A Fuzzy Group Decision-making-based Method for Green Supplier Selection and Order Allocation

doi:10.16182/j.issn1004731x.joss.23-FZ0808E

Abstract

Abstract:

With the intensity of market competitiveness, the worsening of the global environment, and the improvement of public concern about environmental protection, the issue of green purchasing has received considerable attention. The vast majority of existing studies on green purchasing have concentrated on supplier selection with green criteria, so as to realize sustainable operations, whereas it is more feasible and economical for businesses to obtain the proper products from adaptable and suitable suppliers at the right times, rates, and volumes, which is referred to as supplier selection and order allocation. To resolve the aforementioned two crucial challenges, we propose a group decision-making method within an ambiguous context. A fuzzy ranking approach based on the technique for order of preference by similarity to ideal solution and analytic hierarchy process (TOPSIS-AHP) is addressed. The proposed solution enables each of the green and classical criteria to be given a flexible preference under the organization's strategy. Supplier ranks are utilized in a bi-objective optimization model to allocate orders, where the procurement performance is maximized while the entire procurement cost is minimized. The findings show that the proposed method is capable of assessing the performance of providers and optimizing the distribution of orders among candidate suppliers.

Key words: supplier selection, order allocation, fuzzy group decision-making, technique for order of preference by similarity to ideal solution and analytic hierarchy process(TOPSIS-AHP), bi-objective optimization

CLC Number:

TP391.9

Liu Lu, Li Wenxin, Song Xiao, Sun Bingli, Gong Guanghong. A Fuzzy Group Decision-making-based Method for Green Supplier Selection and Order Allocation[J]. Journal of System Simulation, 2023, 35(10): 2133-2149.

Figures/Tables 29

Fig. 1

Table 1

Table 2

Table 3

Table 4

Table 5

Table 6

Table 9

Table 7

Table 8

Table 10

Table 11

Table 12

Differences between four fuzzy TOPSIS methods

	Case A	Case B	Case C	Case D
Aggregated fuzzy rating	$x i j = 1 N ∑ n = 1 N x i j n y i j = 1 N ∑ n = 1 N y i j n z i j = 1 N ∑ n = 1 N z i j n$	$x i j = 1 N ∑ n = 1 N x i j n y i j = 1 N ∑ n = 1 N y i j n z i j = 1 N ∑ n = 1 N z i j n$	$x i j = m i n n x i j n y i j = 1 N ∑ n = 1 N y i j n z i j = m a x n z i j n$	$x i j = m i n n x i j n y i j = 1 N ∑ n = 1 N y i j n z i j = m a x n z i j n$
Aggregated fuzzy weight	$α j 1 = 1 N ∑ n = 1 n α j 1 n α j 2 = 1 N ∑ n = 1 n α j 2 n α j 3 = 1 N ∑ n = 1 n α j 3 n$	$α j 1 = 1 N ∑ n = 1 n α j 1 n α j 2 = 1 N ∑ n = 1 n α j 2 n α j 3 = 1 N ∑ n = 1 n α j 3 n$	$α j 1 = m i n n α j 1 n α j 2 = 1 N ∑ n = 1 N α j 2 n α j 3 = m a x n α j 3 n$	$α j 1 = m i n n α j 1 n α j 2 = 1 N ∑ n = 1 N α j 2 n α j 3 = m a x n α j 3 n$
FPIS	$u ˜ j + = (1,1, 1)$	$u ˜ j + = m a x i (u i j 1, u i j 2, u i j 3)$	$u ˜ j + = (1,1, 1)$	$u ˜ j + = m a x i (u i j 1, u i j 2, u i j 3)$
FNIS	$u ˜ j - = (0,0, 0)$	$u ˜ j - = m i n i (u i j 1, u i j 2, u i j 3)$	$u ˜ j - = (0,0, 0)$	$u ˜ j - = m i n i (u i j 1, u i j 2, u i j 3)$

