Table 1
PD for small instances.
Table 2
PD for midsize instances.
Table 3
PD for large instances.
Table 4
Average number of iterations in instances.
Table 5
Time (in months) to complete projects based on number of professionals.
Table 6
Costs of employee i in project j.
Table 7
Time penalty in relation to professional know-how in project j.
Table 8
Time penalty in relation to shared professional i.
Table 9
Human resource allocation in the first scenario.
Table 10
Human resource allocation in the second scenario.
Instance
Problem Size (NE x n)
Cbc
GS
GA
PIO
ILS Best
Average
σ
Time (s)
Optimal
Time (s)
Value
Time (s)
Best
Average
σ
Time (s)
Best
Average
σ
Time (s)
l1
5x3
105,43
6,20E-03
107,21
1,79E-06
105,43
105,9
0,486
2,99E-04
105,43
106,61
1,456
1,24E-04
105,43
105,6
0,12
1,33E-05
l2
5x5
174,01
7,80E-03
176,08
4,26E-06
174,01
174,75
0,748
3,67E-04
174,74
177,77
1,74
1,59E-04
174,01
174,05
0,125
2,99E-05
l3
5x10
311,84
1,71E-02
313,84
1,18E-05
312,19
315,47
2,459
5,74E-04
319,52
324,57
4,037
2,49E-04
311,84
312,69
0,605
9,59E-05
l4
5x15
560,28
1,86E-02
562,57
2,68E-05
562,81
567,46
3,959
8,43E-04
588,38
602,56
8,62
3,57E-04
560,28
560,87
0,908
2,05E-04
l5
10x3
111,28
1,39E-02
111,83
6,54E-06
111,28
114,68
2,527
3,93E-04
118,3
127,56
5,313
1,69E-04
111,28
111,44
0,265
4,12E-05
l6
10x5
150,65
2,00E-02
150,65
1,24E-05
151,12
154,11
2,928
5,34E-04
160,44
168,41
6,96
2,38E-04
150,65
150,65
0
9,42E-05
l7
10x10
308,66
3,87E-02
312,74
4,16E-05
310,58
314,44
2,751
1,09E-03
335,6
356,13
13,061
4,39E-04
309,38
310,47
0,919
3,65E-04
l8
10x15
598,93
2,44E-02
603,36
9,24E-05
599,61
601,97
1,583
1,91E-03
658,89
680,57
11,004
6,08E-04
598,93
599,36
0,462
8,82E-04
l9
15x3
88,04
4,21E-02
88,04
1,39E-05
91,62
97,36
3,792
4,72E-04
106,43
117,76
7,843
2,29E-04
88,04
88,04
0,004
7,95E-05
l10
15x5
200,89
9,53E-02
201,28
2,86E-05
202,84
208,12
3,953
7,86E-04
233,71
239,88
5,889
3,35E-04
200,89
201,09
0,156
2,12E-04
l11
15x10
320,19
8,44E-02
322,47
7,57E-05
326,68
331,05
4,309
1,71E-03
420,73
447,56
12,63
6,45E-04
320,84
321,92
0,496
8,23E-04
l12
15x15
561,54
1,52E-01
567,09
1,55E-04
565,97
568,84
1,888
3,06E-03
714,23
740,85
19,118
9,19E-04
563,11
564,17
1,02
1,86E-03
l13
20x3
109,35
1,13E-01
110,1
2,58E-05
114
117,69
3,009
6,18E-04
133,02
184,27
65,471
2,64E-04
109,35
109,98
0,232
1,56E-04
l14
20x5
160,75
2,33E-01
161,06
5,39E-05
163,51
170,48
3,957
9,77E-04
218,54
226,84
7,09
4,05E-04
160,75
161,01
0,107
3,74E-04
l15
20x10
360,19
3,41E-01
361,2
1,64E-04
363,96
370,07
4,993
2,69E-03
496,58
514,82
11,765
8,33E-04
360,19
360,76
0,38
1,58E-03
l16
20x15
534,29
4,71E-01
539,21
3,56E-04
538,44
543,06
3,339
4,48E-03
727,54
761,08
21,085
1,25E-03
534,29
536,6
1,29
3,49E-03
Instance
Problem Size (NE x n)
Cbc
GS
GA
PIO
ILS Best
Average
σ
Time (s)
Optimal
Time (s)
Value
Time (s)
Best
Average
σ
Time (s)
Best
Average
σ
Time (s)
m1
20x18
637,44
6,97E-01
640,58
4,84E-04
642,9
645,95
2,237
5,80E-03
899,99
930,94
21,034
1,38E-03
638,4
639,5
0,696
5,02E-03
m2
20x22
841,12
6,59E-01
847,11
6,97E-04
843,83
845,78
1,874
7,91E-03
1181,05
1240,39
31,69
1,65E-03
841,21
841,63
0,348
7,50E-03
m3
20x26
910,43
8,10E-01
918,9
9,16E-04
914,13
917,7
3,038
1,01E-02
1354,63
1404,43
22,194
1,95E-03
910,67
911,79
0,511
1,07E-02
m4
20x30
1103,88
1,05E+00
1112,23
1,32E-03
1107,29
1111,44
2,953
1,33E-02
1593,07
1786,28
397,441
2,53E-03
1104,31
1105,09
0,806
1,39E-02
m5
24x18
662,37
1,37E+00
667,62
6,53E-04
667,22
