A Column Generation Algorithm for the Resource-Constrained Order Acceptance and Scheduling on Unrelated Parallel Machines
Table 8
Computation results of large-sized instances with |N| = 90.
|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
90 × 3
0.2
0.2∗
1.60
8.56
11.68
0
0
0
0
5
2082.23
357.67
0.21
301.68
12.66
43.12
0.6∗
2.94
5.18
6.30
0
0
0
0
5
1148.00
296.32
0.18
239.84
10.71
45.59
1 ∗
0.39
5.83
11.97
0
0
0
0
5
2100.61
218.42
0.19
160.60
7.19
50.44
0.6
0.2
0
11.74
18.28
0
0
0
1
5
2880.21
248.82
0.07
192.12
19.90
36.73
0.6
8.33
12.87
16.63
0
0
0
0
5
3600
223.36
0.06
177.00
9.51
36.79
1 ∗
7.73
14.48
20.38
0
0
0
0
5
2964.35
228.28
0.07
173.02
7.57
47.62
1
0.2
0
0.11
0.55
0
0.06
0.30
4
4
1080.89
121.08
0.04
63.77
10.48
46.79
0.6
0
6.69
19.25
0
0
0
3
5
1848.10
107.61
0.05
62.12
3.71
41.73
1 ∗
11.19
13.13
15.63
0
0
0
0
5
2412.80
133.22
0.04
77.58
9.30
46.30
90 × 4
0.2
0.2
0
5.82
14.11
0
0
0
0
5
3600
316.04
0.13
254.71
7.06
54.14
0.6
1.30
3.68
11.07
0
0
0
0
5
3600
274.33
0.14
214.28
7.76
52.15
1∗
-
-
-
0
0
0
0
5
414.81
225.31
0.12
164.48
4.54
56.17
0.6
0.2
0
6.76
15.99
0
0
0
2
5
2376.00
308.20
0.05
243.17
9.73
55.25
0.6
0
5.00
13.70
0
0
0
1
5
1762.24
271.05
0.04
200.51
9.40
61.10
1
0
17.51
78.60
0
0
0
1
5
1139.31
189.58
0.04
125.93
5.68
57.93
1
0.2
0
0
0
0
0
0
5
5
302.12
67.80
0.04
29.61
1.53
36.62
0.6
0
0
0
0
0
0
5
5
408.08
88.78
0.03
43.62
3.08
42.05
1
0
4.49
11.29
0
0
0
2
5
2423.28
112.08
0.04
58.96
4.43
48.65
Average
—
—
1.97
7.17
15.61
0
0.00
0.02
—
—
2007.95
210.44
0.09
154.61
8.01
47.73
“-”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.
