table 3.

Based on the provided results from fuzzy DEMATEL (Table 3), we can find the most significant green criteria for GSDPs evaluation. This method prioritises green criteria based on their importance. The $W_i$ (Table 3) represents the importance of each green criterion in comparison with others. As seen, ‘Flexibility’ (C4) from supplier operational performance category and ‘Energy Usage’ (C17) from supplier environmental performance got the highest scores, (0.0691) and (0.0702), respectively. These results also indicate, ‘Process Management’ (C7) and ‘Noise’ (C18) has the lowest significance among green criteria for these two categories. In this study, the first eight green criteria which got the highest score based on importance ($W_i$) were selected as the main factors for GSDPs evaluation.

3.2. Obtaining the weights of green criteria using fuzzy AHP

The AHP method is a quantitative technique that organises a multi-attribute, multi-person and multi-period problem hierarchically so that solutions are facilitated (Saaty 1980). A fuzzy extension of AHP was developed to cover shortages of the original AHP technique and to solve the hierarchical fuzzy problems. The scholars developed several fuzzy AHP methods (Pourjavad and Peng 2017). We used the developed fuzzy AHP method by Ayag and Ozdemir (2007) to calculate the weights of green criteria. Triangular fuzzy numbers ($\tilde{1}$,$\tilde{3}$, $\tilde{5}$, $\tilde{7}$, $\tilde{9}$) are applied to show the relative strength of each pair of elements in the same hierarchy (Table 4).

3.3. Ranking GSDPs using fuzzy TOPSIS

In the third step, the fuzzy TOPSIS method is implemented to prioritise the green supplier development programs based on green criteria. This method includes the following steps:

Step 1: the linguistic rating values are defined for the GSDPs with respect to the selected green criteria (Table 4).

Step 2: the aggregated fuzzy ratings ($\tilde{R}$= $\left(a,b,c\right)$) of the GSDPs are calculated as:

$a=min\left\{a_k\right\}$, $=\frac{1}{K}\sum _{k=1}^k{b}_k$, $c=max\left\{c_k\right\}$, (9)

when the fuzzy ratings of experts are presented by TFNs as ${\tilde{R}}_k$= ($a_k$, $b_k$, $c_k$), $k=1,2,\dots K$.

If ${\tilde{X}}_{ijk}$ = ($a_{ijk}$, $b_{ijk}$, $c_{ijk}$), $i=1,2,\dots ..m$; $j=1,2,\dots ..n$, represents the fuzzy rating of the $k^{th}$ decision-maker, the aggregated fuzzy rating ${\tilde{X}}_{ij}=\left({\mathrm{a}}_{ij},{\mathrm{b}}_{ij},{\mathrm{c}}_{ij}\right)$ is represented as:

$a_{ij}=min\left\{a_{ijk}\right\}$, $b_{ij}=\frac{1}{K}\sum _{k=1}^k{b}_{ijk}$

(10) $c_{ij}=max\left\{c_{ijk}\right\}$(10)

Step 3: the fuzzy decision matrix is established.

Step 4: the normalised fuzzy decision matrix ($\tilde{R}$) is constructed as:

$\tilde{R}$ = ${\left[r_{ij}\right]}_{m\times n}$, $i=1,2,\dots ..m$;

(11) $j=1,2,\dots ,n$(11)

where:

(12) ${\tilde{r}}_{ij}=\left(\frac{a_{ij}}{c_j^{*}},\frac{b_{ij}}{c_j^{*}},\frac{c_{ij}}{c_j^{*}}\right)\text{and}{c}_j^{*}=max{c}_{ij}\left(positivecriteria\right)$(12)

(13) ${\tilde{r}}_{ij}=\left(\frac{a_j^{-}}{c_{ij}},\frac{a_j^{-}}{b_{ij}},\frac{a_j^{-}}{a_{ij}}\right)\mathrm{a}\mathrm{n}\mathrm{d}{a}_j^{-}=min{a}_{ij}\left(negativecriteria\right)$(13)

Step 5: the weighted normalised matrix ($\tilde{V}$) is built up as:

(14) $\tilde{V}={\left[{\tilde{v}}_{ij}\right]}_{m\times n}i=1,2,\dots ,m;j=1,2,\dots ,n$(14)

where ${\tilde{v}}_{ij}$ = ${\tilde{r}}_{ij}{W}_j$. The ($W_j$) represents the weights of green criteria which is calculated by fuzzy AHP, the ${\tilde{r}}_{ij}$ denotes the normalised fuzzy decision matrix.

