Abstract
For remanufacturing or recycling companies, a reverse supply chain is of prime importance since it facilitates in recovering parts and materials from end-of-life products. In reverse supply chains, selective separation of desired parts and materials from returned products is achieved by means of disassembly which is a process of systematic separation of an assembly into its components, subassemblies or other groupings. Due to its high productivity and suitability for automation, disassembly line is the most efficient layout for product recovery operations. A disassembly line must be balanced to optimize the use of resources (viz., labor, money and time). In this paper, we consider a sequence-dependent disassembly line balancing problem (SDDLBP) with multiple objectives that requires the assignment of disassembly tasks to a set of ordered disassembly workstations while satisfying the disassembly precedence constraints and optimizing the effectiveness of several measures considering sequence dependent time increments. A hybrid algorithm that combines a genetic algorithm with a variable neighborhood search method (VNSGA) is proposed to solve the SDDLBP. The performance of VNSGA was thoroughly investigated using numerous data instances that have been gathered and adapted from the disassembly and the assembly line balancing literature. Using the data instances, the performance of VNSGA was compared with the best known metaheuristic methods reported in the literature. The tests demonstrated the superiority of the proposed method among all the methods considered.
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Appendix
Appendix
Arcus1
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 1 | 17 | 10 | 1 | 80 | 19 | 0 | 12 | 28 | 0 | 41 | 37 | 0 | 56 |
2 | 1 | 26 | 11 | 0 | 13 | 20 | 0 | 96 | 29 | 1 | 83 | 38 | 0 | 96 |
3 | 0 | 12 | 12 | 0 | 48 | 21 | 0 | 70 | 30 | 1 | 87 | 39 | 0 | 28 |
4 | 0 | 83 | 13 | 1 | 59 | 22 | 0 | 95 | 31 | 1 | 96 | 40 | 0 | 22 |
5 | 0 | 35 | 14 | 1 | 94 | 23 | 1 | 85 | 32 | 0 | 8 | 41 | 0 | 36 |
6 | 0 | 62 | 15 | 1 | 52 | 24 | 0 | 79 | 33 | 1 | 66 | 42 | 0 | 30 |
7 | 0 | 7 | 16 | 0 | 36 | 25 | 0 | 7 | 34 | 1 | 65 | 43 | 0 | 2 |
8 | 0 | 91 | 17 | 0 | 65 | 26 | 1 | 100 | 35 | 0 | 49 | 44 | 0 | 96 |
9 | 0 | 21 | 18 | 0 | 69 | 27 | 0 | 22 | 36 | 0 | 41 | 45 | 0 | 1 |
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