Table 12

Table 13

Fig. 2

Fig. 3

Table 14

Optimal TVP values in Case A with various criteria weights βG/βT under different weight factors ω1/ω2

$ω 1 / ω 2$	$β G / β T$
$ω 1 / ω 2$	0.2/0.8	0.4/0.6	0.6/0.4	0.8/0.2
0.1/0.9	4 280.660	4 350.212	4 419.763	4 489.315
0.3/0.7	4 322.240	4 383.435	4 444.630	4 505.825
0.5/0.5	4 387.232	4 411.947	4 474.198	4 536.449
0.7/0.3	4 416.676	4 440.459	4 498.614	4 541.553
0.9/0.1	4 416.676	4 464.100	4 511.525	4 558.949

Table 14

Table 17

Optimal TVP values in Case D with various criteria weights βG/βT under different weight factors ω1/ω2

$ω 1 / ω 2$	$β G / β T$
$ω 1 / ω 2$	0.2/0.8	0.4/0.6	0.6/0.4	0.8/0.2
0.1/0.9	4 751.198	4 524.612	4 298.025	4 056.929
0.3/0.7	4 964.222	4 713.060	4 398.345	4 186.639
0.5/0.5	5 070.365	4 795.543	4 478.617	4 205.839
0.7/0.3	5 070.365	4 795.543	4 520.720	4 229.935
0.9/0.1	5 070.365	4 795.543	4 520.720	4 245.898

Table 17

Fig. 4

Fig. 5

Table 15

Optimal TVP values in Case B with various criteria weights βG/βT under different weight factors ω1/ω2

$ω 1 / ω 2$	$β G / β T$
$ω 1 / ω 2$	0.2/0.8	0.4/0.6	0.6/0.4	0.8/0.2
0.1/0.9	4 703.152	4 474.735	4 246.319	4 020.128
0.3/0.7	4 906.480	4 664.431	4 363.439	4 147.502
0.5/0.5	4 995.489	4 738.221	4 441.903	4 201.934
0.7/0.3	4 995.489	4 738.221	4 480.953	4 223.685
0.9/0.1	4 995.489	4 738.221	4 480.953	4 223.685

Table 15

Table 16

Optimal TVP values in Case C with various criteria weights βG/βT under different weight factors ω1/ω2

$ω 1 / ω 2$	$β G / β T$
$ω 1 / ω 2$	0.2/0.8	0.4/0.6	0.6/0.4	0.8/0.2
0.1/0.9	4 074.115	4 149.426	4 224.738	4 300.049
0.3/0.7	4 107.040	4 176.199	4 241.639	4 311.608
0.5/0.5	4 158.304	4 176.199	4 245.359	4 335.254
0.7/0.3	4 184.698	4 219.687	4 281.071	4 335.254
0.9/0.1	4 184.698	4 240.025	4 295.353	4 345.910

Table 16

Table 18

Closeness coefficients of SC in Case A

Supplier	$β G / β T$
Supplier	0.2/0.8	0.4/0.6	0.6/0.4	0.8/0.2
Sum	2.354 4	2.423 8	2.493 2	2.562 6
1	0.561 6	0.580 2	0.598 8	0.617 4
2	0.690 6	0.683 2	0.675 8	0.668 4
3	0.618 8	0.639 6	0.660 4	0.681 2
4	0.483 4	0.520 8	0.558 2	0.595 6

Table 18

Table 19

Closeness coefficients of SC in Case D

Supplier	$β G / β T$
Supplier	0.2/0.8	0.4/0.6	0.6/0.4	0.8/0.2
Sum	2.302 8	2.257 6	2.212 4	2.167 2
1	0.518 8	0.488 6	0.458 4	0.428 2
2	0.896 2	0.828 4	0.760 6	0.692 8
3	0.665 8	0.666 6	0.667 4	0.668 2
4	0.222 0	0.274 0	0.326 0	0.378 0