Step 6: the Fuzzy Positive Ideal Solution (FPIS) and Fuzzy Negative Ideal Solution (FNIS) are calculated as:

$A^{\ast }$ = (${\tilde{v}}_1^{\ast }$, ${\tilde{v}}_2^{\ast }$, …, ${\tilde{v}}_n^{\ast }$) where ${\tilde{v}}_j^{\ast }$ = (${\tilde{c}}_j^{\ast }$, ${\tilde{c}}_j^{\ast }$, ${\tilde{c}}_j^{\ast }$) and ${\tilde{c}}_j^{\ast }$= max {${\tilde{c}}_{ij}$} (15)

$A^{-}$ = (${\tilde{v}}_1^{-}$, ${\tilde{v}}_2^{-}$, …, ${\tilde{v}}_n^{-}$) where ${\tilde{v}}_j^{-}$ = ($a_j^{-}$, ${\tilde{a}}_j^{-}$, ${\tilde{a}}_j^{-}$) and ${\tilde{a}}_j^{-}$= min {${\tilde{a}}_{ij}$} (16)

$\mathrm{\forall }i$= $1,2,\dots ,m$ and $j=1,2,\dots ,n$

Step 7: the distance green supplier development program from FPIS ($d_i^{+}$) and FNIS ($d_i^{-}$) is calculated as:

$d_i^{+}$ = $\sum _{j=1}^{n}dv({\tilde{v}}_{ij},{\tilde{v}}_j^{\ast }$) $i=1,2,\dots ,m$ (17)

$d_i^{-}$ = $\sum _{j=1}^{n}dv({\tilde{v}}_{ij},{\tilde{v}}_j^{-}$) $i=1,2,\dots ,m$ (18)

Step 8: the closeness coefficient (CCi) of each green supplier development program is provided as:

CC_i =

(19) $\frac{d_i^{-}}{d_i^{-}+d_i^{+}}$(19)

The green supplier development programs are prioritised based on the calculated CC_i .

4. Case Study

In this section, the proposed approach is applied to evaluate GSDPs of painting industries in IRAN. These programs are labelled ‘setting long-term contracts with environmental dimensions incorporated’ (P1); ‘building top management commitment for suppliers for green supply practices’ (P2); ‘requiring ISO 14,000 certification for suppliers’ (P3); ‘training suppliers on environmental issues’ (P4); and ‘providing green technological advice to suppliers’ (P5).

Ten academic experts along with 20 senior supply managers of the painting industries participated to evaluate the GSDPs according to green criteria. First, the experts make pair-wise comparisons of two main categories and eight green criteria (extracted from fuzzy DEMATEL) using linguistic variables (Table 4). The pair-wise comparisons of the green criteria are displayed in Table 5. Then, the weights of green criteria are provided by fuzzy AHP (Table 6).