672,06
2,885
7,59E-03
1018,69
1054,28
26,375
1,64E-03
663,04
663,46
0,339
7,22E-03
m6
24x22
809,91
2,46E+00
815,05
8,94E-04
816,83
820,15
4,217
9,75E-03
1255,85
1307,02
29,958
2,13E-03
810,78
812,07
0,916
1,07E-02
m7
24x26
1043,88
3,07E+00
1051,03
1,35E-03
1048,97
1051,3
2,356
1,39E-02
1572,35
1624,62
37,8
2,63E-03
1044,45
1045,47
0,58
1,54E-02
m8
24x30
961,23
3,57E+00
967,19
1,50E-03
965,7
969,45
2,467
1,76E-02
1642,03
2118,22
559,623
2,79E-03
961,45
962,16
0,406
1,99E-02
m9
28x18
563,25
4,92E+00
567,47
6,41E-04
571,49
577,66
4,531
9,02E-03
1027,43
1087,07
36,961
1,87E-03
565,11
566,57
0,902
9,45E-03
m10
28x22
807,21
7,95E+00
810,3
1,13E-03
813,79
817,69
3,411
1,32E-02
1345,99
1498,13
313,215
2,61E-03
807,6
808,55
0,86
1,46E-02
m11
28x26
916,57
6,64E+00
921,87
1,61E-03
923,81
927,98
2,97
1,78E-02
1586,84
1715,82
60,223
2,82E-03
917,31
918,72
0,709
2,06E-02
m12
28x30
1002,99
1,04E+01
1010,12
2,18E-03
1008,68
1014,7
3,692
2,19E-02
1877,97
1917,66
26,318
3,24E-03
1004,11
1005,8
1,351
2,76E-02
m13
32x18
552,96
1,36E+01
556,71
9,05E-04
560,15
569,26
4,34
1,23E-02
1068,66
1205,5
237,805
2,46E-03
554,54
555,95
0,726
1,26E-02
m14
32x22
687,63
2,05E+01
691,63
1,35E-03
695,05
700,49
4,37
1,63E-02
1382,61
1428,91
27,712
2,72E-03
688,45
689,92
0,972
1,92E-02
m15
32x26
882,2
1,42E+02
887,09
1,90E-03
889,93
893,56
2,348
2,01E-02
1784,15
1847,19
44,946
3,50E-03
883,52
884,59
1,034
2,78E-02
m16
32x30
999,26
7,56E+02
1003,81
2,55E-03
1007,88
1012,71
4,321
2,73E-02
2016,41
2086,17
47,336
3,66E-03
1001,56
1001,97
0,332
3,54E-02
Instance
Problem Size (NE x n)
GS
GA
PIO
ILS Best
Σ
Time (s)
Value
Time (s)
Best
Average
Σ
Time (s)
Best
Average
Σ
Time (s)
Average
l1
50x20
647,6
2,43E-03
662,84
669,27
4,96
2,74E-02
1815,54
1883,98
44,443
3,81E-03
647,42
647,58
0,054
3,73E-02
l2
50x30
958,61
4,80E-03
972,11
980,52
4,673
6,17E-02
2806,04
2897,39
57,749
6,23E-03
957,84
958,34
0,302
8,38E-02
l3
50x40
1162,91
7,68E-03
1169,38
1188,29
10,994
9,42E-02
3847,68
3946,63
52,358
9,27E-03
1158,26
1159,36
1,234
1,55E-01
l4
50x50
1668,86
1,40E-02
1664,92
1672,75
5,418
1,60E-01
4864,78
4974,52
70,664
1,13E-02
1654,08
1656,46
1,127
2,40E-01
l5
100x20
494,43
7,02E-03
548,78
572,63
11,841
8,82E-02
3327,82
3828,87
462,153
8,45E-03
494,43
494,43
0
1,46E-01
l6
100x30
784,01
1,33E-02
830,39
845,8
17,039
2,01E-01
5318,98
5542,33
132,748
1,46E-02
784,01
784,01
0
3,30E-01
l7
100x40
1120,06
2,44E-02
1163,28
1176,34
9,735
3,61E-01
7350,05
7451,53
96,372
1,85E-02
1120,06
1120,06
0
6,09E-01
l8
100x50
1387,39
4,00E-02
1430,23
1441,53
10,327
5,63E-01
9517,15
9616,45
72,689
2,40E-02
1386,16
1387,25
0,389
9,71E-01
l9
150x20
464,39
1,35E-02
589,93
610,57
19,047
1,78E-01
5170,81
5532,44
158,098
1,50E-02
464,39
464,39
0
3,24E-01
l10
150x30
718,12
2,68E-02
815,95
827,32
8,47
4,34E-01
8133,02
8327,38
114,815
2,34E-02
718,12
718,12
0
7,72E-01
l11
150x40
1040,98
4,73E-02
1122,07
1142,54
16,823
7,60E-01
10726,66
11416,5
262,881
2,84E-02
1040,98
1040,98
0
1,37E+00
l12
150x50
1419,76
6,75E-02
1503,75
1519,47
12,97
1,20E+00
14750,99
15482,93
1001,286
3,67E-02
1419,76
1419,76
0
2,19E+00
l13
200x20
389,04
2,21E-02
567,43
589,33
13,53
3,07E-01
6914,72
7151,34
105,042
1,79E-02
389,04
389,04
0
5,94E-01
l14
200x30
685,35
4,44E-02
815,26
849,39
18,468
7,44E-01
11253,41
11463,24
159,847
3,16E-02
685,35
685,35
0
1,38E+00
l15
200x40
978,94
7,75E-02
1103,8
1131,97
20,987
1,28E+00
15194,58
15497,11
149,538
4,21E-02
978,94
978,94
0
2,44E+00