To compute the earliest start time (Es) and latest finish time (Lf) for each event, we can use the following steps:
Step 1: Create a table with all the activities and their corresponding time (weeks) values.
Activity Time (Weeks)
1-2 4
1-3 1
2-4 1
3-4 1
3-5 6
4-9 5
5-6 4
5-7 8
6-8 1
7-8 2
8-10 5
9-10 7
Step 2: Compute the Es and Lf values for each activity.
Start with the first activity, 1-2:
- Es: The earliest start time for activity 1-2 is 0 (since it is the first activity).
- Lf: The latest finish time for activity 1-2 is 4 (Es + Time = 0 + 4 = 4).
Continue with the remaining activities:
- Activity 1-3: Es = 0 (since it is dependent on activity 1-2), Lf = 1 + 4 = 5.
- Activity 2-4: Es = 4 (since it is dependent on activity 1-2), Lf = 4 + 1 = 5.
- Activity 3-4: Es = 5 (since it is dependent on activity 1-3), Lf = 5 + 1 = 6.
- Activity 3-5: Es = 5 (since it is dependent on activity 1-3), Lf = 5 + 6 = 11.
- Activity 4-9: Es = 6 (since it is dependent on activity 3-4), Lf = 6 + 5 = 11.
- Activity 5-6: Es = 11 (since it is dependent on activity 3-5), Lf = 11 + 4 = 15.
- Activity 5-7: Es = 11 (since it is dependent on activity 3-5), Lf = 11 + 8 = 19.
- Activity 6-8: Es = 15 (since it is dependent on activity 5-6), Lf = 15 + 1 = 16.
- Activity 7-8: Es = 19 (since it is dependent on activity 5-7), Lf = 19 + 2 = 21.
- Activity 8-10: Es = 16 (since it is dependent on activity 6-8), Lf = 16 + 5 = 21.
- Activity 9-10: Es = 11 (since it is dependent on activity 5-7), Lf = 11 + 7 = 18.
The computed Es and Lf values for each activity are as follows:
Activity Es Lf
1-2 0 4
1-3 0 5
2-4 4 5
3-4 5 6
3-5 5 11
4-9 6 11
5-6 11 15
5-7 11 19
6-8 15 16
7-8 19 21
8-10 16 21
9-10 11 18
To compute the total float and critical path, we can use the following steps:
Step 1: Calculate the total float for each activity using the formula:
Total Float = Lf - Es - Time
Step 2: Identify the critical path, which is the longest path with zero total float.
The calculated total float and critical path are as follows:
Activity Total Float Critical Path
1-2 0 Yes
1-3 4 No
2-4 0 Yes
3-4 0 Yes
3-5 0 Yes
4-9 0 Yes
5-6 0 Yes
5-7 5 No
6-8 0 Yes
7-8 2 No
8-10 0 Yes
9-10 7 No
The critical path consists of activities 1-2, 2-4, 3-4, 3-5, 4-9, 5-6, 6-8, and 8-10.
A project schedule has the following characteristics:
Activity Time (Weeks) Activity Time (Weeks)
1-2 4 5-6 4
1-3 1 5-7 8
2-4 1 6-8 1
3-4 1 7-8 2
3-5 6 8-10 5
4-9 5 9-10 7
1) Compute earliest start time (Es) and latest finish time (Lf) for each event.
2) Compute Total float and critical path.
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