Table 5. Fuzzy comparison matrix of the green criteria using TFNs

	Cr 1	Cr 2	Cr 3	Cr 4	Cr 5	Cr 6	Cr 7	Cr 8
Cr 1	1	$\tilde{5}$	$\tilde{5}$	$\tilde{5}$	$\tilde{7}$	${\tilde{3}}^{-1}$	${\tilde{3}}^{-1}$	$\tilde{3}$
Cr 2	${\tilde{5}}^{-1}$	1	$\tilde{3}$	${\tilde{3}}^{-1}$	${\tilde{5}}^{-1}$	${\tilde{9}}^{-1}$	${\tilde{7}}^{-1}$	${\tilde{3}}^{-1}$
Cr 3	${\tilde{5}}^{-1}$	${\tilde{3}}^{-1}$	1	${\tilde{3}}^{-1}$	$\tilde{3}$	${\tilde{9}}^{-1}$	${\tilde{7}}^{-1}$	${\tilde{5}}^{-1}$
Cr 4	${\tilde{5}}^{-1}$	$\tilde{3}$	$\tilde{3}$	1	$\tilde{5}$	${\tilde{5}}^{-1}$	${\tilde{3}}^{-1}$	${\tilde{3}}^{-1}$
Cr 5	${\tilde{7}}^{-1}$	$\tilde{5}$	${\tilde{3}}^{-1}$	${\tilde{5}}^{-1}$	1	${\tilde{9}}^{-1}$	${\tilde{7}}^{-1}$	${\tilde{3}}^{-1}$
Cr 6	$\tilde{3}$	$\tilde{9}$	$\tilde{9}$	$\tilde{5}$	$\tilde{9}$	1	$\tilde{3}$	$\tilde{5}$
Cr 7	$\tilde{3}$	$\tilde{7}$	$\tilde{7}$	$\tilde{3}$	$\tilde{7}$	${\tilde{3}}^{-1}$	1	$\tilde{3}$
Cr 8	${\tilde{3}}^{-1}$	$\tilde{3}$	$\tilde{5}$	$\tilde{3}$	$\tilde{3}$	${\tilde{5}}^{-1}$	${\tilde{3}}^{-1}$	1

Table 6. Eigenvector for comparison matrix of the green criteria (CR = 0.075)

	Cr 1	Cr 2	Cr 3	Cr 4	Cr 5	Cr 6	Cr 7	Cr 8	e-vector
Cr 1	1	5	5	5	7	0.375	0.375	3	0.169
Cr 2	0.21	1	3	0.375	0.21	0.113	0.146	0.375	0.029
Cr 3	0.21	0.375	1	0.375	3	0.113	0.146	0.21	0.029
Cr 4	0.21	3	3	1	3	0.21	0.375	0.375	0.064
Cr 5	0.146	5	0.375	0.21	1	0.113	0.146	0.375	0.030
Cr 6	3	9	9	5	9	1	3	5	0.361
Cr 7	3	7	7	3	7	0.375	1	3	0.223
Cr 8	0.375	3	5	3	3	0.21	0.375	1	0.096

Then, a fuzzy evaluation matrix is formed according to experts’ opinions to compare green supplier development programs based on green criteria (Table 7). The upper and lower half of Table 7 show the linguistic variables and triangular fuzzy numbers, respectively. In this section, the linguistic evaluation matrix and fuzzy evaluation matrix of one of the experts are only shown due to space limitation. In the next step, the aggregate fuzzy weights of the GSDPs are provided by Eq.(10)(10) $c_{ij}=max\left\{c_{ijk}\right\}$(10) and their values are normalised by Eq. (12)(12) ${\tilde{r}}_{ij}=\left(\frac{a_{ij}}{c_j^{*}},\frac{b_{ij}}{c_j^{*}},\frac{c_{ij}}{c_j^{*}}\right)\text{and}{c}_j^{*}=max{c}_{ij}\left(positivecriteria\right)$(12) and Eq. (13)(13) ${\tilde{r}}_{ij}=\left(\frac{a_j^{-}}{c_{ij}},\frac{a_j^{-}}{b_{ij}},\frac{a_j^{-}}{a_{ij}}\right)\mathrm{a}\mathrm{n}\mathrm{d}{a}_j^{-}=min{a}_{ij}\left(negativecriteria\right)$(13) . Then, the weighted evaluation matrix is provided by the Eq. (14)(14) $\tilde{V}={\left[{\tilde{v}}_{ij}\right]}_{m\times n}i=1,2,\dots ,m;j=1,2,\dots ,n$(14) .

