A fuzzy AHP approach to select suppliers in the Brazilian food supply chain

Ramos, Mayra Oliveira; Silva, Eliciane Maria da; Lima-Júnior, Francisco Rodrigues

doi:10.1590/0103-6513.20200013

Mayra Oliveira Ramos ^* * mayraolira@gmail.com

Universidade Metodista de Piracicaba, Santa Barbara d’Oeste, SP, Brasil

https://orcid.org/0000-0003-0369-4071

Eliciane Maria da Silva

Universidade Metodista de Piracicaba, Santa Barbara d’Oeste, SP, Brasil

https://orcid.org/0000-0002-9772-9265

Francisco Rodrigues Lima-Júnior

Universidade Tecnológica Federal do Paraná, Curitiba, PR, Brasil

https://orcid.org/0000-0001-7053-5519

* mayraolira@gmail.com

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Figure 1
The intersection between S₁ and S₂. Source: Based on Chang (1996) and Lima-Junior et al. (2014).

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Figure 2
Hierarchical structure of the first, second and third level criteria. GMP: Good manufacturing practices; HACCP: Hazard Analysis of Critical Control Point; QMS: Quality Management System; ES: Environmental System. Source: Elaborated by the authors.

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Table 1
Decision techniques for supplier selection models in the food industry.

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Table 2
Comparative linguistic scale used to assess the importance of the criteria and alternatives.

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Table 3
Expert linguistic judgments about the importance of first-level decision criteria.

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Table 4
Linguistic judgments about supplier performance for Conservation status (E1).

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Table 5
Fuzzy number values corresponding to first level criteria weights.

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Table 6
Fuzzy numbers values of the alternative ratings related to criterion E_1.

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Table 7
Normalized weight vectors of criteria and alternatives

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Table 8
Global performance of alternatives and outranking using min. operator

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Decision Methods	Authors
Fuzzy ANP and Goal Programming	Magdalena et al. (2020)
Intuitionistic Fuzzy AHP	Kaviani et al. (2020)
Fuzzy BWM and Piece wise linear values	Jafarzadeh Ghoushchi et al. (2019)
Fuzzy DEA	Hatami-Marbini et al. (2017)
Fuzzy Axiomatic Design	Kannan et al. (2015)
Fuzzy MOM	Hashim et al. (2017)
Fuzzy AHP	Lu et al. (2007); Zimmer et al. (2017); Azadnia et al. (2015); Khan et al. (2019)
Fuzzy AHP and VIKOR	Awasthi et al. (2018)
Fuzzy TOPSIS	Govindan et al. (2013); Kannan et al. (2014); Sen et al. (2016)
Fuzzy SWARA and MOORA	Mavi et al. (2017)
Fuzzy TOPSIS and CRITICS	Rostamzadeh et al. (2018)
Fuzzy Delphi DEMATEL, ANP and PROMETHEE	Govindan et al. (2017)
Fuzzy TOPSIS and SCOR	Lima-Junior & Carpinetti (2016)
SEM, Fuzzy AHP and MOLP	Jakhar (2015)
Fuzzy TOPSIS and MSGP	Liao (2012)
Taguchi loss function and Fuzzy AHP	Magdalena (2012)
Fuzzy AHP and TOPSIS	Rathore et al. (2017); Liu et al. (2019); Wang et al. (2020)
Fuzzy Delphi and AHP	Lin & Wu (2011)
Fuzzy AHP, TOPSIS and ELECTREE	Nakandala et al. (2017)
PROMETHEE	Araújo et al. (2015)
AHP	Freitas et al. (2020)

Linguistic Terms	Fuzzy Triangular Number
Equally Preferable (EP)	(1.00, 1.00, 3.00)
Slightly Preferable (SP)	(1.00, 3.00, 5.00)
Fairly Preferable (FP)	(3.00, 5.00, 7.00)
Extremely Preferable (EXP)	(5.00, 7.00, 9.00)
Absolutely Preferable (AP)	(7.00, 9.00, 9.00)

