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THE USE OF SIMULATED ANNEALING AND GENETIC ALGORITHMS
FOR A MULTI-MODE RESOURCE-CONSTRAINED PROJECT
SCHEDULING PROBLEM WITH DISCOUNTED CASH FLOWS

M. Seifi, R. Tavakkoli-Moghaddam & F. Jolai

Department of Industrial Engineering, Faculty of Engineering, University of Tehran
[email protected], [email protected], [email protected]
Abstract: This paper presents a multi-mode resource-constrained project scheduling problem (MRCPSP) with maximizing the net present value (NPV) form the project contractor’s point of view. Positive and negative cash flows are considered in this model. Furthermore, to make the model close to the real situations, four different models for positive cash flows are considered. Two meta-heuristics, called simulated annealing and genetic algorithms, are used in order to solve the proposed model of the forgoing problem. To schedule all activities, a bi-directional scheduling generation scheme (SGS) for the multi-mode version is proposed, and the activity list structure selects for presenting a permutation of activities. Finally, computational results for a set of test problems taken from the project scheduling problem library (PSPLIB) are presented and discussed.

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RR α
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2 1.25 0.05
3 1.50 0.01
4 1.50 0.05
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Problem Size Data Set Number of the best solution Best Objective Relative Gap Ave. (%) Absolute Gap Ave. (%) CPU Ave. (Sec.)
GA SA GA SA GA SA GA SA GA SA
j10 1
2
3
4 7*
7*
7*
6* 3
3
3
5 2907.3*
1084.5*
3978.1*
1621.39
* 2863.2 915.1
3933.0
1599.69 7.40* 2.90*
5.57*
5.14 8.33 6.96 7.62
1.33* 9.65* 4.31*
6.67*
1.10* 12.03 17.98
9.74
5.39 2.68* 2.69*
2.68*
2.69* 4.07 4.06 4.08
4.09
j12 1
2
3
4 9*
5*
8*
2 1
5
2
8* 3156.1* 705.6
4471.5*
1270.5 2967.8 725.8* 4203.8
1309.7* 7.31* 7.70
6.60*
2.58* 7.92
7.07*
6.70
6.41 7.54*
11.88* 7.54*
10.24* 13.56 12.77 12.96
10.89 3.59* 3.61*
3.58*
3.59* 5.73 5.72 5.72
5.72
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Problem Size Data Set Number of the best solution Best Objective Relative Gap Ave. (%) Absolute Gap Ave. (%) CPU Ave. (Sec.)
GA SA GA SA GA SA GA SA GA SA
j14 1
2
3
4 4
5*
10*
9* 6*
5*
0
1 3646.0*
1023.2*
5183.2*
1764.7* 3645.8 962.1
4883.1
1504.7 1.33*
4.04* 6.74
6.38* 6.71
14.89 6.14*
7.10 4.18* 8.63*
6.74*
7.31* 8.33
22.18 11.68
20.58 4.81* 4.80*
4.82*
4.82* 8.21 8.20 8.21
8.21
j16 1
2
3
4 5*
9*
7*
7* 5*
1
4
3 3379.6* 194.3*
4831.0*
604.9* 3347.1 -31.0
4715.1
508.6 5.61* 7.89
5.10*
5.83* 9.12
5.80* 5.94
10.56 8.32*
14.07
5.85*
8.48* 12.29 9.07* 8.92
16.66 7.86* 7.87*
7.87*
7.89* 12.54 12.54 12.58
12.54
j18 1
2
3
4 8*
9*
6*
4 2
1
4
6* 3800.2* 196.8*
5590.6*
782.6* 3601.6 -6.6
5407.0
701.3 8.32*
15.21 6.36*
19.87 8.62
5.45*
7.32
15.83* 9.08*
21.72 7.11*
30.32 14.32
8.18* 10.66
25.56* 11.07* 11.08*
11.06*
11.08* 18.20 18.16 18.15
18.17
j20 1
2
3
4 9*
9*
7*
5* 1
1
3
5* 4268.1* 473.7*
6106.7*
958.6 4056.3 87.0
5975.3 964.1* 9.14* 6.77
6.22*
10.15 9.33
4.95* 7.32
10.35 9.79* 9.15* 6.76*
8.92* 14.63 12.85 9.97
16.71 14.30* 14.32* 14.30*
14.31* 23.66 23.73 23.70
23.72