Table 7. Linguistic scale evaluation matrix for GSDPs

GSDPs	Cr 1	Cr 2	Cr 3	Cr 4	Cr 5	Cr6	Cr7	Cr8
P1	M	M	H	H	VL	VH	H	H
P2	H	VL	M	VL	L	VL	VL	M
P3	VL	H	L	VH	M	M	VH	M
P4	H	H	VL	M	L	VH	VH	H
P5	VH	L	VH	M	H	H	M	L
P1	(4,5,6)	(4,5,6)	(6,7,8)	(6,7,8)	(1,1,2)	(8,9,10)	(6,7,8)	(6,7,8)
P2	(6,7,8)	(1,1,2)	(4,5,6)	(1,1,2)	(2,3,4)	(1,1,2)	(1,1,2)	(4,5,6)
P3	(1,1,2)	(6,7,8)	(2,3,4)	(8,9,10)	(4,5,6)	(4,5,6)	(8,9,10)	(4,5,6)
P4	(6,7,8)	(6,7,8)	(1,1,2)	(4,5,6)	(2,3,4)	(8,9,10)	(8,9,10)	(6,7,8)
P5	(8,9,10)	(2,3,4)	(8,9,10)	(4,5,6)	(6,7,8)	(6,7,8)	(4,5,6)	(2,3,4)

The type of used green criteria in this paper is negative (cost) and positive (benefit) criteria. For this reason, the FPSI ($A^{\ast }$) and FNIS ($A^{-}$) are determined as ${\tilde{v}}^{\ast }$= (1, 1, 1) and ${\tilde{v}}^{-}$= (0, 0, 0) for benefit criteria, and ${\tilde{v}}^{\ast }$= (0, 0, 0) and ${\tilde{v}}^{-}$= (1, 1, 1) for cost criteria. The Cr1, Cr7, and Cr8 are categorised into cost criteria and the rest criteria are considered as benefit criteria. Then, the distance of each green supplier development programmes from FPIS ($d_i^{+}$) and FNIS ($d_i^{-}$) are provided by Eqs. (26) and (27). Finally, CC_i are calculated for all green supplier development programs (Table 8).

Table 8. The GSDPs ranking by fuzzy TOPSIS

GSDPs	$d_i^{+}$	$d_i^{-}$	CCi	Rank
P1	4.467	2.288	0.339	4
P2	4.649	2.375	0.338	5
P3	4.281	2.651	0.382	1
P4	4.262	2.589	0.378	2
P5	4.413	2.604	0.371	3

Table 8 demonstrates the environmental performance of GSDPs in terms of eight green criteria for greening the suppliers. As seen, P3 and P4 with 0.382 and 0.378 values were ranked as the first and second, respectively. It means they have a relatively significant positive effect on improving the performance of suppliers based on green criteria. In contrast, P1 and P2 have a relatively weak positive effect on supplier performance, with values of 0.339 and 0.338, respectively. P5 got the third rank with 0.371 value.

5. Discussion

In this section, firstly the provided solutions by our approach are discussed and compared with other studies, then the impact of green criteria for prioritising the GSDPs is analysed (Section 5.1), finally, the managerial implications of this study are presented (Section 5.2).

The obtained results of investigating and ranking GSDPs based on green criteria are displayed in Table 8. These results provide analytical information for selecting those GSDPs that improve supplier environmental performance. The results show P3 and P2 are identified as the most and less effective GSDPs for suppliers of painting industries, respectively. It means, requiring ISO 14,000 certification for suppliers (P3) has the best environmental performance for the suppliers of the painting companies. In contrast, building top management commitment to using green supply practices for suppliers (P2), has the lowest importance to improve the environmental performance of suppliers. The acquired results also reveal that other GSDPs (P4, P5, and P1) are relatively useful for greening suppliers.

The obtained results can be variously interpreted by supply chain managers of the painting industries to enhance the performance of suppliers based on green criteria. The low efficient GSDPs are eliminated to manage limited resources, while still obtaining good performance results by initially implementing the GSDPs that considerably improve the green performance of suppliers. Supply chain managers initially seek to execute GSDPs more likely to be successful programs, while they understand some green programs are more likely to give larger overall benefits. Hence, it is highly recommended that companies focus on encouraging suppliers to be involved in GSDPs that got the highest scores based on green factors.

