Concept · under Schedule management
Critical path, float and schedule compression for the PMP® exam
The critical path is the longest chain of dependent activities through the schedule network, and its length is the shortest time the project can take. Activities on it have no float, so a day lost on any of them is a day lost at the finish. Everything else on this page builds on that: which kind of float an activity has, and what you give up when you compress the schedule.
- Exam
- PMP
- Domain
- Process
- Domain weight
- 41%
- Packages
- 9
- Updated
- Oct 13, 2026
01Why the longest path sets the date
A network finishes when its last chain of dependencies finishes. Shorter paths wait for it, and the time they can wait is their float. Shorten an activity that is not on the critical path and the end date stays where it was; you have only added float to an activity that already had some.
The durations come from estimates. When an estimate is shaky, three-point estimating gives an expected duration and a spread, and that expected value is what goes into the forward pass. The rest of schedule planning, from baselines to leveling, sits in schedule management.
02A small network drawn as bars
03Total float and free float, side by side
| Activity | Early start–finish | Late start–finish | Total float | Free float |
|---|---|---|---|---|
| Survey | 0–4 | 0–4 | 0 | 0 |
| Design | 4–9 | 4–9 | 0 | 0 |
| Permit | 4–10 | 6–12 | 2 | 2 |
| Order equipment | 9–12 | 9–12 | 0 | 0 |
| Write manuals | 9–11 | 12–14 | 3 | 0 |
| Train users | 11–13 | 14–16 | 3 | 3 |
| Install | 12–16 | 12–16 | 0 | 0 |
| Go-live | 16–17 | 16–17 | 0 | 0 |
Total float = late start − early start (or late finish − early finish): how far an activity can slip before the project finish moves. Free float = the earliest early start among its successors − its own early finish: how far it can slip before the next activity moves. Write manuals shows the difference: three days of slack for the project, none for Train users. Courses that start the first activity on day 1 shift every date by one; the float values come out the same.
04Two ways to buy back time
| Point | Crashing | Fast-tracking |
|---|---|---|
| ≠What you do | Add resources to critical activities: people, overtime, equipment | Overlap activities that were planned to run in sequence |
| ≠What it costs | Money, straight away | Risk of rework, because the later activity starts on unfinished inputs |
| ≠Where it works | Activities whose duration really shrinks with more effort | Discretionary dependencies, where the order was a preference |
| ≠Where it fails | Work that cannot be split, such as curing concrete or a supplier's lead time | Mandatory dependencies, such as testing a build that does not exist yet |
| Which activities | Critical path only | Critical path only |
≠ marks a row where the two differ. Compressing one path can promote another. Cut Install in the example from 4 days to 1 and the finish moves to day 14, where the Write manuals and Train users chain becomes critical as well; any further saving now has to shorten both paths.
05Walk the network
Dependency tables, float and compression choices, all built on the network logic above.
Work packages 9
WP 01In a marketing campaign, the strategy development phase has an early start of 9, an early finish of 12, and a late start of 16. What is the float for this phase?
Debrief answer to open the notes
- A10 does not follow from any float formula with these values.
- B3 is the duration (EF − ES), not the float.
- CCorrect: total float = LS − ES = 16 − 9 = 7.
- D5 matches no float formula with the given dates.
WP 02A project manager is analyzing which route through the project network will take the longest to complete. Which method is being used?
Debrief answer to open the notes
- APDM draws activity dependencies but does not by itself compute the longest path.
- BResource leveling adjusts dates for resource limits, not to find the longest path.
- CCorrect: the critical path method identifies the longest path through the network, which sets the shortest possible project duration.
- DPERT estimates activity durations from three points; it does not identify the longest route.
WP 03A project manager needs to determine which project activities can be delayed without affecting the project end date. Which scheduling technique should be used?
Debrief answer to open the notes
- ACritical chain manages resource-constrained schedules with buffers; it is not the technique for checking activity slack.
- BResource leveling changes dates to fit resources rather than showing allowable delay.
- CCorrect: float analysis shows how long each activity can slip; an activity can be delayed by its total float without moving the end date.
- DMonte Carlo shows the range of outcomes, not each activity's allowable delay.
WP 04A project is two weeks behind schedule. The sponsor demands immediate corrective action without exceeding the tight budget. Reviewing the schedule network, the project manager notes several parallel paths, but only one is critical. What is the most appropriate schedule compression approach?
Debrief answer to open the notes
- ACorrect: compression only helps on the critical path, and fast-tracking adds little direct cost, which suits a tight budget if dependency risks are checked.
