Multi-criteria Decision Making Using Hybrid methods for Supplier Selection in the Clothing Industry

Lahdhiri, Mourad; Babay, Amel; Jmali, Mohamed

doi:10.2478/ftee-2022-0004

Figures & Tables

Ratio of coincidence of supplier rankings between the AHP-TOPSIS, AHP-WSM, and AHP-WPM models and the choice of supply chain manager

MCDM application interface for supplier selection

Normalised matrix

	C1	C2	C3	….	Cm
A1	Y11	Y12	Y13	…	Y1m
A2	Y11	Y22	Y23	…	Y2m
A3	Y31	Y32	Y33	…	Y3m
..	…	…	…	…	…
An	Yn1	Yn2	Yn3	…	Ynm

Investigation results for the 10 experts

Investigation	First 4 criteria	Weight	Investigation	First 4 criteria	Weight
Expert 1	Quality	0.06	Expert 6	Compliance to deadlines	0.06
	Cost	0.10		Cost	0.11
	Compliance to deadlines	0.32		Quality	0.29
	Compliance to quantity	0.53		Compliance to quantity	0.54
Expert 2	Cost	0.50	Expert 7	Ease of production	0.07
	Guarantee	0.17		Social relationship	0.12
	Ease of production	0.05		Quantity	0.26
	Compliance to deadlines	0.27		Management and organisation	0.56
Expert 3	Compliance to quantity	0.07	Expert 8	Ease of production	0.06
	Quality	0.15		Financial situation	0.10
	Cost	0.29		Compliance to quantity	0.32
	Compliance to deadlines	0.49		Quality	0.53
Expert 4	Development	0.55	Expert 9	Quality	0.55
	Geographical location	0.26		Compliance to quantity	0.26
	Cost	0.14		Compliance to deadlines	0.14
	Quality	0.05		Guarantee	0.05
Expert 5	Guarantee	0.06	Expert 10	Environment	0.06
	Financial situation	0.10		Financial situation	0.10
	Cost	0.32		Compliance to quantity	0.32
	Quality	0.53		Compliance to de+adlines	0.53

ANOVA for the three MCDM methods

Source of variation	SS	Df	MS	F	P-value	F crit
Between groups	0.143	2	0.071	15.131	1.431E-06	3.073
Within groups	0.555	117	0.004
Total	0.699	119

Pair-wise comparison matrix of criterion

Criteria	C1	C2	C3	….	Cn
C1	1	W₁/W₂	W₁/W₃	….	W₁/W_n
C2	W₂/W₁	1	W₂/W₃	….	W₂/W_n
C3	W₃/W₁	W₃/W₂	1	….	W₃/W_n
..	…	….	…	1	…
Cn	W_n/W₁	W_n/W₂	W_n/W₃	W_n/W..	1

Separation measures

	Cost	Quality	Compliance to quantity	Compliance to deadlines	Si+	Si−
S1	0.02	0.10	0.13	0.33	0.01	0.05
S2	0.07	0.10	0.13	0.33	0.05	0.03
S3	0.01	0.06	0.13	0.32	0.03	0.05

Normalisation Matrix

Criteria	C1	C2	C3	….	Cn
C1	X₁₁	X₁₂	X₁₃	…	X_1n
C2	X₁₁	X₂₂	X₂₃	…	X_2n
C3	X₃₁	X₃₂	X₃₃	…	X_3n
..	…	…	…	…	…
Cn	X_n1	X_n2	X_n3	…	X_nn

Pair-wise comparison matrix

Criteria	Cost piece	Quality	Compliance to quantity	Compliance to deadlines
Cost/piece	1	0.33	0.2	0.14
Quality	3	1	0.5	0.33
Compliance to quantity	5	2	1	0.2
Compliance to deadlines	7	3	5	1

Weighted normalised decision matrix

	C1	C2	C3	….	Cm
A1	Y₁₁ ^W₁	Y₁₂^W₂	Y₁₃^W₃	…	Y_1m^W_m
A2	Y₁₁^W₁	Y₂₂^W₂	Y₂₃^W₃	…	Y_2m^W_m
A3	Y₃₁^W₁	Y₃₂^W₂	Y₃₃^W₃	…	Y_3m^W_m
..	…	…	…	…	…
An	Y_n1^W₁	Y_n2^W₂	Y_n3^W₃	…	Y_nm^W_m

Normalisation matrix

	Cost	Quality	Compliance to quantity	Compliance to deadlines
S1	0.31	0.64	0.58	0.58
S2	0.93	0.64	0.58	0.58
S3	0.19	0.43	0.58	0.57