46 | 0 | 12 | 55 | 0 | 86 | 64 | 0 | 16 | 73 | 0 | 63 | 82 | 0 | 6 |
47 | 0 | 54 | 56 | 0 | 35 | 65 | 0 | 39 | 74 | 0 | 12 | 83 | 1 | 89 |
48 | 0 | 7 | 57 | 0 | 57 | 66 | 0 | 12 | 75 | 0 | 95 | |||
49 | 0 | 36 | 58 | 1 | 81 | 67 | 1 | 17 | 76 | 1 | 3 | |||
50 | 1 | 95 | 59 | 0 | 27 | 68 | 0 | 70 | 77 | 0 | 62 | |||
51 | 0 | 67 | 60 | 0 | 44 | 69 | 0 | 79 | 78 | 1 | 20 | |||
52 | 0 | 76 | 61 | 0 | 85 | 70 | 0 | 64 | 79 | 0 | 12 | |||
53 | 1 | 66 | 62 | 1 | 52 | 71 | 1 | 84 | 80 | 1 | 69 | |||
54 | 0 | 32 | 63 | 1 | 46 | 72 | 0 | 31 | 81 | 0 | 71 |
Arcus2
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 1 | 70 | 13 | 0 | 22 | 25 | 0 | 76 | 37 | 1 | 80 | 49 | 0 | 2 |
2 | 0 | 5 | 14 | 1 | 42 | 26 | 1 | 97 | 38 | 0 | 6 | 50 | 1 | 61 |
3 | 0 | 78 | 15 | 1 | 93 | 27 | 0 | 30 | 39 | 1 | 91 | 51 | 0 | 20 |
4 | 0 | 86 | 16 | 1 | 64 | 28 | 0 | 89 | 40 | 0 | 1 | 52 | 0 | 17 |
5 | 1 | 62 | 17 | 0 | 35 | 29 | 0 | 63 | 41 | 0 | 97 | 53 | 0 | 69 |
6 | 0 | 45 | 18 | 0 | 36 | 30 | 0 | 66 | 42 | 1 | 57 | 54 | 0 | 50 |
7 | 0 | 95 | 19 | 0 | 2 | 31 | 0 | 69 | 43 | 1 | 39 | 55 | 1 | 11 |
8 | 0 | 70 | 20 | 0 | 72 | 32 | 0 | 91 | 44 | 0 | 76 | 56 | 0 | 100 |
9 | 0 | 44 | 21 | 0 | 36 | 33 | 0 | 40 | 45 | 1 | 10 | 57 | 0 | 51 |
10 | 0 | 68 | 22 | 0 | 38 | 34 | 1 | 88 | 46 | 0 | 39 | 58 | 0 | 9 |
11 | 1 | 87 | 23 | 0 | 23 | 35 | 0 | 54 | 47 | 0 | 69 | 59 | 0 | 11 |
12 | 0 | 71 | 24 | 1 | 34 | 36 | 0 | 76 | 48 | 1 | 73 | 60 | 1 | 18 |
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
61 | 1 | 77 | 73 | 1 | 50 | 85 | 1 | 35 | 97 | 0 | 89 | 109 | 0 | 59 |
62 | 0 | 78 | 74 | 0 | 97 | 86 | 1 | 87 | 98 | 0 | 62 | 110 | 0 | 93 |
63 | 0 | 84 | 75 | 0 | 58 | 87 | 1 | 86 | 99 | 0 | 30 | 111 | 0 | 2 |
64 | 0 | 39 | 76 | 0 | 73 | 88 | 1 | 70 | 100 | 0 | 15 | |||
65 | 1 | 95 | 77 | 0 | 57 | 89 | 0 | 41 | 101 | 1 | 68 | |||
66 | 1 | 67 | 78 | 0 | 18 | 90 | 1 | 34 | 102 | 0 | 75 | |||
67 | 0 | 59 | 79 | 0 | 83 | 91 | 0 | 80 | 103 | 1 | 54 | |||
68 | 0 | 84 | 80 | 0 | 63 | 92 | 0 | 5 | 104 | 1 | 5 | |||
69 | 0 | 20 | 81 | 1 | 17 | 93 | 1 | 70 | 105 | 0 | 8 | |||
70 | 1 | 46 | 82 | 0 | 41 | 94 | 0 | 93 | 106 | 0 | 3 | |||
71 | 0 | 47 | 83 | 0 | 89 | 95 | 1 | 65 | 107 | 0 | 45 | |||
72 | 0 | 45 | 84 | 0 | 93 | 96 | 0 | 54 | 108 | 0 | 26 |
Barthol2
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 1 | 44 | 16 | 0 | 36 | 31 | 0 | 22 | 46 | 0 | 50 | 61 | 0 | 58 |
2 | 1 | 80 | 17 | 1 | 48 | 32 | 0 | 41 | 47 | 0 | 85 | 62 | 0 | 59 |
