Consider the following project:
Task ID | Duration (Days) | Predecessors |
2 | 70 | - |
3 | 30 | 2 |
4 | 120 | 3 |
5 | 120 | 2 |
6 | 120 | 5 |
7 | 120 | 3,6 |
8 | 150 | 3,6 |
9 | 115 | 3,6 |
10 | 130 | 7,9 |
11 | 90 | 7,9 |
12 | 30 | 7,9 |
13 | 120 | 7,9 |
14 | 75 | 10 |
15 | 30 | 14 |
16 | 85 | 6 |
17 | 165 | 16 |
18 | 90 | 16 |
19 | 90 | 17,18 |
20 | 20 | 8,11,13,15,19 |
What is the slack for task 8?
Answer:
step 1 | find early start, and early finish from the start of the project for each activity | ||||
step 2 | Find Maximum EF and keep it as the LF of last activities. Max of EF's is 685 | ||||
step 3 | calculate LS for each activity after calculating its EF |
Activity | Duration, D | Early start, ES=Max of early finish of preceding activities | Early finish, EF = ES + D | Late finish, LF= Min of LS of successor activities | Late start, LS= LF - D | Total slack= LF-EF |
2 | 70 | 0 | 70 | |||
3 | 30 | 70 | 100 | |||
4 | 120 | 100 | 220 | |||
5 | 120 | 70 | 190 | |||
6 | 120 | 190 | 310 | |||
7 | 120 | 310 | 430 | |||
8 | 150 | 310 | 460 | 665 | 515 | 205 |
9 | 115 | 310 | 425 | |||
10 | 130 | 430 | 560 | |||
11 | 90 | 430 | 520 | |||
12 | 30 | 430 | 460 | |||
13 | 120 | 430 | 550 | |||
14 | 75 | 560 | 635 | |||
15 | 30 | 635 | 665 | |||
16 | 85 | 310 | 395 | |||
17 | 165 | 395 | 560 | |||
18 | 90 | 395 | 485 | |||
19 | 90 | 560 | 650 | |||
20 | 20 | 665 | 685 | 685 | 665 | 0 |
the slack for task 8 is 205
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