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

Figures & data

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

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)

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)

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

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)

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 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

Figure 1.. Flowchart of proposed approach

Figure 2. Sensitivity analysis results

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