A Column Generation Algorithm for the Resource-Constrained Order Acceptance and Scheduling on Unrelated Parallel Machines
Table 9
Computation results of large-sized instances with |N| = 100.
|N| × |M|
TF
R
Gap (%)
No. of optimal solutions
CPU(s)
MILP
CG
MILP
CG
Min
Ave
Max
Min
Ave
Max
MILP
CG
Total
Total
CH
LP
MILP
DE
100 × 3
0.2
0.2∗
2.24
8.00
13.92
0
0
0
0
5
571.84
374.27
0.25
208.58
10.50
154.94
0.6∗
5.38
7.31
8.67
0
0
0
0
5
627.31
247.86
0.24
147.80
10.56
89.26
1∗
-
-
-
0
0
0
0
5
436.57
200.05
0.26
129.56
8.90
61.33
0.6
0.2
10.04
15.24
19.45
0
0
0
0
5
3600
359.94
0.1
192.67
122.71
44.46
0.6
10.37
15.57
20.41
0
0
0
0
5
3600
254.40
0.07
185.37
12.27
56.69
1∗
14.24
15.05
16.00
0
0
0
0
5
1711.34
248.25
0.07
165.48
11.87
70.83
1
0.2∗
0
0.41
1.35
0
0.32
0.86
3
3
1198.63
147.54
0.06
73.95
12.42
61.11
0.6∗
0
8.54
18.24
0
0
0
1
5
2454.21
160.96
0.09
88.21
12.60
60.06
1∗
10.02
10.81
12.25
0
0
0
0
5
1055.10
176.53
0.05
99.08
7.47
69.93
100 × 4
0.2
0.2∗
3.97
5.57
7.04
0
0
0
0
5
1751.80
488.65
0.32
389.70
12.00
86.63
0.6∗
0.82
4.79
8.75
0
0
0
0
5
519.20
489.11
0.25
376.24
14.41
98.21
1∗
-
-
-
0
0
0
0
5
457.40
402.91
0.35
264.66
12.91
124.99
0.6
0.2
0
7.49
13.13
0
0
0
1
5
3000
793.43
0.06
619.86
24.58
148.93
0.6∗
9.51
12.12
17.90
0
0
0
0
5
2977.87
562.54
0.09
395.90
20.20
146.35
1∗
7.54
7.54
7.54
0
0
0
0
5
438.96
337.99
0.08
142.00
21.61
174.30
1
0.2
0
0
0
0
0
0
5
5
410.21
121.41
0.06
39.76
6.27
75.32
0.6
0
1.28
6.42
0
0
0
4
5
1164.28
141.24
0.06
73.00
6.22
61.96
1∗
0.55
5.62
9.39
0
0
0
0
5
1073.99
155.21
0.07
78.84
6.34
69.96
Average
—
—
4.67
7.83
11.28
0
0.02
0.05
—
—
1502.71
314.57
0.14
203.93
18.55
91.96
“-” indicates that the CPLEX fails to find feasible solutions for this subclass. “∗” indicates that the CPLEX runs of memory when solving some instances of this subclass.
