A framework for sustainable supplier selection with transportation criteria

Figures & data

Figure 1. Framework of sustainable supplier selection.

Table 1. Linguistic terms and corresponding fuzzy scales (Kabir and Hasin 2012; Şen and Çinar 2010).

Linguistic Term	Fuzzy Number	TFN $\left(l,m,u\right)$
Extreme unimportance	${\tilde{9}}^{-1}$	$\left(1/9,1/9,1/9\right)$
Intermediate values between ${\tilde{7}}^{-1}$ and ${\tilde{9}}^{-1}$	${\tilde{8}}^{-1}$	$\left(1/7,1/8,1/7\right)$
Intermediate values between	${\tilde{7}}^{-1}$	$\left(1/8,1/7,1/6\right)$
Intermediate values between ${\tilde{5}}^{-1}$ and ${\tilde{7}}^{-1}$	${\tilde{6}}^{-1}$	$\left(1/7,1/6,1/5\right)$
Essential unimportance	${\tilde{5}}^{-1}$	$\left(1/6,1/5,1/4\right)$
Intermediate values between ${\tilde{3}}^{-1}$ and ${\tilde{5}}^{-1}$	${\tilde{4}}^{-1}$	$\left(1/5,1/4,1/3\right)$
Moderate unimportance	${\tilde{3}}^{-1}$	$\left(1/4,1/3,1/2\right)$
Intermediate values between ${\tilde{1}}^{-1}$ and ${\tilde{3}}^{-1}$	${\tilde{2}}^{-1}$	$\left(1/3,1/2,1/1\right)$
Equally importance	$\tilde{1}$	$\left(1,1,1\right)$
Intermediate values between $\tilde{1}$ and $\tilde{3}$	$\tilde{2}$	$\left(1,2,3\right)$
Moderate importance	$\tilde{3}$	$\left(2,3,4\right)$
Intermediate values between $\tilde{3}$ and $\tilde{5}$	$\tilde{4}$	$\left(3,4,5\right)$
Essential importance	$\tilde{5}$	$\left(4,5,6\right)$
Intermediate values between $\tilde{5}$ and $\tilde{7}$	$\tilde{6}$	$\left(5,6,7\right)$
Very vital importance	$\tilde{7}$	$\left(6,7,8\right)$
Intermediate values between $\tilde{7}$ and $\tilde{9}$	$\tilde{8}$	$\left(7,8,9\right)$
Extreme importance	$\tilde{9}$	$\left(9,9,9\right)$

Table 2. RI for different sizes of matrix (Mani, Agarwal, and Sharma 2014).

N	2	3	4	5	6	7	8	9	10
RI	0	0.58	0.9	1.12	1.24	1.32	1.41	1.45	1.51

Figure 2. The intersection between ${\tilde{S}}_i$ and ${\tilde{S}}_j$.

Table 3. Types of generalized criteria of preference function (Modified from Gervásio and Da Silva 2012).

Type	Generalized criterion	Definition	Parameter to fix
Type-I: usual criterion		$P\left(x\right)=\left\{\begin{array}{c}0,x\le 0\\ 1,x>0\end{array}\right.$	-
Type-II: U shaped quasi criterion		$P\left(x\right)=\left\{\begin{array}{c}0,x\le a\\ 1,x>a\end{array}\right.$	$a$
Type-III: V-shaped linear preference criterion		$P\left(x\right)=\left\{\begin{array}{c}0,x\le 0\\ x/b,0<x\le b\\ 1,x>b\end{array}\right.$	$b$
Type-IV: levelled criterion		$P\left(x\right)=\left\{\begin{array}{c}0,x\le a\\ 1/2,a<x\le b\\ 1,x>b\end{array}\right.$	$a,b$
Type-V: criterion having indifference area and linear preference		$P\left(x\right)=\left\{\begin{array}{c}0,x\le a\\ \frac{x-a}{b-a},a<x\le b\\ 1,x>b\end{array}\right.$	$a,b$
Type-VI: Gaussian criterion		$P\left(x\right)=\left\{\begin{array}{c}0,x\le 0\\ 1-e^{\frac{-x^2}{2c^2}},x>0\end{array}\right.$	c

Figure 3. Decision hierarchy model (Source: Amindoust et al. 2012; Dobos and Vörösmarty 2014; Gold and Awasthi 2015; Hashemi, Karimi, and Tavana 2015; Mani, Agarwal, and Sharma 2014; Rao et al. 2017a, 2017c; Zimmer, Fröhling, and Schultmann 2016.