	C2	C3	C4
C1	SP	EXP	EP
C2		SP	SP
C3			EP

	S2	S3	S4
S1	1/SP	1/SP	SP
S2		1/SP	FP
S3			FP
S4

	C1	C2		C3	C4
C1	(1.00, 1.00, 1.00)	(1.00, 3.00, 5.00)		(5.00, 7.00, 9.00)	(3.00, 5.00, 7.00)
C2	(0.20, 0.33, 1.00)	(1.00, 1.00, 1.00)		(1.00, 3.00, 5.00)	(1.00, 3.00, 5.00)
C3	(0.11, 0.14, 0.20)	(0.20, 0.33, 1.00)		(1.00, 1.00, 1.00)	(1.00,1.00, 3.00)
C4	(0.14, 0.20, 0.33)	(0.20, 0.33, 1.00)		(0.33, 1.00, 1.00)	(1.00, 1.00, 1.00)
CCI			0.026

	S1	S2		S3	S4
S1	(1.00, 1.00, 1.00)	(0.20, 0.33, 1.00)		(0.20, 0.33, 1.00)	(1.00, 3.00, 5.00)
S2	(1.00, 3.00, 5.00)	(1.00, 1.00, 1.00)		(0.20, 0.33, 1.00)	(3.00, 5.00, 7.00)
S3	(1.00, 3.00, 5.00)	(1.00, 3.00, 5.00)		(1.00, 1.00, 1.00)	(3.00, 5.00, 7.00)
S4	(0.20, 0.33, 1.00)	(0.14, 0.20, 0.33)		(0.14, 0.20, 0.33)	(1.00, 1.00, 1.00)
CCI			0.026

First level criteria	Second level criteria	Third level criteria	$W'_{S 1}$	$W'_{S 2}$	$W'_{S 3}$	$W'_{S 4}$
$W'_{C 1}$ = 0.61	$W'_{D 1} = 0.45$	$W'_{E 1} = 0.44$	0.23	0.34	0.39	0.03
		$W'_{E 2} = 0.36$	0.03	0.52	0.19	0.24
		$W'_{E 3} = 0.19$	0.11	0.31	0.35	0.22
	$W'_{D 2} = 0.30$	$W'_{E 4} = 0.36$	0.06	0.29	0.37	0.27
		$W'_{E 5} = 0.44$	0.25	0.25	0.25	0.25
		$W'_{E 6} = 0.00$	0.07	0.09	0.34	0.49
	$W'_{D 3} = 0.25$	$W'_{E 7} = 0.44$	0.26	0.10	0.25	0.39
		$W'_{E 8} = 0.55$	0.25	0.11	0.32	0.31
		$W'_{E 9} = 0.00$	0.26	0.11	0.38	0.24
		$W'_{E 10} = 0.87$	0.28	0.36	0.25	0.10
	$W'_{D 4} = 0.00$	$W'_{E 11} = 0.12$	0.25	0.00	0.18	0.56
		$W'_{E 12} = 0.00$	0.25	0.15	0.32	0.26
		$W'_{E 13} = 0.00$	0.25	0.25	0.25	0.25
$W'_{C 2}$ = 0.33			0.23	0.13	0.30	0.32
$W'_{C 3}$ = 0.07	$W'_{D 5} = 0.33$	$W'_{E 14} = 0.28$	0.25	0.25	0.25	0.25
		$W'_{E 15} = 0.43$	0.18	0.39	0.35	0.08
		$W'_{E 16} = 0.20$	0.25	0.12	0.32	0.31
		$W'_{E 17} = 0.08$	0.27	0.21	0.34	0.17
	$W'_{D 6} = 0.33$	$W'_{E 18} = 0.70$	0.11	0.37	0.30	0.22
	$W'_{D 6} = 0.33$	$W'_{E 19} = 0.30$	0.25	0.25	0.25	0.25
	$W'_{D 7} = 0.33$	$W'_{E 20} = 0.50$	0.24	0.30	0.30	0.14
	$W'_{D 7} = 0.33$	$W'_{E 21} = 0.50$	0.25	0.25	0.25	0.25
$W'_{C 4}$ = 0.00	$W'_{D 8} = 0.70$		0.20	0.26	0.26	0.27
	$W'_{D 9} = 0.29$	$W'_{E 22} = 0.00$	0.25	0.25	0.25	0.25
	$W'_{D 9} = 0.29$	$W'_{E 23} = 0.00$	0.22	0.34	0.40	0.03

Alternative	Normalized global scores	Rank
S1	0.19	4^th
S2	0.27	2^nd
S3	0.30	1^st
S4	0.26	3^rd