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Problem Size Data Set Number of the best solution Best Objective Relative Gap Ave. (%) Absolute Gap Ave. (%) CPU Ave.
(Sec.)
GA SA GA SA GA SA GA SA GA SA
j10 1
2
3
4 6*
8*
5*
8* 4
2
5*
2 3425.0*
2548.5*
4547.5*
3357.1* 3376.9
2440.7
4575.4
3239.2 5.18*
7.60
3.84*
5.05 6.64
6.55*
4.90
4.87* 6.05* 7.92* 4.86*
5.22* 8.49
10.28
5.45
8.05 2.68* 2.69* 2.68*
2.69* 4.07 4.06
4.08
4.09
j12 1
2
3
4 9*
8*
8*
5* 1
2
2
5* 3903.3*
2724.0*
5293.1*
3731.0* 3765.0
2652.6
5116.1
3712.7 6.18
6.05*
4.80
5.46* 5.09*
7.12
4.34*
7.46 6.49* 7.08* 5.58*
6.79* 8.79
10.38
8.08
9.25 3.59* 3.61* 3.58*
3.59* 5.73 5.72
5.72
5.72
j14 1
2
3
4 7*
10*
9*
6* 3
0
1
4 4577.6*
3304.9*
6184.1*
4430.6* 4458.0
3145.6
5973.2
4249.2 5.98* 6.35* 4.79*
5.07 7.76 7.73 5.34
4.93* 6.90* 6.43* 5.24*
6.33* 11.08 12.46
8.93
9.77 4.81* 4.80* 4.82*
4.82* 8.21 8.20 8.21
8.21
j16 1
2
3
4 7*
5*
6*
9* 3
5*
4
1 4741.4*
2738.6*
6433.7*
3785.8* 4620.9
2696.8
6360.9
3697.8 4.83 5.37
3.64*
4.75 4.35* 5.19*
4.27
3.60* 5.21* 6.18* 3.97*
4.96* 6.97 7.44 5.61
5.82 7.86* 7.87* 7.87*
7.89* 12.54 12.54 12.58
12.54
j18 1
2
3
4 5*
6*
6*
6* 5*
4
4
4 5284.0*
3284.3*
7225.0*
4509.1* 5153.6
3269.2
7161.6
4493.0 6.05* 4.95*
3.77*
4.57 6.52 7.53 4.54
5.40* 6.76* 7.64* 4.54*
6.04* 9.55 9.80
6.06
7.15 11.07* 11.08* 11.06*
11.08* 18.20 18.16 18.15
18.17
j20 1
2
3
4 7*
6*
7*
8* 3
4
3
2 5691.8*
3809.8*
7865.0*
5285.4* 5584.5
3716.3
7814.4
5024.4 5.82
6.75*
3.95*
5.77 5.61*
5.81
5.72
4.65* 6.43* 8.42* 4.93*
6.36* 7.87
10.04
7.24
9.61 14.30* 14.32* 14.30*
14.31* 23.66 23.73
23.70
23.72
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Sprecher, A., Kolisch, R., Drexl, A., “Semi-Active, Active, and Non-Delay Schedules for the Resource-Constrained Project Scheduling Problem”, European Journal of Operational Research, Vol. 80, 1995, PP. 94-102.

Icmeli, O., Erenguc, S.S., Zappa, C.J., “Project Scheduling Problems: A Survey”, International Journal of Operations and Production Management, Vol. 13, 1993, PP. 80-91.

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قیمت: تومان


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