Table 19

Table 20

Optimal TCP and TVP values with βG/βT = 0.2/0.8

$ω 1 / ω 2$	Case A		Case B		Case C		Case D
$ω 1 / ω 2$	TCP	TVP	TCP	TVP	TCP	TVP	TCP	TVP
0.1/0.9	205 230.8	4 280.660	205 529.2	4 703.152	205 230.8	4 074.115	205 529.2	4 751.198
0.2/0.8	205 449.2	4 315.470	206 462.2	4 795.312	205 449.2	4 101.700	205 529.2	4 751.198
0.3/0.7	205 529.2	4 322.240	208 012.2	4 906.480	205 529.2	4 107.040	208 012.2	4 964.222
0.4/0.6	205 529.2	4 322.240	208 012.2	4 906.480	205 529.2	4 107.040	210 665.4	5 070.365
0.5/0.5	208 012.2	4 387.232	210 665.4	4 995.489	208 012.2	4 158.304	210 665.4	5 070.365
0.6/0.4	208 012.2	4 387.232	210 665.4	4 995.489	208 012.2	4 158.304	210 665.4	5 070.365
0.7/0.3	210 665.4	4 416.676	210 665.4	4 995.489	210 665.4	4 184.698	210 665.4	5 070.365
0.8/0.2	210 665.4	4 416.676	210 665.4	4 995.489	210 665.4	4 184.698	210 665.4	5 070.365
0.9/0.1	210 665.4	4 416.676	210 665.4	4 995.489	210 665.4	4 184.698	210 665.4	5 070.365

Table 20

Table 23

Optimal TCP and TVP values with βG/βT=0.8/0.2

$ω 1 / ω 2$	Case A		Case B		Case C		Case D
$ω 1 / ω 2$	TCP	TVP	TCP	TVP	TCP	TVP	TCP	TVP
0.1/0.9	205 230.8	4 489.315	205 538.2	4 020.128	205 230.8	4 300.049	205 449.2	4 056.929
0.2/0.8	205 230.8	4 489.315	206 462.2	4 147.502	205 230.8	4 300.049	206 462.2	4 186.639
0.3/0.7	205 529.2	4 505.825	206 462.2	4 147.502	205 449.2	4 311.608	206 462.2	4 186.639
0.4/0.6	205 538.2	4 506.209	206 982.2	4 169.102	205 529.2	4 314.518	206 982.2	4 205.839
0.5/0.5	206 462.2	4 536.449	208 532.2	4 201.934	206 462.2	4 335.254	206 982.2	4 205.839
0.6/0.4	206 462.2	4 536.449	208 532.2	4 201.934	206 462.2	4 335.254	208 532.2	4 229.935
0.7/0.3	206 982.2	4 541.553	210 665.4	4 223.685	206 462.2	4 335.254	208 532.2	4 229.935
0.8/0.2	208 532.2	4 552.017	210 665.4	4 223.685	206 982.2	4 338.710	210 665.4	4 245.898
0.9/0.1	210 665.4	4 558.949	210 665.4	4 223.685	208 532.2	4 345.910	210 665.4	4 245.898

