Critical Path Method and Schedule Calculation
This domain tests the forward and backward pass, float calculation, critical path identification, and interpretation of multiple or negative-float paths. CAPES questions often require you to calculate ES, EF, LS, LF, total float, and free float from a small network, then explain what the result means. The exam also checks whether you understand that the critical path is the longest path with the least total float, not simply the path with the most activities.
Calculation rules
- Forward pass: ES = maximum EF of predecessors; EF = ES + duration. Use the activity calendar.
- Backward pass: LF = minimum LS of successors; LS = LF − duration. The project finish sets the final LF.
- Total float = LS − ES = LF − EF. Free float = earliest successor ES − activity EF.
- Critical activities have the minimum total float in the network. Multiple critical paths are possible.
- Constraints can force dates and produce negative float; negative float indicates the plan cannot meet an imposed date without change.
Worked example
Network: A (2 days) precedes B (3 days) and C (4 days); B and C precede D (2 days); D precedes E (3 days). Paths: A–B–D–E = 2+3+2+3 = 10 days; A–C–D–E = 2+4+2+3 = 11 days. Critical path is A–C–D–E. Forward pass: A 0–2; B 2–5; C 2–6; D 6–8; E 8–11. Backward pass: E 8–11; D 6–8; C 2–6; B 3–6; A 0–2. Total float: B = 1 day; all others = 0. Free float of B = D's ES 6 − B's EF 5 = 1 day. If B slips two days, it becomes critical and pushes D and E by one day.
Traps that cost marks
Calling the longest path critical when a constraint creates a shorter negative-float path; ignoring multiple calendars; forgetting that free float uses only the earliest successor; and treating total float as owned by one activity. Float belongs to the path, and consuming it on one activity can affect every activity sharing that path.