Dataset Table RBSM

42 Numerical Examples (Paper, Synthetic data, and Real case)

1.        Data sourced from 32 sets of journals can be seen in Table 1:

 

Table 1

 

No

Reference

Name

Size TP

Optimal

Solution

Matrix

1

(Ramadan & Ramadan, 2012)

N01

3x3

5600

[Cij]3x3 = [32 40 120; 60 68 104; 200 80 60]

[Si]3x1 = [20 30 45]

[Dj]1x3 = [30 35 30]

2

(Samuel, 2012)

N02

3x4

28

[Cij]3x4 = [1 2 3 4; 4 3 2 0; 0 2 2 1]

[Si]3x1 = [6 8 10]

[Dj]1x3 = [4 6 8 6]

3

(Karagul & Sahin, 2020)

N03

5x5

1102

Cij]5x5 = [73 40 9 79 20; 62 93 96 8 13; 96 65 80 50 65; 57 58 29 12 87; 56 23 87 18 12]

[Si]5x1 = [8 7 9 3 5]

[Dj]1x5 = [6 8 10 4 4]

4

(Kaur et al., 2018)

N04

3x5

1580

[Cij]3x5 = [6 4 4 7 5; 5 6 7 4 8; 3 4 6 3 4]
[Si]3x1 = [100, 125, 175]
[Dj]1x5 = [60, 80, 85, 105, 70]

5

(Hussein & Shiker, 2020)

N05

4x4

410

[Cij]4x4 = [7 5 9 11; 4 3 8 6; 3 8 10 5; 2 6 7 3]
[Si]4x1 = [30, 25, 20, 15]
[Dj]1x4 = [30, 30, 20, 10]

6

(Wireko et al., 2025)

N06

3x4

7750

[Cij]3x4 = [10 8 4 3;12 14 20 2;6 9 23 25]

[Si]3x1 = [500 400 300]

[Dj]1x3 = [250 350 600 150]

7

(Das et al., 2014)

N07

3x4

1160

[Cij]3x4 = [6 1 9 3; 11 5 2 8; 10 12 4 7]
[Si]3x1 = [70, 55, 90]
[Dj]1x4 = [85, 35, 50, 45]

8

(Murugesan & Esakkiammal, 2020)

N09

4x4

111

[Cij]4x4 = [4 6 5 2; 6 4 1 4; 5 2 3 1; 4 6 7 8]
[Si]4x1 = [6 10 12 14]
[Dj]1x4 = [9 16 10 7]

9

(Amaliah et al., 2019)

N10

3x4

910

[Cij]3x4 = [20 2 20 11; 24 7 9 20; 8 14 16 18]
[Si]3x1 = [30, 50, 20]
[Dj]1x4 = [10, 30, 30, 30]

10

(Amaliah et al., 2019)

N11

3x4

2460

[Cij]3x4 = [10 2 20 22; 12 7 9 40; 4 14 16 32]
[Si]3x1 = [60, 100, 40]
[Dj]1x4 = [20, 60, 60, 60]

11

(Amaliah et al., 2019)

N12

3x3

425

[Cij]3x3 = [15 7 25; 8 12 14; 17 19 21]
[Si]3x1 = [12 17 7]
[Dj]1x3 = [12 10 14]

12

(Juman & Hoque, 2015)

N13

3x3

4525

[Cij]3x3 = [6 8 10; 7 11 11; 4 5 12]
[Si]3x1 = [150, 175, 275]
[Dj]1x3 = [200, 100, 300]

13

(Juman & Hoque, 2015)

N14

3x4

920

Cij]3x4 = [4 6 8 8; 6 8 6 7; 5 7 6 8]

[Si]3x1 = [40, 60, 50]

[Dj]1x4 = [20, 30, 50, 50]

14

(Ahmed et al., 2016)

N15

3x4

156

[Cij]3x4 = [4 6 9 5; 2 6 4 1; 5 7 2 9]

[Si]3x1 = [16 12 15]

[Di]1x4 = [12 14 9 8]

15

(Amreen, 2024)

N16

3x4

1510

[Cij]3x4 = [22 17 25 15; 13 10 16 20; 16 19 9 5]

[Si]3x1 = [30 50 50]