Table 23

Fig. 6

Table 21

Optimal TCP and TVP values with βG/βT = 0.4/0.6

$ω 1 / ω 2$	Case A		Case B		Case C		Case D
$ω 1 / ω 2$	TCP	TVP	TCP	TVP	TCP	TVP	TCP	TVP
0.1/0.9	205 230.8	4 350.212	205 529.2	4 474.735	205 230.8	4 149.426	205 529.2	4 524.612
0.2/0.8	205 449.2	4 377.495	206 462.2	4 579.375	205 449.2	4 171.669	205 529.2	4 524.612
0.3/0.7	205 529.2	4 383.435	208 012.2	4 664.431	205 529.2	4 176.199	208 012.2	4 713.060
0.4/0.6	205 529.2	4 383.435	208 012.2	4 664.431	205 529.2	4 176.199	208 012.2	4 713.060
0.5/0.5	206 462.2	4 411.947	210 665.4	4 738.221	205 529.2	4 176.199	210 665.4	4 795.543
0.6/0.4	208 012.2	4 440.459	210 665.4	4 738.221	208 012.2	4 219.687	210 665.4	4 795.543
0.7/0.3	208 012.2	4 440.459	210 665.4	4 738.221	208 012.2	4 219.687	210 665.4	4 795.543
0.8/0.2	210 665.4	4 464.100	210 665.4	4 738.221	210 665.4	4 240.025	210 665.4	4 795.543
0.9/0.1	210 665.4	4 464.100	210 665.4	4 738.221	210 665.4	4 240.025	210 665.4	4 795.543

Table 21

Table 22

Optimal TCP and TVP values with βG/βT = 0.6/0.4

$ω 1 / ω 2$	Case A		Case B		Case C		Case D
$ω 1 / ω 2$	TCP	TVP	TCP	TVP	TCP	TVP	TCP	TVP
0.1/0.9	205 230.8	4 419.763	205 529.2	4 246.319	205 230.8	4 224.738	205 529.2	4 298.025
0.2/0.8	205 449.2	4 439.520	206 462.2	4 363.439	205 230.8	4 224.738	206 462.2	4 398.345
0.3/0.7	205 529.2	4 444.630	206 462.2	4 363.439	205 449.2	4 241.639	206 462.2	4 398.345
0.4/0.6	205 529.2	4 444.630	208 532.2	4 441.903	205 529.2	4 245.359	208 012.2	4 461.897
0.5/0.5	206 462.2	4 474.198	208 532.2	4 441.903	205 529.2	4 245.359	208 532.2	4 478.617
0.6/0.4	206 462.2	4 474.198	210 665.4	4 480.953	206 462.2	4 264.271	210 665.4	4 520.720
0.7/0.3	208 532.2	4 498.614	210 665.4	4 480.953	208 012.2	4 281.071	210 665.4	4 520.720
0.8/0.2	210 665.4	4 511.525	210 665.4	4 480.953	208 532.2	4 284.223	210 665.4	4 520.720
0.9/0.1	210 665.4	4 511.525	210 665.4	4 480.953	210 665.4	4 295.353	210 665.4	4 520.720

Table 22

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Linguistic variable	TFN
Very low (VL)	(0, 0, 0.1)
Low (L)	(0, 0.1, 0.3)
Medium low (ML)	(0.1, 0.3, 0.5)
Medium (M)	(0.3, 0.5, 0.7)
Medium high (MH)	(0.5, 0.7, 0.9)
High (H)	(0.7, 0.9, 1.0)
Very high (VH)	(0.9, 1.0, 1.0)

Linguistic variable	TFN
Very poor (VP)	(0, 0, 1)
Poor (P)	(0, 1, 3)
Medium poor (MP)	(1, 3, 5)
Fair (F)	(3, 5, 7)
Medium good (MG)	(5, 7, 9)
Good (G)	(7, 9, 10)
Very good (VG)	(9, 10, 10)

Intensity of importance	Definition
1	Equally important
3	Moderately important
5	Very important
7	Strongly important
9	Extremely important
2, 4, 6, 8	Intermediate values

Supplier	1st phase	2nd phase	3rd phase	4th phase
1	2 792	2 923	2 718	2 953
2	2 602	2 589	2 655	2 990
3	2 645	2 615	2 962	2 719
4	2 730	2 585	2 715	2 555

Phase	Demand	Holding cost	Shortage cost	Available Suppliers
1	1 750	4	8	S1, S2, S3, S4
2	1 800	4	9	S1, S2, S3
3	1 765	3	8	S2, S3
4	1 630	5	8	S1, S2, S4