Forward pass: ES + duration = EF; ES of a following activity is the max EF of predecessors. Backward pass: LS = LF − duration. Total float is the time an activity can slip without delaying the project. Free float is slip without delaying a successor’s ES.
ES,EF
Early start / early finish
LS,LF
Late start / late finish
TF(days)
Total float
Step-by-step solved example
Activity C: predecessors A (EF=4) and B (EF=6), duration 5, project LF through C is 14. Find ES, EF, LS, TF.
Activity-on-node: TF = LS − ES. Critical when TF = 0.
1. Forward
ES = max(4,6) = 6. EF = 11.
2. Backward
LF = 14, LS = 9. TF = 9 − 6 = 3 d.
TF=3d
Answer: ES=6, EF=11, LS=9, TF=3 d
10 practice questions
0/10 correct
1.A critical activity has
2.Project duration equals
3.Free float is always
4.Crashing a project means
5.FS relationship means
6.ES = 10, duration = 4. EF =
7.If all paths but one have float, the critical path is