Relative closeness and rank of suppliers

	Si+	Si−	Ri	Rank
S1	0.01	0.05	0.87	1
S2	0.05	0.03	0.39	3
S3	0.03	0.05	0.61	2

AHP-WSM Normalised matrix

	Cost	Quality	Compliance to quantity	Compliance to deadlines
S1	0.63	1.00	1	1.00
S2	0.21	1.00	1	1.00
S3	1.00	0.67	1	0.98

Decision matrix

	Cost	Quality	Compliance to quantity	Compliance to deadlines
S1	0.197	3	1	0.96
S2	0.6	3	1	0.96
S3	0.125	2	1	0,94

AHP-WPM suppliers rank

	Score	Suppliers rank
S1	0.97	1
S2	0.94	2
S3	0.93	3

Normalization Matrix

Criteria	Cost / piece	Quality	Compliance to quantity	Compliance to deadlines	Average vector: W
Cost/piece	0.06	0.05	0.03	0.09	0.07
Quality	0.19	0.16	0.07	0.20	0.15
Compliance to quantity	0.31	0.32	0.15	0.12	0.22
Compliance to deadlines	0.44	0.47	0.75	0.60	0.56

Decision Matrix

	C1	C2	C3	….	Cm
A1	X₁₁	X₁₂	X₁₃	…	X_1n
A2	X₁₁	X₂₂	X₂₃	…	X_2n
A3	X₃₁	X₃₂	X₃₃	…	X_3n
..	…	…	…	…	…
An	X_n1	X_n2	X_n3	…	X_nn

AHP-WSM Weighted normalised matrix

	Cost	Quality	Compliance to quantity	Compliance to deadlines
S1	0.63	1.00	1	1.00
S2	0.21	1.00	1	1.00
S3	1.00	0.67	1	0.98

List of criteria

N°	Criteria	N°	Criteria
1	Cost	11	Ease of production
2	Quality	12	Environment
3	Compliance to quantity	13	Free sampling
4	Compliance to deadlines	14	Minimum production capacity
5	Social relationship	15	Technical capacity
6	Guarantee	16	Purchase volume in the past
7	Financial situation	17	Process conformity
8	Development	18	Certification
9	Geographical location	19	Control of operations
10	Management and organisation	20	Training and support

Saaty’s 1–9 scale for pair-wise comparisons

Numerical rate	Verbal judgment of preference
1	Equal importance
3	Weak importance of one over another
5	Essential or strong importance
7	Demonstrated importance
9	Absolute importance
2, 4, 6, 8	Intermediate values between the two adjacent judgments

Positive ideal and negative ideal solution

	Cost	Quality	Compliance to quantity	Compliance to deadlines
S1	0.02	0.10	0.13	0.33
S2	0.07	0.10	0.13	0.33
S3	0.01	0.06	0.13	0.32
V+	0.01	0.10	0.13	0.33
V−	0.07	0.06	0.13	0.32

Statistical study of each method pair

Method pair	σ xy	σ x	σ y	R xy	standard deviation
AHP-TOPSIS and AHP-WSM	0.0015	0.11	0.05	0.29	0.089
AHP-TOPSIS and AHP-WPM	0.00094	0.1	0.018	0.47	0.08
AHP-WSM and AHP-WPM	0.00014	0.048	0..018	0.16	0.03

AHP-WSM Suppliers rank

	Score	Supplier’s rank
S1	0.97	1
S2	0.94	2
S3	0.93	3

AHP-WPM weighted normalised matrix

	Cost	Quality	Compliance to quantity	Compliance to deadlines
S1	0.63	1.00	1	1.00
S2	0.21	1.00	1	1,00
S3	1.00	0.67	1	0.98

Weighted normalised matrix

	Cost	Quality	Compliance to quantity	Compliance to deadlines
S1	0.02	0.10	0.13	0.33
S2	0.07	0.10	0.13	0.33
S3	0.01	0.06	0.13	0.32

Test evaluation (part 1)

