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Question
Construct the network for the project whose activities are given below.
| Activity | 0 - 1 | 1 - 2 | 1 - 3 | 2 - 4 | 2 - 5 | 3 - 4 | 3 - 6 | 4 - 7 | 5 - 7 | 6 - 7 |
| Duration (in week) | 3 | 8 | 12 | 6 | 3 | 3 | 8 | 5 | 3 | 8 |
Calculate the earliest start time, earliest finish time, latest start time and latest finish time of each activity. Determine the critical path and the project completion time.
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Solution
E1 = 0 + 3 = 3
E2 = E1 + t12 = 8 + 3 = 11
E3 = 3 + 12 = 15
E4 = 15 + 3 = 18
E5 = E2 + 3 = 11 + 3 = 14
E6 = E3 + 8 = 15 + 8 = 23
E7 = E6 + 8 = 23 + 8 = 31
L7 = 31
L6 = L7 – 8 = 31 – 8 = 23
L5 = L7 – 3 = 31 – 3 = 28
L4 = L7 – 5 = 31 – 5 = 26
L3 = L6 – 8 = 23 – 8 = 15
L2 = L5 – 3 or L4 which is minimum
= (28 – 3) or (26 – 6)
= 25 or 20
= 20 (which is minimum)
L1 = L2 – 8 or L3 – 12
whichever is minimum
= (20 – 8) or (15 – 12)
= 12 or 3
= 3
L0 = 0
| Activity | Duration tij |
EST | EFT = EST + tij | LST = LFT – tij | LFT |
| 0 - 1 | 3 | 0 | 3 | 3 | 3 |
| 1 - 2 | 8 | 3 | 11 | 20 – 8 = 12 | 20 |
| 1 - 3 | 12 | 3 | 15 | 15 – 12 = 3 | 15 |
| 2 - 4 | 6 | 11 | 17 | 26 – 6= 20 | 26 |
| 2 - 5 | 3 | 11 | 14 | 28 – 3 = 25 | 28 |
| 3 - 4 | 3 | 15 | 18 | 26 – 3 = 23 | 26 |
| 3 - 6 | 8 | 15 | 23 | 23 – 8 = 15 | 23 |
| 4 - 7 | 5 | 18 | 23 | 31 – 5 = 26 | 31 |
| 5 - 7 | 3 | 14 | 14 | 31 – 3 = 28 | 31 |
| 6 - 7 | 8 | 23 | 31 | 31 – 8 = 23 | 31 |
The critical path is 0 - 1 - 3 - 6 - 7 and the project completion time is 31 weeks.
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