Table 4. Symbols and qualitative scales.

Scale		Symbol
Very Low	Very Bad	VB
Low	Bad	B
Moderate	Average	A
High	Good	G
Very High	Very Good	VG

Table 5. Alternative suppliers’ performance with respect to criteria.

No.	Sub-criteria	Type	Alternate Suppliers
			S1	S2	S3	S4	S5
1	PP	Min	$ 4110	$ 3827	$ 3950	$ 3898	$ 4019
2	PR	Max	Very High	Moderate	Moderate	Moderate	Moderate
3	QP	Max	Moderate	High	Very High	High	High
4	FL	Max	Average	Very Good	Good	Good	Very Bad
5	PC	Max	Good	Good	Very Good	Good	Average
6	DT	Min	Average	Good	Good	Good	Average
7	LT	Min	7 Days	5 Days	7 Days	7 Days	10 Days
8	EM	Max	Very Good	Good	Average	Average	Average
9	GL	Max	Average	Average	Average	Average	Average
10	WM	Max	Very Good	Good	Good	Average	Average
11	EC	Min	Very Low	Low	Moderate	Moderate	Moderate
12	OHS	Max	Good	Very Good	Very Good	Average	Very Good
13	IE	Max	Average	Very Good	Good	Average	Good
14	RS	Max	Average	Good	Good	Average	Good
15	IS	Max	No	No	No	No	No
16	TC	Min	Moderate	Low	Low	Low	High
17	TT	Min	5 Hour	4 Hour	3 Hour	3 Hour	8 Hour
18	DS	Min	18 Km	60 Km	40 Km	20 Km	247 Km
19	TA	Max	No	No	No	No	No
20	RF	Min	Moderate	Low	Low	Low	Very High

Table 6. Pairwise comparison matrix and weights with respect to major criteria.

Goal	ECO	ENV	SOC	TRANS	Weight (Wi)
ECO	$\left(1,1,1\right)$	$\left(2,3,4\right)$	$\left(3,4,5\right)$	$\left(5,6,7\right)$	0.521
ENV	$\left(1/4,1/3,1/2\right)$	$\left(1,1,1\right)$	$\left(1,2,3\right)$	$\left(3,4,5\right)$	0.277
SOC	$\left(1/4,1/3,1/2\right)$	$\left(1/4,1/3,1/2\right)$	$\left(1,1,1\right)$	$\left(1,1,1\right)$	0.109
TRANS	$\left(1/4,1/3,1/2\right)$	$\left(1/4,1/3,1/2\right)$	$\left(1/4,1/3,1/2\right)$	$\left(1,1,1\right)$	0.093

Table 7. Weight distribution of all Sub-criteria.

Criteria		Sub-Criteria
Factors	Local Weights	Factors	Local Weights	Global Weight
Economic	0.521	PP	0.305	0.159
		PR	0.200	0.104
		QP	0.183	0.095
		FL	0.089	0.047
		PC	0.108	0.056
		DT	0.077	0.040
		LT	0.038	0.020
Environmental	0.277	EM	0.377	0.104
		GL	0.322	0.089
		WM	0.214	0.059
		EC	0.087	0.024
Social	0.109	OHS	0.447	0.049
		IE	0.352	0.038
		RS	0.144	0.016
		IS	0.057	0.006
Transportation	0.093	TC	0.354	0.033
		TT	0.303	0.028
		DS	0.18	0.017
		TA	0.119	0.011
		RF	0.044	0.004

Figure A1. Stainable supplier selection using Visual PROMETHEE. a,PROMETHEE I partial ranking. b) PROMETHEE II complete ranking.

