Balancing Lexicographic Multi-Objective Assembly Lines with Multi-Manned Stations
Table 8
For given target values of the number of stations and workers, results for small and medium size instances for minimizing smoothness index.
Problem
Ct
Target
VNS result
RVNS result
VNDS result
MIP
# stations
# workers
Result
CPU
P11
7
2
6
8
6; 8; 4
6; 8; 4
6; 8; 4
0
0
6; 8; 4
0.14; 0.08; 0.33
4
5
9
5; 9; 10
5; 9; 10
5; 9; 10
0
0
5; 9; 10
0.16; 0.08; 0.09
10
2
4
5
4; 5; 3
4; 5; 3
4; 5; 3
0
0
4; 5; 3
0.13; 0.11; 0.31
4
3
6
3; 6; 5
3; 6; 5
3; 6; 5
0
0
3; 6; 5
0.08; 0.08; 0.09
21
2
2
3
2; 3; 1
2; 3; 1
2; 3; 1
0
0
2; 3; 1
0.11; 0.08; 0.23
4
2
3
2; 3; 1
2; 3; 1
2; 3; 1
0
0
2; 3; 1
0.09; 0.08; 0.19
P21
14
2
7
8
7; 8; 6
7; 8; 6
7; 8; 6
0
0
7; 8; 6
0.58; 0.27; 0.39
4
7
8
7; 8; 6
7; 8; 6
7; 8; 6
0
0
7; 8; 6
2.22; 0.83; 0.91
21
2
4
6
4; 6; 2
4; 6; 2
4; 6; 2
0
0
4; 6; 2
0.92; 0.28; 0.58
4
4
6
4; 6; 2
4; 6; 2
4; 6; 2
0
0
4; 6; 2
2.62; 0.59; 0.89
35
2
3
3
3; 3; 0
3; 3; 0
3; 3; 0
0
0
3; 3; 0
0.58; 1.61; 0.17
4
3
3
3; 3; 0
3; 3; 0
3; 3; 0
0
0
3; 3; 0
2.06; 1.2; 0.28
P30
25
2
8
14
8; 14; 2
8; 14; 2
8; 14; 2
0
0
8; 14; 2
13.03; 0.81; 1.37
4
8
14
8; 14; 2
8; 14; 2
8; 14; 2
0
0
8; 14; 2
6.02; 4.57; 6.3
30
2
7
12
7; 12; 2
6.8; 12; 1.6
7; 12; 2
0
0
7; 12; 0
7.55; 1.29; 8.18
4
6
12
6; 12; 8
6; 12; 10
6; 12; 6
0
0
6; 12; 0
15.12; 1.3; 62.39
41
2
5
9
5; 9; 1
5; 9; 1
5; 9; 1
0
0
5; 8; 0
11.73; 1.36; 142.48
4
4
9
4; 9; 3
4; 8.8; 2.4
4; 9; 3
0
0
4; 8; 0
10.17; 2.96; 2977.37
P45
57
2
6
10
6; 10; 2
6; 10; 2
6; 10; 2
0
No
6; No; —
253.24; 3346.86; —
4
5
10
5; 10; 7
5; 10; 7
5; 10; 7
0
0
5;10;No
73.68; 106.18; 3420.32
110
2
3
6
3; 6; 0
3; 6; 0
3; 6; 0
0
0
3; 6; 0
53.95; 2.28; 2.23
4
3
6
3; 6; 0
3; 6; 0
3; 6; 0
0
0
3; 6; 0
95.22; 7.64; 23.46
184
2
2
3
2; 3; 1
2; 3; 1
2; 3; 1
0
0
2; 3; No
39.22; 527.08; 3033.8
4
2
3
2; 3; 1
2; 3; 1
2; 3; 1
0
0
2; 3; 1
60.23; 2601.69; 938.55
P70
176
2
12
22
12; 22; 2
12; 22; 2
12; 22; 2
No
—
No; —; —
3600.27; —; —
4
9
23
9; 23; 6
9; 23; 5.2
9; 23; 9.4
0
0
9; 23; No
496.6; 121.28; 2982.48
364
2
6
10
6; 10; 2
6; 10; 2
6; 10; 2
No
—
No; —; —
3600.27; —; —
4
4
12
4; 12; 0
4; 12; 0
4; 12; 0
0
0
4; 12; 0
398.05; 66.35; 75.41
468
2
4
8
4; 8; 0
4; 8; 0
4; 8; 0
No
—
No; —; —
3600.3; —; —
4
3
9
3; 9; 0
3; 9; 0
3; 9; 0
0
0
3; 9; 0
355.39; 62.01; 137.83
Mean number of stations. Mean number of workers. Mean smoothness index (without square root). Integer solution was found within a given CPU time limit. No: no solution was found within a given CPU time limit. —: phase was not performed since previous phases had consumed the given CPU time.