μ_{S_{2}} (d) = \{\begin{matrix} 1, i f m_{2} \geq m_{1} \\ 0, i f l_{1} \geq u_{2} \frac{l_{1} - u_{2}}{(m_{2} - u_{2}) - (m_{1} - l_{1})}, \\ o t h e r w i s e \end{matrix}\}

d^{'} (C_{1}) = V [(S_{C 1} \geq S_{C 2}) a n d (S_{C 1} \geq S_{C 3}) a n d (S_{C 1} \geq S_{C 4}) a n d (S_{C 1} \geq S_{C 5})] = m i n (1.00, 1.00, 1.00) = 1.00

d^{'} (C_{2}) = V [(S_{C 2} \geq S_{C 1}) a n d (S_{C 2} \geq S_{C 3}) a n d (S_{C 2} \geq S_{C 4}) a n d (S_{C 2} \geq S_{C 5})] = m i n (0.54, 1.00, 1.00) = 0.54

d^{'} (C_{3}) = V [(S_{C 3} \geq S_{C 1}) a n d (S_{C 3} \geq S_{C 2}) a n d (S_{C 3} \geq S_{C 4}) a n d (S_{C 3} \geq S_{C 5})] = m i n (0.11, 0.60, 0.99) = 0.11

d^{'} (C_{4}) = V [(S_{C 4} \geq S_{C 1}) a n d (S_{C 4} \geq S_{C 2}) a n d (S_{C 4} \geq S_{C 3}) a n d (S_{C 4} \geq S_{C 5})] = m i n (0.00, 0.44, 1.00) = 0.00

d^{'} (S_{1}) = V [(S_{S 1} \geq S_{S 2}) a n d (S_{S 1} \geq S_{S 3}) a n d (S_{S 1} \geq S_{S 4}) a n d (S_{S 1} \geq S_{S 5})] = m i n (0.71, 0.60, 1.00) = 0.60

d^{'} (S_{2}) = V [(S_{S 2} \geq S_{S 1}) a n d (S_{S 2} \geq S_{S 3}) a n d (S_{S 2} \geq S_{S 4}) a n d (S_{S 2} \geq S_{S 5})] = m i n (1.00, 0.89, 1.00) = 0.89

d^{'} (S_{3}) = V [(S_{S 3} \geq S_{S 1}) a n d (S_{S 3} \geq S_{S 2}) a n d (S_{S 3} \geq S_{S 4}) a n d (S_{S 3} \geq S_{S 5})] = m i n (1.00, 1.00, 1.00) = 1.00

d^{'} (S_{4}) = V [(S_{S 4} \geq S_{S 1}) a n d (S_{S 4} \geq S_{S 2}) a n d (S_{S 4} \geq S_{S 3}) a n d (S_{S 4} \geq S_{S 5})] = m i n (0.53, 0.17, 0.09) = 0.09

\begin{array}{l} D (S_{1}) = (d' (S_{1 E 1}) \times d' (E_{1}) \times d' (D_{1}) \times d' (C_{1})) + \\ ((d^{'} (S_{1 E 2}) \times d^{'} (E_{2}) \times d^{'} (D_{1}) \times d^{'} (C_{1})) + \\ ((d' (S_{1 E 3}) \times d' (E_{3}) \times d' (D_{1}) \times d' (C_{1})) + ... + \\ (d' (S_{1 E 23}) \times d' (E_{23}) \times d' (D_{9}) \times d' (C_{4})) = 0.19 \end{array}

[1] AHP: Analytical Hierarchy Process; ANP: Analytic Network Process; BWM: Best-Worst Method; CRITICS: Criteria Importance Through Inter-criteria Correlation; DEA: Data Envelopment Analysis; DEMATEL: Decision making trial and evaluation laboratory; MOLP: Multi-objective Linear Programming; MOM: Mean of Maximum; MOORA: Multi-Objective Optimization based on Ratio Analysis; MSGP: Multi-Segment Goal Programming; PROMETHEE: Preference Ranking Organization Method for Enrichment Evaluations; SCOR: Supply Chain Operation Reference; SEM: Supplier Risk Management; TOPSIS: Technique for Ordering Preference by Similarity to Ideal Solution; SWARA: The Step-wise Weight Assessment Ratio Analysis; VIKOR: Multicriteria Optimization and Compromise Solution; ELECTREE: Elimination Et Choix Traduisant la REalité. Source: Elaborated by the authors.

A fuzzy AHP approach to select suppliers in the Brazilian food supply chain

Abstract