- BCrashing every activity spends money on non-critical paths that cannot shorten the project.
- CAdding resources to non-critical tasks does not recover any time on the critical path.
- DFast-tracking non-critical work adds risk without shortening the project.
WP 05During a project with a fixed deadline, the critical path activities are taking longer than planned. If additional resources are available, which schedule compression technique should the project manager implement?
Debrief answer to open the notes
- AResource leveling resolves overallocation and often extends the schedule.
- BCorrect: crashing adds resources to critical-path activities to shorten them, which fits when extra resources are available.
- CFast tracking could also help, but it adds rework risk and does not use the available resources.
- DLeads and lags fine-tune logic but are not the main compression technique here.
WP 06The project must recover five days with minimal added cost. Which sequence of compression techniques is most appropriate?
Debrief answer to open the notes
- AFast-tracking everything regardless of risk invites rework that can cost more time than it saves.
- BMoving the finish date first gives up before trying techniques within the project's control.
- CCutting scope first is a bigger trade-off than needed and requires approval.
- DCorrect: use the cheapest options first: safe overlaps, then added resources, and negotiate scope only if time is still short.
WP 07You are managing the production of a new product which involves several dependent steps, each with a specific duration. Analyze the table below and determine the critical path for completing the entire manufacturing process.
Step Dependencies Duration (Days) Step A 3 Step B A 5 Step C A 4 Step D B 2 Step E B, C 3 Step F C 1 Debrief answer to open the notes
- AA-C-F totals 3 + 4 + 1 = 8 days; it is the shortest path, not the longest.
- BD depends on B, not C, so A-C-D is not a path in this network.
- CA-B-D totals 3 + 5 + 2 = 10 days, one day shorter than A-B-E.
- DCorrect: A-B-E = 3 + 5 + 3 = 11 days, the longest path; A-B-D is 10, A-C-E is 10 and A-C-F is 8.
WP 08Based on the provided network logic table, identify the critical path and its total duration.
Activity Predecessor(s) Duration (days) Modifier (Lead/Lag) A None 5 None B A 4 None C A 6 FS + 2 days (Lag) D B 5 FS - 1 day (Lead) E C 4 None F D, E 3 None Debrief answer to open the notes
- A18 days ignores C's 2-day lag; the lag adds waiting time to the path, so it must be counted.
- BCorrect: A ends day 5, C runs days 7-13 after the lag, E ends day 17, F day 20: 5 + 2 + 6 + 4 + 3 = 20.
- CA-B-D-F is 5 + 4 - 1 + 5 + 3 = 16 days with D's lead, shorter than A-C-E-F.
- DD follows B, not C, so A-C-D-F is not a path in this network.
WP 09All activities listed in the table are on the project's single critical path. What is the most cost-effective strategy to accelerate the schedule by exactly two weeks, and what is the incremental cost?
Activity Normal Duration Crash Duration Normal Cost Crash Cost Activity A 4 weeks 3 weeks $10,000 $14,000 Activity B 5 weeks 3 weeks $20,000 $26,000 Activity C 3 weeks 2 weeks $15,000 $21,000 Activity D 6 weeks 5 weeks $30,000 $32,000 Debrief answer to open the notes
- AC costs $6,000 per week and B $3,000, so this spends $9,000 when cheaper weeks are available.
- BCorrect: slopes per week are A $4,000, B $3,000, C $6,000, D $2,000. Crash D one week ($2,000) and B one week ($3,000) = $5,000.
- CA at $4,000 a week is pricier than B at $3,000, so this costs $6,000 instead of $5,000.
- DA and C are two of the steeper slopes; $4,000 + $6,000 = $10,000 for the same two weeks.
Open a row to answer. Keys: 1–4 or A–D answer, N opens the next row.
06Questions about float and the critical path
Can a project have more than one critical path?
Yes. When two paths tie for the longest duration, both are critical and a delay on either moves the finish. More critical paths mean more schedule risk, because there are more places where a slip hurts.
Can float be negative?
Yes, once the schedule runs past an imposed finish date. Negative total float tells you how many days that path must recover to meet the date, and it is a signal to compress or renegotiate.
Is the critical path where the most important work is?
Importance has nothing to do with it. The critical path is the longest path by duration. A minor activity with zero float is critical; a high-stakes activity with ten days of float is not.
What replaces the critical path on agile projects?
Iterations are timeboxed, so the date tends to be fixed while scope flexes, and the release forecast comes from the team's velocity instead of a forward pass. That side is covered in story points, velocity and burn charts.