3 | 0 | 92 | 18 | 0 | 49 | 33 | 1 | 18 | 48 | 0 | 84 | 63 | 0 | 34 |
4 | 0 | 44 | 19 | 0 | 80 | 34 | 0 | 4 | 49 | 0 | 93 | 64 | 1 | 43 |
5 | 0 | 61 | 20 | 0 | 54 | 35 | 0 | 15 | 50 | 0 | 73 | 65 | 0 | 39 |
6 | 0 | 60 | 21 | 0 | 9 | 36 | 0 | 29 | 51 | 0 | 3 | 66 | 0 | 55 |
7 | 0 | 20 | 22 | 0 | 68 | 37 | 1 | 33 | 52 | 1 | 19 | 67 | 0 | 1 |
8 | 1 | 92 | 23 | 1 | 31 | 38 | 1 | 40 | 53 | 1 | 17 | 68 | 0 | 27 |
9 | 0 | 65 | 24 | 1 | 82 | 39 | 1 | 36 | 54 | 1 | 48 | 69 | 0 | 3 |
10 | 0 | 48 | 25 | 0 | 36 | 40 | 0 | 17 | 55 | 0 | 86 | 70 | 0 | 20 |
11 | 0 | 10 | 26 | 0 | 45 | 41 | 0 | 7 | 56 | 0 | 23 | 71 | 0 | 31 |
12 | 0 | 40 | 27 | 0 | 85 | 42 | 0 | 69 | 57 | 0 | 88 | 72 | 0 | 31 |
13 | 1 | 65 | 28 | 1 | 77 | 43 | 0 | 6 | 58 | 0 | 24 | 73 | 0 | 57 |
14 | 0 | 18 | 29 | 1 | 57 | 44 | 0 | 62 | 59 | 0 | 5 | 74 | 0 | 1 |
15 | 0 | 35 | 30 | 0 | 75 | 45 | 0 | 36 | 60 | 0 | 78 | 75 | 0 | 73 |
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
76 | 0 | 88 | 91 | 1 | 3 | 106 | 1 | 62 | 121 | 0 | 39 | 136 | 0 | 28 |
77 | 0 | 82 | 92 | 1 | 64 | 107 | 0 | 77 | 122 | 0 | 47 | 137 | 0 | 20 |
78 | 0 | 27 | 93 | 1 | 31 | 108 | 1 | 84 | 123 | 0 | 74 | 138 | 1 | 25 |
79 | 0 | 52 | 94 | 0 | 93 | 109 | 1 | 35 | 124 | 1 | 14 | 139 | 0 | 78 |
80 | 0 | 54 | 95 | 0 | 93 | 110 | 0 | 20 | 125 | 0 | 2 | 140 | 0 | 29 |
81 | 0 | 9 | 96 | 0 | 26 | 111 | 0 | 89 | 126 | 0 | 85 | 141 | 1 | 86 |
82 | 1 | 54 | 97 | 0 | 66 | 112 | 0 | 18 | 127 | 0 | 42 | 142 | 1 | 1 |
83 | 0 | 2 | 98 | 0 | 4 | 113 | 0 | 26 | 128 | 1 | 81 | 143 | 0 | 48 |
84 | 0 | 35 | 99 | 0 | 14 | 114 | 0 | 41 | 129 | 0 | 66 | 144 | 0 | 78 |
85 | 0 | 60 | 100 | 0 | 68 | 115 | 1 | 58 | 130 | 1 | 83 | 145 | 0 | 62 |
86 | 0 | 42 | 101 | 0 | 75 | 116 | 0 | 91 | 131 | 0 | 32 | 146 | 1 | 48 |
87 | 1 | 89 | 102 | 0 | 50 | 117 | 0 | 66 | 132 | 0 | 100 | 147 | 0 | 100 |
88 | 0 | 62 | 103 | 1 | 96 | 118 | 0 | 92 | 133 | 0 | 76 | 148 | 1 | 89 |
89 | 1 | 75 | 104 | 0 | 80 | 119 | 0 | 82 | 134 | 1 | 98 | |||
90 | 1 | 38 | 105 | 1 | 49 | 120 | 0 | 5 | 135 | 0 | 82 |
Bowman
# | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 25 | 2 | 1 | 53 | 3 | 1 | 86 | 4 | 0 | 88 |
# | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|
5 | 1 | 66 | 6 | 0 | 19 | 7 | 1 | 34 | 8 | 0 | 73 |
Buxey
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 67 | 4 | 0 | 57 | 7 | 0 | 96 | 10 | 0 | 72 | 13 | 0 | 13 |
2 | 0 | 39 | 5 | 0 | 95 | 8 | 0 | 91 | 11 | 0 | 36 | 14 | 0 | 33 |