The provided results from the developed fuzzy integrated MCDM approach in this study can be compared with conducted studies in this area. The problem of GSDPs evaluation was especially reviewed by Fu, Zhu, and Sarkis (2012), Dou, Zhu, and Sarkis (2014), and Awashti and Kannan (2016). The obtained results from our approach for painting industries show requiring ISO 14,000 certification for the supplier (P3) and training suppliers on environmental issues (P4) were recognised as the best programs for enhancing the environmental performance of suppliers. The importance of these two GSDPs for greening the suppliers has been confirmed by other studies (Fu, Zhu, and Sarkis (2012); Dou, Zhu, and Sarkis (2014); Awashti and Kannan (2016)). In addition, the obtained results from conducted studies by Fu, Zhu, and Sarkis (2012) and Dou, Zhu, and Sarkis (2014) indicate that ‘setting long-term contracts with environmental dimensions incorporated’ (P1) and ‘building top management commitment for suppliers for green supply practices’ (P2) have the lowest impact for improving the environmental performance of suppliers. As can be seen from Table 8, these two GSDPs (P1 and P2) got also the lowest importance for greening suppliers in our study.

5.1. Sensitivity analysis

In this section, we conduct a sensitivity analysis to evaluate the impact of green criteria on prioritising the GSDPs. The eleven (11) experiments are designed and conducted (Table 9). For this purpose, the different weights are devoted to green criteria. For the first eight experiments, we devote the highest value (0.6) to each green criterion and give the same values (0.075) to the rest of the criteria. For example, for the experiment #1, the value of 0.6 is set for the first criterion (cost) and 0.075 for weights of other criteria ($c{r}_2-c{r}_8$). It should be noted that the sum weights of all green criteria are equal to 1. For the experiment #9, the same weight (0.125) is considered for all green criteria. The used green criteria are divided into two categories, cost and benefit criteria. For the experiment #10, we devote 0 to weights of cost criteria ($c{r}_1,c{r}_7-c{r}_8$) and 0.2 to benefit criteria ($c{r}_2-c{r}_6$). For the experiment #11, the values of 0 and 0.33 are considered for weights of benefit criteria ($c{r}_2$–$c{r}_6$) and cost criteria ($c{r}_1,c{r}_7-c{r}_8$), respectively.

Table 9. Experiments for sensitivity analysis

Experiment	Definition	P1	P2	P3	P4	P5
1	$W_{c{r}_1}$=0.6,$W_{c{r}_2-c{r}_8}$=0.057	0.355	0.348	0.378	0.362	0.360
2	$W_{c{r}_2}$=0.6,$W_{c{r}_1,c{r}_3-c{r}_8}$=0.057	0.368	0.371	0.375	0.391	0.381
3	$W_{c{r}_3}$=0.6,$W_{c{r}_1-c{r}_2,c{r}_4-c{r}_8}$=0.057	0.362	0.351	0.389	0.380	0.377
4	$W_{c{r}_4}$=0.6,$W_{c{r}_1-c{r}_3,c{r}_5-c{r}_8}$=0.057	0.357	0.371	0.385	0.380	0.369
5	$W_{c{r}_5}$=0.6,$W_{c{r}_1-c{r}_4,c{r}_6-c{r}_8}$=0.057	0.358	0.360	0.370	0.366	0.361
6	$W_{c{r}_6}$=0.6,$W_{c{r}_1-c{r}_5,c{r}_7-c{r}_8}$=0.057	0.351	0.353	0.391	0.358	0.365
7	$W_{c{r}_7}$=0.6,$W_{c{r}_1-c{r}_6,c{r}_8}$=0.057	0.365	0.360	0.388	0.371	0.370
8	$W_{c{r}_8}$=0.6,$W_{c{r}_1-c{r}_7}$=0.057	0.366	0.351	0.381	0.375	0.371
9	$W_{c{r}_1-c{r}_8}$=0.125	0.332	0.330	0.364	0.341	0.338
10	$W_{c{r}_1,c{r}_7-c{r}_8}$=0, $W_{c{r}_2-c{r}_6}$=0.2	0.367	0.386	0.364	0.358	0.355
11	$W_{c{r}_1,c{r}_7-c{r}_8}$=0.33, $W_{c{r}_2-c{r}_6}$=0	0.361	0.364	0.375	0.380	0.378

