Identifying the Critical Path

What the critical path is

It sounds backwards that the longest path gives the shortest possible duration — but that's exactly it: you can't finish until the longest chain of must-happen-in-order work is done. Every other path is shorter and therefore has slack. The critical path is the project's binding constraint on time.

The forward and backward pass

The CPM finds the critical path with two sweeps through the network. You don't have to do this by hand — the software does — but understanding it is what separates a planner from a button-pusher.

• Forward pass → work left to right. Compute each activity's Early Start (ES) and Early Finish (EF) — the soonest it can happen. EF = ES + duration; the next activity's ES is the latest EF of its predecessors. The largest EF at the end = the project duration.
• ← Backward pass work right to left from the end date. Compute each activity's Late Finish (LF) and Late Start (LS) — the latest it can happen without delaying the project. LS = LF − duration.

Float — the difference between paths

Off the critical path, activities have float (slack): time they can slip before causing a problem. Two kinds matter:

Find the critical path

What distorts the critical path

The CPM only finds the true critical path if the network is honest. Several things quietly corrupt it:

• Constraints — hard date constraints override the calculated path and can hide the real critical chain.
• Open ends — missing predecessors/successors break float calculations, so criticality is wrong.
• Excessive lags — long lags can sit on the critical path as invisible, unmanageable "work."
• Multiple calendars — mixing calendars can make float values look odd; understand why before trusting them.

Ten things to remember

1. The critical path is the longest chain — and its length is the shortest possible project duration.
2. Delay anything on it and the finish slips — everything else has slack.
3. Forward pass gives Early Start/Finish; backward pass gives Late Start/Finish.
4. Total Float = LS − ES = LF − EF — zero float marks the critical path.
5. Total float = slack before the project slips; free float = before the next activity slips.
6. "Critical" means zero float — not important or expensive.
7. The critical path can move — re-check it after any duration or logic change.
8. Constraints, open ends, big lags, and mixed calendars distort it — keep the network clean.
9. Watch near-critical paths too — a small slip turns them critical.
10. The critical path is the spine of delay analysis — Track 6 lives or dies on it.