[Di]1x4 = [30 30 50 20]

16

(Gupta, 2020)

N17

3x4

743

[Cij]3x4 = [19 30 50 10; 70 30 40 60; 40 8 70 20]

[Si]3x1 = [7 9 18]

[Di]1x4 = [5 8 7 14]

17

(Goyal, 1984)

N18

3x3

1650

[Cij]3x3 = [6 10 14; 12 19 21; 15 14 17 ]

[Si]3x1 = [50 50 50]

[Di]1x3 = [30 40 55]

18

(Amreen, 2024)

N21

3x3

4205

[Cij]3x3 = [135 71 260; 81 126 144; 170 189 201]

[Si]3x1 = [12 17 7]

[Di]1x3 = [12 10 14]

19

(Rafi & Islam, 2020)

N22

3x4

12075

[Cij]3x4 = [11 13 17 14; 16 18 14 10; 21 24 13 10]
[Si]3x1 = [250 300 400]
[Dj]1x4 = [200 225 275 250]

20

(Kaur et al., 2018)

N23

3x4

23

[Cij]3x4 = [7 2 3 7; 1 5 4 5; 7 2 4 5]

[Si]3x1 = [2 1 3]

[Dj]1x4 = [2 1 1 2]

21

(Juman & Hoque, 2015)

N24

3x4

3460

[Cij]3x4 = [20 22 17 4; 24 37 9 7; 32 37 20 15]
[Si]3x1 = [120, 70, 50]
[Dj]1x4 = [60, 40, 30, 110]

22

(Juman & Hoque, 2015)

N25

3x4

809

[Cij]3x4 = [19 30 50 12; 70 30 40 60; 40 10 60 20]
[Si]3x1 = [7 10 18]
[Dj]1x4 = [5 7 8 15]

23

(G.Patel et al., 2017)

N26

4x5

490

[Cij]4x5 = [20 4 6 8 9; 4 10 8 18 8; 9 11 20 40 6; 7 6 9 14 16]
[Si]4x1 = [20 30 15 13]
[Dj]1x5 = [40 6 8 18 6]

24

(Korukoǧlu & Balli, 2011)

N27

5x5

59356

[Cij]5x5=[46 74 9 28 99; 12 75 6 36 48; 35 199 4 5 71; 61 81 44 88 9; 85 60 14 25 79] [Si]5x1=[461 277 356 488 393]

[Dj]1x5=[278 60 461 116 1060]

25

(M Selim Reza et al., 2019)

N28

3x4

2090

[Cij]3x4=[3 1 7 4;2 6 5 9;8 3 3 2]

[Si]3x1=[300 400 270]

[Dj]1x4=[250 350 290 450]

26

(Kousalya1 & Malarvizhi, 2016)

N29

3x4

3857

[Cij]3x4 = [15 1 42 33; 80 42 26 81; 90 40 66 60]
[Si]3x1 = [23 44 33]
[Dj]1x4 = [23 31 16 30]

27

(Ahmed et al., 2015)

N30

3x3

465

[Cij]3x3 = [13 21 14; 8 12 21; 15 17 19]

[Si]3x1 = [13 20 5]

[Di]1x3 = [12 15 11]

28

(Kirca et al., 1990)

N31

3x4

1480

[Cij]3x4 = [15 27 13 19; 18 21 24 14; 21 15 16 17]
[Si]3x1 = [40 40 20]
[Dj]1x4 = [30 20 30 20]

29

(Babu et al., 2020)

N32

4x5

1780

[Cij]4x5 = [4 4 9 10 13;7 9 8 10 4;9 3 7 10 6;11 4 10 6 9]
[Si]4x1 = [100 90 80 70]
[Dj]1x5 = [60 40 90 70 80]

30

(Amreen & B, 2024)

N33

3x3

1250

[Cij]3x3 = [3 3 5;

6 5 4;

6 10 7]
[Si]3x1 = [90 80 100]
[Dj]1x3 = [70 120 80]

31

(Sahito, 2021)

N34

4x5

510

[Cij]4x5 = [7 6 4 5 9; 8 5 6 7 8; 6 8 9 6 5; 5 7 7 8 6]
[Si]4x1 = [40 30 20 10]
[Dj]1x5 = [30 30 15 20 5]