3 | 1 | 53 | 6 | 0 | 81 | 9 | 0 | 57 | 12 | 0 | 79 | 15 | 0 | 93 |
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
16 | 0 | 7 | 19 | 0 | 34 | 22 | 0 | 17 | 25 | 1 | 40 | 28 | 0 | 1 |
17 | 0 | 55 | 20 | 0 | 84 | 23 | 0 | 23 | 26 | 0 | 5 | 29 | 1 | 8 |
18 | 0 | 39 | 21 | 0 | 96 | 24 | 0 | 21 | 27 | 0 | 42 |
Gunther
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 88 | 5 | 0 | 48 | 9 | 0 | 6 | 13 | 0 | 45 | 17 | 0 | 23 |
2 | 0 | 95 | 6 | 0 | 80 | 10 | 0 | 19 | 14 | 0 | 95 | 18 | 0 | 48 |
3 | 0 | 45 | 7 | 1 | 99 | 11 | 0 | 3 | 15 | 0 | 82 | 19 | 1 | 82 |
4 | 0 | 25 | 8 | 1 | 31 | 12 | 0 | 1 | 16 | 0 | 90 | 20 | 0 | 62 |
# | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|
21 | 0 | 93 | 25 | 0 | 35 | 29 | 0 | 57 | 33 | 0 | 68 |
22 | 0 | 69 | 26 | 1 | 97 | 30 | 0 | 34 | 34 | 1 | 29 |
23 | 0 | 86 | 27 | 1 | 12 | 31 | 0 | 64 | 35 | 0 | 67 |
24 | 1 | 88 | 28 | 1 | 74 | 32 | 0 | 61 |
Hahn
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 33 | 7 | 0 | 75 | 13 | 1 | 83 | 19 | 1 | 4 | 25 | 0 | 3 |
2 | 0 | 64 | 8 | 0 | 20 | 14 | 0 | 65 | 20 | 0 | 86 | 26 | 0 | 38 |
3 | 0 | 67 | 9 | 0 | 16 | 15 | 0 | 59 | 21 | 0 | 94 | 27 | 0 | 5 |
4 | 0 | 29 | 10 | 0 | 31 | 16 | 0 | 13 | 22 | 0 | 8 | 28 | 0 | 88 |
5 | 1 | 88 | 11 | 1 | 68 | 17 | 0 | 51 | 23 | 0 | 83 | 29 | 1 | 11 |
6 | 0 | 15 | 12 | 0 | 63 | 18 | 0 | 24 | 24 | 0 | 45 | 30 | 1 | 3 |
# | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|
31 | 0 | 58 | 37 | 0 | 69 | 43 | 1 | 69 | 49 | 1 | 83 |
32 | 0 | 27 | 38 | 0 | 72 | 44 | 1 | 54 | 50 | 1 | 16 |
33 | 0 | 94 | 39 | 0 | 85 | 45 | 0 | 68 | 51 | 0 | 82 |
34 | 0 | 51 | 40 | 0 | 92 | 46 | 0 | 24 | 52 | 0 | 1 |
35 | 0 | 52 | 41 | 0 | 7 | 47 | 0 | 51 | 53 | 0 | 100 |
36 | 1 | 61 | 42 | 1 | 76 | 48 | 0 | 73 |
Heskiaoff
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 1 | 90 | 4 | 0 | 9 | 7 | 0 | 99 | 10 | 0 | 71 | 13 | 0 | 7 |
2 | 0 | 86 | 5 | 1 | 5 | 8 | 1 | 92 | 11 | 0 | 71 | 14 | 0 | 84 |
3 | 0 | 15 | 6 | 0 | 20 | 9 | 1 | 23 | 12 | 0 | 47 | 15 | 1 | 26 |
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
16 | 0 | 15 | 19 | 0 | 56 | 22 | 0 | 48 | 25 | 1 | 1 | 28 | 0 | 26 |
17 | 0 | 85 | 20 | 1 | 48 | 23 | 0 | 76 | 26 | 0 | 1 | |||
18 | 0 | 69 | 21 | 0 | 55 | 24 | 0 | 51 | 27 | 0 | 46 |
Jackson
# | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|
1 | 0 | 35 | 3 | 0 | 56 | 5 | 1 | 30 |
2 | 0 | 30 | 4 | 0 | 74 | 6 | 1 | 40 |
# | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|
7 | 0 | 90 | 9 | 0 | 19 | 11 | 0 | 44 |
8 | 1 | 84 | 10 | 1 | 80 |
Jaeschke
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 17 | 2 | 1 | 9 | 3 | 0 | 80 | 4 | 1 | 57 | 5 | 0 | 63 |
# | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|
6 | 0 | 27 | 7 | 1 | 91 | 8 | 1 | 79 | 9 | 0 | 1 |
Kilbridge
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 39 | 6 | 1 | 88 | 11 | 0 | 97 | 16 | 0 | 14 | 21 | 0 | 22 |
2 | 1 | 37 | 7 | 0 | 75 | 12 | 1 | 78 | 17 | 0 | 45 | 22 | 0 | 36 |
3 | 0 | 89 | 8 | 0 | 73 | 13 | 0 | 73 | 18 | 0 | 96 | 23 | 0 | 78 |
4 | 0 | 78 | 9 | 0 | 98 | 14 | 0 | 21 | 19 | 0 | 3 | 24 | 0 | 37 |
5 | 0 | 78 | 10 | 0 | 76 | 15 | 0 | 5 | 20 | 0 | 64 | 25 | 0 | 64 |
# | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|
26 | 0 | 51 | 31 | 0 | 82 | 36 | 1 | 34 | 41 | 0 | 9 |
27 | 0 | 21 | 32 | 1 | 25 | 37 | 1 | 18 | 42 | 0 | 34 |
28 | 0 | 97 | 33 | 1 | 40 | 38 | 0 | 2 | 43 | 0 | 98 |
29 | 1 | 11 | 34 | 1 | 12 | 39 | 0 | 41 | 44 | 1 | 27 |
30 | 0 | 46 | 35 | 0 | 97 | 40 | 0 | 1 | 45 | 0 | 2 |
Lutz1
# | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 1 | 36 | 5 | 0 | 60 | 9 | 0 | 4 | 13 | 0 | 69 |
2 | 0 | 42 | 6 | 0 | 65 | 10 | 0 | 52 | 14 | 0 | 59 |
3 | 1 | 78 | 7 | 0 | 8 | 11 | 1 | 2 | 15 | 0 | 20 |
4 | 0 | 32 | 8 | 0 | 23 | 12 | 1 | 58 | 16 | 0 | 28 |
# | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|
17 | 0 | 63 | 21 | 1 | 35 | 25 | 0 | 47 | 29 | 0 | 88 |
18 | 0 | 29 | 22 | 0 | 3 | 26 | 1 | 98 | 30 | 0 | 43 |
19 | 0 | 92 | 23 | 0 | 26 | 27 | 0 | 53 | 31 | 1 | 65 |
20 | 1 | 8 | 24 | 0 | 31 | 28 | 0 | 60 | 32 | 0 | 38 |
Lutz2
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 7 | 10 | 0 | 72 | 19 | 1 | 10 | 28 | 0 | 64 | 37 | 0 | 42 |
2 | 0 | 43 | 11 | 0 | 41 | 20 | 0 | 92 | 29 | 0 | 22 | 38 | 0 | 55 |
3 | 0 | 18 | 12 | 0 | 81 | 21 | 0 | 62 | 30 | 0 | 100 | 39 | 0 | 13 |
4 | 0 | 64 | 13 | 0 | 47 | 22 | 1 | 70 | 31 | 1 | 54 | 40 | 0 | 72 |
5 | 0 | 7 | 14 | 0 | 25 | 23 | 0 | 79 | 32 | 1 | 97 | 41 | 0 | 27 |
6 | 0 | 19 | 15 | 1 | 47 | 24 | 0 | 3 | 33 | 0 | 18 | 42 | 1 | 33 |
7 | 0 | 12 | 16 | 1 | 51 | 25 | 0 | 2 | 34 | 0 | 18 | 43 | 1 | 44 |
8 | 0 | 65 | 17 | 0 | 36 | 26 | 0 | 97 | 35 | 0 | 66 | 44 | 0 | 93 |
9 | 1 | 69 | 18 | 1 | 49 | 27 | 0 | 54 | 36 | 0 | 97 | 45 | 1 | 72 |
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
46 | 0 | 51 | 55 | 1 | 38 | 64 | 1 | 4 | 73 | 0 | 81 | 82 | 0 | 100 |
