Schedule questions on the PMP rarely ask you to draw a full network. They test whether you understand what the critical path is and what float means when something slips. One worked example covers almost everything you need.
The key ideas
- The critical path is the longest path through the network. It sets the shortest possible project duration.
- Total float is how long an activity can slip without delaying the project finish.
- Free float is how long an activity can slip without delaying the next activity's early start.
- Activities on the critical path normally have zero total float.
The network
A small project has six activities:
| Activity | Duration (days) | Depends on |
|---|---|---|
| A | 3 | Start |
| B | 4 | A |
| C | 2 | A |
| D | 5 | B |
| E | 3 | C |
| F | 2 | D and E |
Step 1: list the paths
There are two paths from start to finish:
- A → B → D → F = 3 + 4 + 5 + 2 = 14 days
- A → C → E → F = 3 + 2 + 3 + 2 = 10 days
The longest is A, B, D, F. That is the critical path, and the project takes 14 days.
Step 2: the forward pass
The forward pass gives each activity its early start (ES) and early finish (EF). Work from left to right: EF = ES + duration, and an activity starts when all its predecessors finish.
| Activity | ES | EF |
|---|---|---|
| A | 0 | 3 |
| B | 3 | 7 |
| C | 3 | 5 |
| D | 7 | 12 |
| E | 5 | 8 |
| F | 12 | 14 |
F waits for both D and E, so its ES is the later of the two: 12.
Step 3: the backward pass
The backward pass gives each activity its late finish (LF) and late start (LS). Work from right to left: LS = LF − duration, and an activity must finish before the earliest late start of its successors.
| Activity | LS | LF |
|---|---|---|
| F | 12 | 14 |
| D | 7 | 12 |
| E | 9 | 12 |
| B | 3 | 7 |
| C | 7 | 9 |
| A | 0 | 3 |
A feeds both B (LS 3) and C (LS 7), so A must finish by the earlier one: day 3.
Step 4: calculate float
Total float = LS − ES (or LF − EF) Free float = ES of the next activity − EF of this activity
| Activity | Total float | Free float |
|---|---|---|
| A | 0 | 0 |
| B | 0 | 0 |
| C | 4 | 0 |
| D | 0 | 0 |
| E | 4 | 4 |
| F | 0 | 0 |
The activities with zero total float are A, B, D and F, which confirms the critical path.
Now look at C and E. They share the same 4 days of total float, but only E has free float:
- If C slips by 1 day, E starts 1 day later, because C has no free float. The project still ends on day 14, because there is still 3 days of float on the path.
- If E slips by up to 4 days, nothing else moves at all.
That difference is exactly what the exam tests.
A typical exam question
An activity has total float of 4 days and free float of 1 day. It finishes 6 days late. Assuming no other changes to the network, which statement is correct?
Work it out in two steps:
- The successor is delayed by 6 − 1 = 5 days (the delay beyond free float).
- The project finish is delayed by 6 − 4 = 2 days (the delay beyond total float).
So the successor's early start slips 5 days and the project finish slips 2 days.
Day 0 or day 1?
Some textbooks start the first activity on day 1 instead of day 0. Then EF = ES + duration − 1, and every date shifts by one. The float values do not change, and that is what the questions ask about. Pick one convention and use it consistently.
Four more things to know
- Negative float means the schedule cannot meet an imposed date. The project is already late on paper.
- A near-critical path has very little float. Watch it closely, because a small delay can make it critical.
- There can be more than one critical path. More critical paths mean more schedule risk.
- To shorten the schedule, compress activities on the critical path. Crashing adds resources (more cost). Fast tracking overlaps activities (more risk). Shortening an activity that is not critical does not shorten the project.
Practice
Float questions are easy points once you separate the two kinds: free float protects the next activity, total float protects the project. For every other formula on the exam, see the PMP formulas cheat sheet, then try the free 30-question PMP quiz.