32

(Amaliah et al., 2022)

N35

3x4

280

[Cij]3x4 = [1 6 5 9;3 2 4 15;8 9 3 10]

[Si]3x1 = [20 25 15]

[Di]1x4 = [15 15 10 20]

 

2.        Data sourced from 5 sets of synthesis can be seen in Table 2:

 

Table 2

No

Name

Size TP

Optimal

Solution

Matrix

1

S1

5x5

18855

[Cij]5x5 = [27 27 9 33 9;

36 15 33 30 15;

18 21 27 36 33;

33 36 21 24 9;

27 9 9 21 15]
[Si]5x1 = [150 240 135 300 285]
[Dj]1x5 = [270 195 210 270 165]

2

S2

5x5

2790

[Cij]5x5 = [80 80 20 100 20;

110 40 100 90 40;

50 60 80 110 100;

100 110 60 70 20;

80 20 20 60 40]
[Si]5x1 = [400 700 350 900 850]
[Dj]1x5 = [800 550 600 800 450]

3

S3

11x12

1044180

[Cij]11x12 = [1 52 53 54 55 56 57 58 59 60 61 12;

63 14 65 66 67 68 69 70 71 72 73 74;

75 76 27 78 79 80 81 82 83 84 85 86;

87 88 89 40 91 92 93 94 95 96 97 98;

99 100 101 102 53 104 105 106 107 108 109 110;

111 112 113 114 115 66 117 118 119 120 121 122;

123 124 125 126 127 128 79 130 131 132 133 134;

135 136 137 138 139 140 141 92 143 144 145 146;

147 148 149 150 151 152 153 154 105 156 157 158;

159 160 161 162 163 164 165 166 167 118 169 170;

171 172 173 174 175 176 177 178 179 180 131 182]
[Si]11x1 = [50 60 70 80 90 100 110 120 130 140 310]
[Dj]1x12 = [50 60 70 80 90 100 110 120 130 140 150 160]

4

S4

11x12

92212

[Cij]11x12 = [13 35 30 36 35 30 30 33 31 36 15 39;

39 30 25 32 28 13 11 32 34 27 14 25;

12 39 15 11 13 30 30 31 12 25 32 13;

33 10 14 38 38 12 12 15 13 15 37 14;

37 11 25 10 14 35 29 14 33 14 37 37;

79 88 70 70 83 71 92 93 77 95 82 77;

80 98 98 84 73 91 88 86 81 78 73 73;

83 94 77 94 76 91 81 70 85 91 99 84;

78 75 78 81 79 81 81 98 83 95 88 77;

99 81 79 87 89 81 76 74 76 78 89 94;

91 83 80 92 97 97 80 89 92 71 83 99]
[Si]11x1 = [200 106 139 137 249 171 172 113 230 241 199]
[Dj]1x12 = [315 309 41 43 110 162 274 184 70 201 125 123]

5

S5

11x12

116020

[Cij]11x12 = [1 52 53 54 55 56 57 58 59 60 61 12;

63 14 65 66 67 68 69 70 71 72 73 74;

75 76 27 78 79 80 81 82 83 84 85 86;

87 88 89 40 91 92 93 94 95 96 97 98;

99 100 101 102 53 104 105 106 107 108 109 110;

111 112 113 114 115 66 117 118 119 120 121 122;

123 124 125 126 127 128 79 130 131 132 133 134;

135 136 137 138 139 140 141 92 143 144 145 146;

147 148 149 150 151 152 153 154 105 156 157 158;

159 160 161 162 163 164 165 166 167 118 169 170;

171 172 173 174 175 176 177 178 179 180 131 182]
[Si]11x1 = [50 60 70 80 90 100 110 120 130 140 310]
[Dj]1x12 = [50 60 70 80 90 100 110 120 130 140 150 160]

 