47 | 1 | 60 | 56 | 0 | 6 | 65 | 0 | 92 | 74 | 0 | 13 | 83 | 0 | 89 |
48 | 0 | 73 | 57 | 0 | 35 | 66 | 0 | 8 | 75 | 0 | 2 | 84 | 1 | 13 |
49 | 0 | 59 | 58 | 0 | 91 | 67 | 0 | 39 | 76 | 0 | 48 | 85 | 1 | 90 |
50 | 0 | 68 | 59 | 0 | 74 | 68 | 0 | 5 | 77 | 0 | 46 | 86 | 0 | 13 |
51 | 0 | 50 | 60 | 1 | 62 | 69 | 0 | 61 | 78 | 0 | 11 | 87 | 0 | 47 |
52 | 0 | 15 | 61 | 1 | 35 | 70 | 0 | 42 | 79 | 0 | 98 | 88 | 1 | 79 |
53 | 0 | 18 | 62 | 0 | 73 | 71 | 0 | 9 | 80 | 1 | 29 | 89 | 0 | 48 |
54 | 0 | 47 | 63 | 0 | 78 | 72 | 1 | 45 | 81 | 0 | 46 |
Lutz3
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 60 | 10 | 0 | 90 | 19 | 0 | 78 | 28 | 0 | 24 | 37 | 1 | 3 |
2 | 0 | 91 | 11 | 1 | 50 | 20 | 0 | 47 | 29 | 0 | 10 | 38 | 0 | 66 |
3 | 0 | 16 | 12 | 1 | 9 | 21 | 0 | 53 | 30 | 1 | 12 | 39 | 1 | 36 |
4 | 0 | 69 | 13 | 0 | 2 | 22 | 0 | 23 | 31 | 0 | 39 | 40 | 0 | 63 |
5 | 0 | 94 | 14 | 0 | 11 | 23 | 0 | 29 | 32 | 0 | 48 | 41 | 0 | 5 |
6 | 0 | 84 | 15 | 0 | 68 | 24 | 0 | 76 | 33 | 0 | 2 | 42 | 0 | 28 |
7 | 0 | 29 | 16 | 0 | 55 | 25 | 0 | 66 | 34 | 1 | 41 | 43 | 1 | 25 |
8 | 1 | 63 | 17 | 0 | 48 | 26 | 1 | 99 | 35 | 0 | 69 | 44 | 0 | 26 |
9 | 1 | 34 | 18 | 0 | 100 | 27 | 0 | 30 | 36 | 0 | 99 | 45 | 0 | 98 |
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
46 | 0 | 90 | 55 | 1 | 38 | 64 | 0 | 94 | 73 | 0 | 16 | 82 | 0 | 2 |
47 | 1 | 78 | 56 | 0 | 93 | 65 | 0 | 64 | 74 | 0 | 52 | 83 | 0 | 2 |
48 | 0 | 20 | 57 | 0 | 30 | 66 | 0 | 77 | 75 | 1 | 30 | 84 | 0 | 1 |
49 | 0 | 33 | 58 | 1 | 64 | 67 | 0 | 24 | 76 | 0 | 28 | 85 | 0 | 83 |
50 | 0 | 24 | 59 | 1 | 24 | 68 | 0 | 28 | 77 | 1 | 72 | 86 | 0 | 95 |
51 | 1 | 99 | 60 | 0 | 4 | 69 | 0 | 73 | 78 | 0 | 16 | 87 | 0 | 37 |
52 | 0 | 29 | 61 | 1 | 66 | 70 | 1 | 49 | 79 | 0 | 15 | 88 | 0 | 57 |
53 | 1 | 28 | 62 | 0 | 26 | 71 | 0 | 19 | 80 | 0 | 65 | 89 | 1 | 86 |
54 | 1 | 44 | 63 | 0 | 96 | 72 | 1 | 57 | 81 | 0 | 71 |
Mansoor
# | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|
1 | 1 | 14 | 3 | 0 | 50 | 5 | 0 | 54 |
2 | 1 | 75 | 4 | 0 | 50 | 6 | 1 | 2 |
# | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|
7 | 0 | 20 | 9 | 0 | 47 | 11 | 0 | 32 |
8 | 1 | 98 | 10 | 0 | 45 |
Mertens
# | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 80 | 2 | 1 | 33 | 3 | 1 | 62 | 4 | 0 | 67 |
# | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|
5 | 0 | 10 | 6 | 0 | 94 | 7 | 0 | 51 |
Mitchell
# | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 78 | 4 | 0 | 90 | 7 | 0 | 94 | 10 | 0 | 30 |
2 | 1 | 63 | 5 | 0 | 21 | 8 | 0 | 93 | 11 | 0 | 13 |
