Network diagram:
Forward Pass:
ES of the starting activities = 0
ES of all other activities = Max. (EF of their immediate
predecessors)
EF of an activity = Its ES + Its duration
Backward Pass:
LF of ending activities = Max. (All the EFs)
LF of all other activities = Min. (LS of their immediate
successors)
LS of an activity = Its LF - Its duration
Total slack (or, float) = LF - EF for each activity.
Activity | Duration | ES | EF | LS | LF | Slack |
A | 2 | 0 | 2 | 7 | 9 | 7 |
B | 6 | 2 | 8 | 41 | 47 | 39 |
C | 9 | 0 | 9 | 0 | 9 | 0 |
D | 5 | 0 | 5 | 14 | 19 | 14 |
E | 10 | 9 | 19 | 9 | 19 | 0 |
F | (5+4*7+15)/6 = 8 | 19 | 27 | 19 | 27 | 0 |
G | 4 | 19 | 23 | 37 | 41 | 18 |
H | 6 | 27 | 33 | 41 | 47 | 14 |
I | 8 | 27 | 35 | 27 | 35 | 0 |
J | 8 | 27 | 35 | 27 | 35 | 0 |
K | (7+4*11+21)/6 = 12 | 35 | 47 | 35 | 47 | 0 |
So, there are two critical paths - C-E-F-I-K and C-E-F-J-K both having expected duration = 47 weeks
So, the expected completion time for the project is 47 weeks.
For probability calculation, take the critical path having a higher variance. This is the path C-E-F-J-K.
Activity | E(t) | σ2 |
C | 9 | (11 - 7)2/36 = 0.4444 |
E | 10 | 4 |
F | 8 | 2.7778 |
J | 8 | (12 - 4)2/36 = 1.7778 |
K | 12 | 5.444 |
Totals | 47 | 14.444 |
So,
Mean duration = 47 weeks
Stdev = SQRT(14.444) = 3.8 weeks
Traget=50 weeks, so, z = (50 - 47)/3.8 = 0.789. F(z) = 0.785. So, there is a 78.5% chance that the project will be completed by 50 weeks
Target=45 weeks, so, z = (45 - 47)/3.8 = -0.5263. F(z) = 0.30. So, there is a 30% chance that the project will be completed by 45 weeks and a 70% chance that it takes more than 45 weeks.
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