3.        Data sourced from 5 sets of Real case XYZ Company can be seen in Table 3:

Table 3

NO

Data Real

1

[Cij]2x94 = [22 38 32 17 31 15 23 25 25 20 33 30 18 12 23 18 26 20 15 18 15 25 28 23 16 18 21 28 20 20 25 18 18 18 25 27 21 25 23 26 33 38 29 17 38 17 39 39 22 22 35 25 28 31 33 20 36 31 23 27 25 35 30 31 28 27 28 30 27 54 43 52 56 46 59 53 40 58 44 51 40 43 45 49 48 57 46 46 60 61 66 59 55 56; 26 41 36 21 35 20 27 30 28 25 38 34 23 15 20 15 23 18 14 17 13 23 25 25 17 23 23 33 18 19 28 23 20 18 25 31 20 25 25 23 39 36 28 12 33 14 38 38 20 28 33 28 26 28 31 17 38 30 30 25 22 33 26 29 31 34 28 33 31 49 38 49 52 43 56 49 36 54 40 46 36 39 41 46 44 54 41 43 57 57 62 55 52 51]

[Si]2x1 = [308252 138801]

[Di]1x94 = [3852 4759 1312 3451 7537 2827 3878 15224 2530 5690 2494 2383 32901 7314 2486 0 249 2735 498 1989 4475 6091 373 5492 17978 4305 23799 1597 2773 2556 48509 3279 4183 1303 795 4024 1381 2597 1666 4848 125 0 0 10192 0 4475 3356 0 2611 2984 1368 0 1119 249 0 9447 2984 2362 125 2984 26599 746 249 0 14055 1437 2283 556 812 5786 2034 5911 5026 524 1133 464 1792 1330 1457 1668 3827 7947 297 759 9074 1436 864 2217 1160 519 4166 614 19405 30392]

 

2

[Cij]2x94 = [22 38 32 17 31 15 23 25 25 20 33 30 18 12 23 18 26 20 15 18 15 25 28 23 16 18 21 28 20 20 25 18 18 18 25 27 21 25 23 26 33 38 29 17 38 17 39 39 22 22 35 25 28 31 33 20 36 31 23 27 25 35 30 31 28 27 28 30 27 54 43 52 56 46 59 53 40 58 44 51 40 43 45 49 48 57 46 46 60 61 66 59 55 56; 26 41 36 21 35 20 27 30 28 25 38 34 23 15 20 15 23 18 14 17 13 23 25 25 17 23 23 33 18 19 28 23 20 18 25 31 20 25 25 23 39 36 28 12 33 14 38 38 20 28 33 28 26 28 31 17 38 30 30 25 22 33 26 29 31 34 28 33 31 49 38 49 52 43 56 49 36 54 40 46 36 39 41 46 44 54 41 43 57 57 62 55 52 51]

[Si]2x1 = [341015 138738]

[Di]1x94 = [3332 3976 1252 3494 9871 3027 5214 20029 2437 5584 2615 2184 39154 6641 2735 0 249 2984 746 2238 4848 6837 373 4677 17447 4487 24968 1804 3137 2538 50087 3445 4375 1444 919 4024 1389 2960 1660 5221 125 0 0 11063 0 4972 3729 125 2859 5096 1492 0 871 249 125 10129 3232 2735 249 12554 28961 746 125 0 12664 1382 2405 479 724 6258 1924 5195 5217 536 924 385 2053 1111 1340 1712 3630 8300 321 679 8954 1385 862 2372 1225 480 4369 556 20814 27658]

 

 

 

3

[Cij]2x94 = [22 38 32 17 31 15 23 25 25 20 33 30 18 12 23 18 26 20 15 18 15 25 28 23 16 18 21 28 20 20 25 18 18 18 25 27 21 25 23 26 33 38 29 17 38 17 39 39 22 22 35 25 28 31 33 20 36 31 23 27 25 35 30 31 28 27 28 30 27 54 43 52 56 46 59 53 40 58 44 51 40 43 45 49 48 57 46 46 60 61 66 59 55 56; 26 41 36 21 35 20 27 30 28 25 38 34 23 15 20 15 23 18 14 17 13 23 25 25 17 23 23 33 18 19 28 23 20 18 25 31 20 25 25 23 39 36 28 12 33 14 38 38 20 28 33 28 26 28 31 17 38 30 30 25 22 33 26 29 31 34 28 33 31 49 38 49 52 43 56 49 36 54 40 46 36 39 41 46 44 54 41 43 57 57 62 55 52 51]

