Scheduling and Critical Path
Building the schedule
A schedule network is built from activities, durations and dependencies. Forward pass computes earliest start (ES) and earliest finish (EF); backward pass computes latest start (LS) and latest finish (LF). Float (slack) = LS − ES = LF − EF. Total float is the delay possible without moving the project finish; free float is the delay possible without moving the earliest start of any successor.
Critical path
Activities with zero total float form the critical path - the longest path through the network, which sets the project duration. A project can have more than one critical path. Delaying any critical activity delays the finish; delaying a non-critical activity beyond its float also makes it critical. The critical chain additionally accounts for resource contention and buffers.
Traps in questions
- Confusing total float and free float; a task can have free float but zero total float only if successors are also critical - check the arithmetic.
- Assuming the shortest path is critical; it is the longest.
- Forgetting that a lag on a critical link extends the path.
- Thinking float is a safety margin to be consumed silently; it should be managed.
Rule of thumb
Critical path = path with zero total float = longest duration path. Recompute after any duration, dependency or calendar change; the path can move.
Worked example: A(3)→B(5)→D(2) totals 10 days; A(3)→C(4)→D(2) totals 9 days. The critical path is A-B-D at 10 days. C has total float of 1 day. If C slips 2 days, its path becomes 11 days and the critical path shifts to A-C-D.