Slack LS ES Slack LF EF For nodes with one entering arrow ES EF of the entering

# Slack ls es slack lf ef for nodes with one entering

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Slack = LS – ES Slack = LF – EF For nodes with one entering arrow ES = EF of the entering arrow For activities leaving nodes with multiple entering arrows ES = the largest of the largest entering Early start (ES) Early finish (EF Late Start (LS) Late Finish (LF) L a r g e r v a l u e L a r g e r v a l u e Smaller EF = ES + t LS = LF - t
3 1 7/819 Three recent college graduates have formed a partnership and have opened an advertising firm. Their first project consists of activities listed in the following table. Immediate Time in Days Activity Predecessor Optimistic Most Likely Pessimistic A - 5 6 7 B - 8 8 11 C A 6 8 11 D - 9 12 15 E C 5 6 9 F D 5 6 7 G F 2 3 7 H B 4 4 5 I H 5 7 8 End E,G,I Start 8 7 6 5 4 3 2 I B D A G H F C E End t e 6 8.5 8.17 12 6.33 6 3.5 4.17 6.83 6 4 p m o e t t t t + + = Path Expected Duration A-C-E 6+8.17+6.33=20.50 D-F-G 12+6+3.5=21.50 B-H-I 8.5+4.17+6.83=19.50 The precedence diagram = path on the activities of times expected of mean Path
4 b. What is the probability that the project can be completed in 24 days or less ? 7/819 Immediate Time in Days Activity Predecessor Optimistic Most Likely Pessimistic A - 5 6 7 B - 8 8 11 C A 6 8 11 D - 9 12 15 E C 5 6 9 F D 5 6 7 G F 2 3 7 H B 4 4 5 I H 5 7 8 End E,G,I t e 6 8.5 8.17 12 6.33 6 3.5 4.17 6.83 ( 29 ( 29 69 . 0 6 6 11 25 . 0 6 8 11 2 2 2 2 = - = = - = C B σ σ Variance 0.111 0.250 0.694 1.000 0.444 0.111 0.694 0.028 0.250 Expected Standard Path Duration Variance Deviation A-C-E 20.5 0.111+0.694+0.444=1.249 1.118 D-F-G 21.5 1.000+0.111+.694=1.805 1.344 B-H-I 19.5 0.250+.028+0.250=0.528 0.726 ( 29 = path on activities of Variances path σ deviation standard

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