A Two-Stage Assembly-Type Flowshop Scheduling Problem for Minimizing Total Tardiness
Table 1
Results of the test on the B&B algorithm and CPLEX.
(, )
B&B
CPLEX
ACPUT†
MCPUT‡
NI#
ACPUT
MCPUT
NI
8
(0.1, 0.8)
<0.01
<0.01
10
0.04
0.03
10
(0.1, 1.3)
<0.01
<0.01
10
0.05
0.05
10
(0.1, 1.8)
<0.01
<0.01
10
0.06
0.06
10
(0.3, 0.8)
<0.01
<0.01
10
0.05
0.03
10
(0.3, 1.3)
<0.01
<0.01
10
0.04
0.04
10
(0.3, 1.8)
<0.01
<0.01
10
0.07
0.06
10
(0.5, 0.8)
<0.01
<0.01
10
0.05
0.05
10
(0.5, 1.3)
<0.01
<0.01
10
0.05
0.05
10
(0.5, 1.8)
<0.01
<0.01
10
0.07
0.06
10
12
(0.1, 0.8)
0.04
0.00
10
0.13
0.06
10
(0.1, 1.3)
0.00
0.00
10
0.11
0.05
10
(0.1, 1.8)
0.02
0.00
10
0.55
0.42
10
(0.3, 0.8)
0.03
0.02
10
0.24
0.09
10
(0.3, 1.3)
0.03
0.02
10
0.71
0.40
10
(0.3, 1.8)
0.02
0.02
10
1.14
0.72
10
(0.5, 0.8)
0.05
0.04
10
0.26
0.17
10
(0.5, 1.3)
0.05
0.02
10
0.97
0.35
10
(0.5, 1.8)
0.06
0.02
10
0.66
0.65
10
16
(0.1, 0.8)
0.00
0.00
10
0.07
0.06
10
(0.1, 1.3)
0.06
0.00
10
0.25
0.08
10
(0.1, 1.8)
0.12
0.09
10
4.57
1.15
10
(0.3, 0.8)
1.21
0.91
10
0.62
0.65
10
(0.3, 1.3)
0.10
0.06
10
4.05
1.53
10
(0.3, 1.8)
0.85
0.17
10
77.79
10.82
10
(0.5, 0.8)
2.10
1.20
10
4.10
3.74
10
(0.5, 1.3)
1.26
1.07
10
8.80
4.79
10
(0.5, 1.8)
1.09
0.87
10
208.34
80.99
10
20
(0.1, 0.8)
0.00
0.00
10
0.12
0.11
10
(0.1, 1.3)
0.44
0.00
10
8.82
0.11
10
(0.1, 1.8)
0.85
0.13
10
32.97
2.66
10
(0.3, 0.8)
34.42
24.09
10
18.43
1.88
10
(0.3, 1.3)
7.68
0.66
10
758.16
10.90
8
(0.3, 1.8)
14.57
6.41
10
1804.62
1817.27
5
(0.5, 0.8)
151.51
71.92
10
239.56
40.82
10
(0.5, 1.3)
61.48
11.08
10
386.61
180.46
10
(0.5, 1.8)
32.53
7.96
10
1230.12
275.37
7
24
(0.1, 0.8)
0.00
0.00
10
0.20
0.19
10
(0.1, 1.3)
7.15
0.00
10
18.10
0.40
10
(0.1, 1.8)
5.71
1.02
10
514.38
96.66
9
(0.3, 0.8)
292.95
81.57
10
3.34
2.23
10
(0.3, 1.3)
692.23
9.70
9
1248.93
255.20
7
(0.3, 1.8)
304.40
34.13
10
2905.16
3600.00
2
(0.5, 0.8)
1210.80
431.44
8
1209.62
135.64
7
(0.5, 1.3)
946.30
166.13
8
2129.49
3055.50
5
(0.5, 1.8)
669.19
161.96
9
2634.28
3600.00
3
Average CPU time (3600 seconds was used as the CPU time for the instances that were not solved to optimality in 3600 seconds). ‡Median CPU time. #Number of instances (out of 10 instances) that were solved within 3600 seconds.