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.
1. To compute the earliest start time (ES) and latest finish time (LF) for each event, we will use the Forward Pass and Backward Pass methods.
Forward Pass (ES Calculation):
Start by assigning an initial ES of 0 to the first event (Event 1-2). Then, for each subsequent event, calculate the ES by taking the maximum of the EF (Earliest Finish) of the preceding events.
Activity Time (Weeks) ES EF (ES + Time)
1-2 4 0 4
1-3 1 0 1
2-4 1 4 5
3-4 1 1 2
3-5 6 2 8
4-9 5 5 10
5-6 4 8 12
5-7 8 8 16
6-8 1 12 13
7-8 2 16 18
8-10 5 13 18
9-10 7 10 17
Backward Pass (LF Calculation):
Start by assigning an initial LF value of the EF of the last event (Event 9-10), which is 17. Then, for each preceding event, calculate the LF by taking the minimum of the LS (Latest Start) of the subsequent events.
Activity Time (Weeks) LF (EF in Backward Pass)
9-10 7 17
8-10 5 12
7-8 2 10
6-8 1 8
5-7 8 10
5-6 4 6
4-9 5 6
3-5 6 2
3-4 1 1
2-4 1 0
1-3 1 0
1-2 4 0
2. To compute the Total Float and Critical Path, we can use the formula:
Total Float (TF) = LF - EF
Critical Path = Activities with TF = 0
Activity Time (Weeks) TF (LF - EF) Critical Path?
9-10 7 0 Yes
8-10 5 0 Yes
7-8 2 0 Yes
6-8 1 0 Yes
5-7 8 0 Yes
5-6 4 0 Yes
4-9 5 1 No
3-5 6 0 Yes
3-4 1 0 Yes
2-4 1 0 Yes
1-3 1 0 Yes
1-2 4 0 Yes
The critical path includes all the activities with a Total Float of 0. In this case, all the activities are part of the critical path.