Table 8. The PROMITHEE II complete ranking.

Alternatives	Phi+	Phi-	Phi	Rank
Supplier 2	0.3443	0.0128	0.3316	1
Supplier 3	0.1780	0.1512	0.0270	2
Supplier 4	0.1722	0.1799	−0.0078	3
Supplier 1	0.1674	0.2232	−0.0558	4
Supplier 5	0.0521	0.3471	−0.2950	5

Figure A2. PROMETHEE ranking.

Figure A3. PROMETHEE network of supplier selection.

Figure 4. GAIA plane of supplier selection.

Figure 5. Sensitivity analysis using walking weight.

Table A1. Pairwise comparison matrix according to major criteria (defuzzified).

Goal	ECO	ENV	SOC	TRANS
ECO	1.00	3.00	4.00	6.00
ENV	0.35	1.00	2.00	4.00
SOC	0.26	0.56	1.00	1.00
TRANS	0.17	0.26	1.00	1.00

Table A2. Fuzzy synthetic extent values (S_i) with respect to major criteria.

SECO	0.42	0.53	0.63
SENV	0.19	0.28	0.37
SSOC	0.08	0.10	0.15
STRANS	0.07	0.09	0.12

Table A3. Integral values (I_i) with respect to major criteria.

IECO	0.525
IENV	0.279
ISOC	0.110
ITRANS	0.094

Ilgin, M. A. 2017. “An Integrated Methodology for the Used Product Selection Problem Faced by Third-Party Reverse Logistics Providers.” International Journal of Sustainable Engineering 10 (6): 399–410. doi:10.1080/19397038.2017.1317873.

 Web of Science ®Google Scholar

Wang, Y. M., Y. Luo, and Z. Hua. 2008. “On the Extent Analysis Method for Fuzzy AHP and Its Applications.” European Journal of Operational Research 186: 735–747. doi:10.1016/j.ejor.2007.01.050.

 Web of Science ®Google Scholar

Luthra, S., K. Govindan, D. Kannan, S. K. Mangla, and C. P. Garg. 2017. “An Integrated Framework for Sustainable Supplier Selection and Evaluation in Supply Chains.” Journal of Cleaner Production 140: 1686–1698. doi:10.1016/j.jclepro.2016.09.078.

 Web of Science ®Google Scholar

Chang, D.-Y. 1996. “Applications of the Extent Analysis Method on Fuzzy AHP.” European Journal of Operational Research 95: 649–655. doi:10.1016/0377-2217(95)00300-2.

 Web of Science ®Google Scholar

Amindoust, A., S. Ahmed, A. Saghafinia, and A. Bahreininejad. 2012. “Sustainable Supplier Selection: A Ranking Model Based on Fuzzy Inference System.” Applied Soft Computing 12: 1668–1677. doi:10.1016/j.asoc.2012.01.023.

 Web of Science ®Google Scholar

Gold, S., and A. Awasthi. 2015. “Sustainable Global Supplier Selection Extended Towards Sustainability Risks from (1+N)Th Tier Suppliers Using Fuzzy AHP Based Approach.” IFAC-PapersOnLine 28: 966–971. doi:10.1016/j.ifacol.2015.06.208.

 Google Scholar

Gopal, P. R. C., and J. Thakkar. 2015. “Development of Composite Sustainable Supply Chain Performance Index for the Automobile Industry.” International Journal of Sustainable Engineering 8 (6): 366–385. doi:10.1080/19397038.2014.947392.

 Web of Science ®Google Scholar

Sangwan, K. S., and A. Jindal. 2013. “An Integrated Fuzzy Multi-Criteria Evaluation of Lithium-Ion Battery Recycling Processes.” International Journal of Sustainable Engineering 6 (4): 359–371. doi:10.1080/19397038.2012.735717.

 Google Scholar