As can be seen from Figure 2 and Table 9, ‘requiring ISO 14,000 certification for suppliers’ (P3) has the highest score in 8 out of the 11 experiments. In the remaining three experiments, P4 got the highest score for the two experiments and P2 for one experiment. Based on the results achieved, the ‘green procurement’ is the most significant criterion for evaluating GSDPs. The obtained results also reveal that the proposed fuzzy integrated MCDM approach for evaluating GSDPs is insensitive to the weights of criteria weights with P3 emerging as the winner in the majority of the experiments (8 out of 11).

Figure 1.. Flowchart of proposed approach

Figure 2. Sensitivity analysis results

5.2 Managerial implications

Several managerial implications for supply chain managers can be extracted from the obtained results of the proposed fuzzy MCDM approach. Employing the proposed approach help managers to effectively evaluate the performance of GSDPs or select the best program to execute. The achieved results of approach help managers to focus on GSDPs that provide greater supplier performance and higher supplier involvement. It also facilitates resource and investment allocations for managers. They could identify the poorly performing GSDPs and focus on searching for improvement opportunities for further development. The stability of managers’ decisions is tested by the sensitivity analysis. As mentioned earlier, the uncertainty is an unavoidable reality that exists in the green qualitative criteria for GSDPs evaluation. The proposed approach in this study addresses the uncertainty of GSDPs assessment by fuzzy logic.

6. Conclusions

In this study, an integrated fuzzy MCDM approach was developed to evaluate and prioritise the green supplier development programs using fuzzy DEMATEL and fuzzy AHP-TOPSIS. At first, we applied a fuzzy DEMATEL method to analyse the cause-and-effect relationships of green criteria and select the most important ones. Then, the fuzzy AHP-TOPSIS model was used to evaluate green supplier development programs based on green criteria. The proposed approach was utilised to evaluate GSDPs of painting industries. Based on the results achieved, ‘requiring ISO 14,000 certification for the supplier’ (P3) and ‘training suppliers on environmental issues’ (P4) were recognised as the best GSDPs for greening the suppliers. In addition, a sensitivity analysis was conducted to investigate the effect of green criteria on GSDPs selection. The achieved results of the analysis showed the ‘green procurement’ has the highest effect on prioritising the GSDPs.

The significant contributions and advantages of this study are summarised as (i) this approach considers the imprecise or vague judgements that lead to ambiguity in the evaluation process; (ii) the proposed approach determines the most significant green criteria to prioritise the GSDPs; (iii) the proposed approach contributes to the improvement of environmental performance of companies by selecting the best GSDPs for greening the suppliers. Several future research avenues can be recognised for other scholars. In this study, we developed an integrated fuzzy MCDM approach based on DEMATEL and AHP-TOPSIS for this problem, however there are other MCDM methods that can be used. The original TOPSIS method was used for ranking GSDPs in this study, however it would be substituted with new modified version of TOPSIS (Kuo 2017) for future studies. Also, applying the proposed approach in this study on freely available data for different companies is suggested for future study.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Ehsan Pourjavad

Ehsan Pourjavad is a Postdoctoral researcher at Department of Mathematical and Industrial Engineering at Polytechnique Montreal, Canada. He received a Ph.D. in Industrial Engineering from the University of Regina, Canada in 2018. His research interests include operation research, operation management, supply chain management. Ehsan has published more than 24 papers in international journals and conferences since 2011.

Arash Shahin

Arash Shahin is a Full-time Professor at the Department of Management and the Director of Quality Management Research Group at the University of Isfahan, Iran. He received his Ph.D. in Industrial Engineering–Quality Engineering from the Newcastle University, UK. His research interests include quality engineering and management, supply chain management, maintenance management and innovation management. Professor Shahin has been the author of 11 books, five book chapters and 450 published papers in national and international journals and conferences since 1994.