Purchase order number	Item	Supplier selected by company	Supplier selected by AHP-TOPSIS	Rank of supplier	Supplier selected by AHP-WSM	Rank of supplier	Supplier selected by AHP-WPM	Rank of supplier
1	Stopper	FX	FX	1	FY	2	FY	2
2	Label kontakt	AY	AY	1	AB	4	AB	4
3	Label brice	FS	FS	1	FR	3	FR	2
4	Fringe	XA	XA	1	XR	2	XA	1
5	Yarn 100% cotton	ZD	ZA	2	ZD	1	ZA	2
6	Elastic	CA	CA	1	CX	2	CA	1
7	Zipper L18 cm	DZ	DR	1	DR	1	DR	1
8	Button 2 HOLE 25	IL	IJ	2	IL	1	IJ	2
9	Ribbon	WK	WK	1	WK	1	WK	1
10	Buckle	HI	HX	3	HX	2	HX	2
11	Hangtag –vms	X1	X1	1	X1	1	X1	1
12	Rivet 84061	B1	B1	1	B2	2	B2	2
13	Rivet 84425	C1	C1	1	C1	1	C1	1
14	Button 11631	CF	CF	1	CR	2	CF	1
15	Scotch	Y1	Y1	1	Y1	1	Y1	1
16	Button 4 Hole 28″	A1	A1	1	A1	1	A1	1
17	Zip 14.5cm	G1	G1	1	G1	1	G1	1
18	Buckle 1cm	G1	G1	1	G1	1	G1	1
19	Confection sticker -	H1	H1	1	H1	1	H1	1
20	Bias Tape 100 %	W1	W1	1	W1	1	W1	1
21	Leather10895	U1	U1	1	U1	1	U1	1
22	Zip L16.5cm	G1	G1	1	G1	1	G1	1
23	Yarn Tex 60 Dual Duty 5000mts-fil	T1	T1	1	T1	1	T1	1
24	Sangle nastro spinato 30/2 PXT mm.60	R1	R1	1	O1	2	R1	1
25	Sticker dim 100*150	BR	BR	1	BR	1	BR	1
26	Plastic cover	FR	FR	1	V	1	FR	1
27	Hang Tag Retro	BG	BG	1	BG	1	BG	1
28	Ribbon polyamide	FH	FH	1	FH	1	FH	1
29	Button tack metal	FT	FT	1	FT	1	FT	1
30	Button jeans 20mm	XS	XS	1	XS	1	XS	1
31	Rivet laiton de 2 cm	XS	XS	1	XS	1	V	1
32	Leather belt	GH	GH	1	GH	1	GH	1
33	Yarn col 439 Super Twist N°20 20gr/fil	XR	XR	1	XR	1	XR	1
34	Strap ecru	XY	XY	1	XY	1	XY	1
35	Buckle overalls	BJ	BJ	1	BJ	1	BJ	1
36	Zip L43cm RGKB	BN	BN	1	BN	1	BN	1
37	Confection sticker-Care Label	VH	VH	1	VH	1	VH	1
38	Finishing sticker -VMS	VY	VY	1	VY	1	VY	1
39	Finishing sticker women	SML	SML	1	SML	1	SML	1
40	Metal overalls buckle accessory Internal diameter 3.8 cm White	SF	SF	1	SF	1	SF	1

Multi-criteria Decision Making Using Hybrid methods for Supplier Selection in the Clothing Industry

Figures & Tables

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Normalised matrix

Investigation results for the 10 experts

ANOVA for the three MCDM methods

Pair-wise comparison matrix of criterion

Separation measures

Normalisation Matrix

Pair-wise comparison matrix

Weighted normalised decision matrix

Normalisation matrix

Relative closeness and rank of suppliers

AHP-WSM Normalised matrix

Decision matrix

AHP-WPM suppliers rank

Normalization Matrix

Decision Matrix

AHP-WSM Weighted normalised matrix

List of criteria

Saaty’s 1–9 scale for pair-wise comparisons

Positive ideal and negative ideal solution

Statistical study of each method pair

AHP-WSM Suppliers rank

AHP-WPM weighted normalised matrix

Weighted normalised matrix

Test evaluation (part 1)

Paradigm

My account

	C1	C2	C3	….	Cm
A1	Y11	Y12	Y13	…	Y1m
A2	Y11	Y22	Y23	…	Y2m
A3	Y31	Y32	Y33	…	Y3m
..	…	…	…	…	…
An	Yn1	Yn2	Yn3	…	Ynm

	C1	C2	C3	….	Cm
A1	Y11	Y12	Y13	…	Y1m
A2	Y11	Y22	Y23	…	Y2m
A3	Y31	Y32	Y33	…	Y3m
..	…	…	…	…	…
An	Yn1	Yn2	Yn3	…	Ynm

	C1	C2	C3	….	Cm
A1	Y11	Y12	Y13	…	Y1m
A2	Y11	Y22	Y23	…	Y2m
A3	Y31	Y32	Y33	…	Y3m
..	…	…	…	…	…
An	Yn1	Yn2	Yn3	…	Ynm