Project Scheduling (Depth)
Concepts
Critical path method: activity-on-node networks, forward and backward pass, early and late dates, total float, free float, and multiple critical paths. Precedence logic includes finish-to-start, start-to-start, and lags. Resource leveling changes dates; resource smoothing may not. Crashing shortens the critical path at added cost; fast-tracking overlaps activities. Earned value schedule metrics (SPI, SV) complement CPM.
Traps
Total float is not free float; total float is shared along a path. A long-duration activity is not necessarily critical. Negative float means a constrained schedule. Lag is a duration, not a resource. Calendar days versus workdays. Multiple critical paths are common; crashing one path may not shorten the project.
Worked example
An activity has ES = 10, EF = 18, LS = 14, LF = 22. Total float = LS − ES = 14 − 10 = 4 days, also LF − EF. If its successor has ES = 20, free float = 20 − 18 = 2 days. The activity can slip 2 days without delaying the successor but 4 days before delaying the project.
Rule of thumb
If the critical path has no float, any delay on it delays completion day for day. To shorten a project, crash the critical path with the lowest cost per day saved; recalculate after each change because the critical path can shift.