3 | 0 | 96 | 6 | 0 | 31 | 9 | 0 | 81 | 12 | 0 | 88 |
# | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|
13 | 0 | 70 | 16 | 0 | 40 | 19 | 0 | 22 |
14 | 0 | 2 | 17 | 1 | 33 | 20 | 0 | 84 |
15 | 0 | 97 | 18 | 0 | 41 | 21 | 1 | 61 |
Mukherje
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 4 | 11 | 0 | 13 | 21 | 1 | 18 | 31 | 0 | 15 | 41 | 1 | 21 |
2 | 0 | 88 | 12 | 0 | 49 | 22 | 0 | 47 | 32 | 1 | 68 | 42 | 0 | 75 |
3 | 0 | 74 | 13 | 0 | 52 | 23 | 0 | 85 | 33 | 0 | 93 | 43 | 0 | 42 |
4 | 0 | 65 | 14 | 0 | 97 | 24 | 1 | 66 | 34 | 1 | 15 | 44 | 0 | 60 |
5 | 0 | 58 | 15 | 0 | 59 | 25 | 1 | 12 | 35 | 0 | 70 | 45 | 1 | 11 |
6 | 0 | 63 | 16 | 0 | 100 | 26 | 1 | 24 | 36 | 0 | 99 | 46 | 0 | 54 |
7 | 1 | 15 | 17 | 1 | 38 | 27 | 0 | 42 | 37 | 0 | 76 | 47 | 0 | 88 |
8 | 0 | 30 | 18 | 0 | 60 | 28 | 1 | 58 | 38 | 0 | 35 | 48 | 0 | 61 |
9 | 0 | 43 | 19 | 1 | 47 | 29 | 0 | 15 | 39 | 0 | 73 | 49 | 0 | 62 |
10 | 1 | 49 | 20 | 0 | 47 | 30 | 1 | 69 | 40 | 1 | 16 | 50 | 0 | 6 |
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
51 | 1 | 84 | 61 | 1 | 47 | 71 | 1 | 43 | 81 | 1 | 7 | 91 | 1 | 79 |
52 | 0 | 96 | 62 | 0 | 3 | 72 | 0 | 36 | 82 | 0 | 83 | 92 | 1 | 75 |
53 | 0 | 6 | 63 | 0 | 88 | 73 | 1 | 56 | 83 | 0 | 61 | 93 | 1 | 57 |
54 | 1 | 92 | 64 | 0 | 28 | 74 | 1 | 60 | 84 | 0 | 69 | 94 | 0 | 42 |
55 | 0 | 85 | 65 | 0 | 80 | 75 | 0 | 69 | 85 | 0 | 10 | |||
56 | 0 | 75 | 66 | 1 | 74 | 76 | 1 | 38 | 86 | 1 | 73 | |||
57 | 0 | 70 | 67 | 0 | 16 | 77 | 0 | 28 | 87 | 0 | 20 | |||
58 | 0 | 96 | 68 | 1 | 90 | 78 | 1 | 22 | 88 | 0 | 27 | |||
59 | 0 | 92 | 69 | 1 | 45 | 79 | 0 | 25 | 89 | 0 | 97 | |||
60 | 1 | 63 | 70 | 0 | 99 | 80 | 0 | 66 | 90 | 0 | 19 |
Roszieg
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 29 | 4 | 0 | 86 | 7 | 0 | 29 | 10 | 1 | 14 | 13 | 0 | 57 |
2 | 0 | 69 | 5 | 0 | 47 | 8 | 0 | 70 | 11 | 0 | 85 | 14 | 0 | 6 |
3 | 0 | 23 | 6 | 1 | 51 | 9 | 0 | 74 | 12 | 1 | 34 | 15 | 0 | 64 |
# | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|
16 | 0 | 100 | 19 | 0 | 66 | 22 | 0 | 84 | 25 | 0 | 59 |
17 | 1 | 87 | 20 | 0 | 66 | 23 | 1 | 86 | |||
18 | 0 | 61 | 21 | 0 | 93 | 24 | 0 | 49 |
Tonge
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 1 | 21 | 8 | 0 | 16 | 15 | 0 | 8 | 22 | 0 | 5 | 29 | 1 | 85 |
2 | 1 | 50 | 9 | 0 | 98 | 16 | 0 | 29 | 23 | 0 | 28 | 30 | 1 | 84 |
3 | 0 | 25 | 10 | 0 | 46 | 17 | 0 | 84 | 24 | 0 | 50 | 31 | 0 | 40 |