[Si]2x1 = [280110 138801]

[Di]1x94 = [3300 4628 1250 2852 8202 2916 3912 16157 2695 5526 2699 2271 41855 7074 1616 0 125 1741 373 1243 2859 3854 249 5151 17117 4368 24291 1560 2679 2952 42223 3585 4182 1423 838 3282 1491 2324 1553 3108 125 0 125 6464 0 2859 2238 0 1616 2921 871 0 498 125 0 6091 1865 1616 125 2921 17029 498 249 0 13885 1516 2480 410 799 6616 1980 5900 4721 584 1032 419 1702 1290 1536 1725 3455 7792 341 632 9100 1269 897 2333 1296 452 3957 487 20317 32228]

 

4

[Cij]2x94 = [22 38 32 17 31 15 23 25 25 20 33 30 18 12 23 18 26 20 15 18 15 25 28 23 16 18 21 28 20 20 25 18 18 18 25 27 21 25 23 26 33 38 29 17 38 17 39 39 22 22 35 25 28 31 33 20 36 31 23 27 25 35 30 31 28 27 28 30 27 54 43 52 56 46 59 53 40 58 44 51 40 43 45 49 48 57 46 46 60 61 66 59 55 56; 26 41 36 21 35 20 27 30 28 25 38 34 23 15 20 15 23 18 14 17 13 23 25 25 17 23 23 33 18 19 28 23 20 18 25 31 20 25 25 23 39 36 28 12 33 14 38 38 20 28 33 28 26 28 31 17 38 30 30 25 22 33 26 29 31 34 28 33 31 49 38 49 52 43 56 49 36 54 40 46 36 39 41 46 44 54 41 43 57 57 62 55 52 51]

[Si]2x1 = [350910 142165]

[Di]1x94 = [3512 4300 1291 3477 9394 3031 4597 22500 1776 5384 2824 2530 42638 7341 2735 0 249 2984 746 2238 4848 6837 3737 5858 16806 4210 24717 1715 2549 2520 50440 3185 4359 1437 914 3120 1551 2109 1578 5345 125 0 0 11187 0 4972 3729 125 2859 8452 1492 0 871 249 125 10317 3232 2735 249 8452 29085 746 373 0 13607 1421 2068 554 877 6207 1844 6259 4824 610 1175 403 1840 1110 1389 1739 3546 8113 348 753 8366 1329 970 2121 1181 530 3778 497 19912 34947]

 

5

[Cij]2x94 = [22 38 32 17 31 15 23 25 25 20 33 30 18 12 23 18 26 20 15 18 15 25 28 23 16 18 21 28 20 20 25 18 18 18 25 27 21 25 23 26 33 38 29 17 38 17 39 39 22 22 35 25 28 31 33 20 36 31 23 27 25 35 30 31 28 27 28 30 27 54 43 52 56 46 59 53 40 58 44 51 40 43 45 49 48 57 46 46 60 61 66 59 55 56; 26 41 36 21 35 20 27 30 28 25 38 34 23 15 20 15 23 18 14 17 13 23 25 25 17 23 23 33 18 19 28 23 20 18 25 31 20 25 25 23 39 36 28 12 33 14 38 38 20 28 33 28 26 28 31 17 38 30 30 25 22 33 26 29 31 34 28 33 31 49 38 49 52 43 56 49 36 54 40 46 36 39 41 46 44 54 41 43 57 57 62 55 52 51]

[Si]2x1 = [359746 138801]

[Di]1x94 = [3269 4456 1277 2783 8888 3679 4621 18426 2745 5940 2408 2437 48268 5585 3108 0 249 3356 746 2486 5594 7707 373 4944 19086 3758 27005 1884 3139 2275 48013 3411 4479 1386 911 3405 1402 3198 1657 5967 249 0 0 12678 0 5594 4226 125 3232 7955 1616 0 995 373 125 11560 3605 3108 249 7955 32938 871 249 0 13500 1377 2189 589 752 5974 1588 6085 4578 512 1056 452 2240 1138 1268 1818 3634 8274 300 703 8162 1308 901 2438 1088 454 4199 613 19521 29812]

 

 

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