4 | 0 | 46 | 11 | 0 | 22 | 18 | 0 | 91 | 25 | 1 | 58 | 32 | 1 | 82 |
5 | 0 | 35 | 12 | 0 | 88 | 19 | 0 | 2 | 26 | 0 | 46 | 33 | 0 | 84 |
6 | 0 | 29 | 13 | 0 | 6 | 20 | 1 | 43 | 27 | 0 | 20 | 34 | 0 | 31 |
7 | 0 | 81 | 14 | 0 | 2 | 21 | 0 | 2 | 28 | 0 | 45 | 35 | 0 | 4 |
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
36 | 1 | 46 | 43 | 0 | 80 | 50 | 0 | 98 | 57 | 0 | 84 | 64 | 1 | 30 |
37 | 0 | 93 | 44 | 0 | 29 | 51 | 0 | 86 | 58 | 0 | 21 | 65 | 0 | 22 |
38 | 0 | 13 | 45 | 0 | 24 | 52 | 0 | 27 | 59 | 0 | 21 | 66 | 0 | 63 |
39 | 0 | 1 | 46 | 1 | 95 | 53 | 1 | 58 | 60 | 0 | 17 | 67 | 0 | 77 |
40 | 0 | 64 | 47 | 0 | 94 | 54 | 1 | 20 | 61 | 0 | 85 | 68 | 1 | 70 |
41 | 0 | 44 | 48 | 0 | 39 | 55 | 1 | 23 | 62 | 0 | 100 | 69 | 1 | 33 |
42 | 0 | 47 | 49 | 0 | 4 | 56 | 0 | 3 | 63 | 1 | 56 | 70 | 1 | 25 |
Wee-mag
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 32 | 9 | 0 | 68 | 17 | 1 | 32 | 25 | 0 | 78 | 33 | 0 | 57 |
2 | 0 | 92 | 10 | 0 | 32 | 18 | 0 | 21 | 26 | 1 | 80 | 34 | 1 | 15 |
3 | 0 | 64 | 11 | 1 | 12 | 19 | 0 | 60 | 27 | 0 | 42 | 35 | 1 | 15 |
4 | 1 | 64 | 12 | 0 | 12 | 20 | 0 | 39 | 28 | 0 | 16 | 36 | 0 | 13 |
5 | 0 | 83 | 13 | 0 | 100 | 21 | 0 | 73 | 29 | 0 | 36 | 37 | 0 | 82 |
6 | 0 | 50 | 14 | 0 | 10 | 22 | 1 | 16 | 30 | 0 | 40 | 38 | 1 | 69 |
7 | 1 | 86 | 15 | 0 | 10 | 23 | 0 | 3 | 31 | 0 | 80 | 39 | 0 | 76 |
8 | 0 | 92 | 16 | 1 | 51 | 24 | 0 | 42 | 32 | 0 | 61 | 40 | 0 | 67 |
# | H | D | # | H | D | # | H | D | # | H | D | # | H | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
41 | 0 | 50 | 49 | 0 | 99 | 57 | 1 | 56 | 65 | 0 | 91 | 73 | 0 | 89 |
42 | 0 | 59 | 50 | 1 | 6 | 58 | 0 | 63 | 66 | 1 | 93 | 74 | 0 | 46 |
43 | 0 | 16 | 51 | 0 | 100 | 59 | 0 | 29 | 67 | 1 | 67 | 75 | 0 | 37 |
44 | 0 | 91 | 52 | 0 | 10 | 60 | 0 | 43 | 68 | 0 | 33 | |||
45 | 0 | 88 | 53 | 0 | 12 | 61 | 0 | 40 | 69 | 0 | 46 | |||
46 | 0 | 29 | 54 | 0 | 27 | 62 | 0 | 44 | 70 | 1 | 88 | |||
47 | 0 | 67 | 55 | 0 | 69 | 63 | 0 | 5 | 71 | 0 | 73 | |||
48 | 0 | 31 | 56 | 0 | 68 | 64 | 0 | 72 | 72 | 0 | 68 |
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Kalayci, C.B., Polat, O. & Gupta, S.M. A hybrid genetic algorithm for sequence-dependent disassembly line balancing problem. Ann Oper Res 242, 321–354 (2016). https://doi.org/10.1007/s10479-014-1641-3
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DOI: https://doi.org/10.1007/s10479-014-1641-3