The four ideas answer different questions
Critical path identifies the dependency chain controlling the earliest finish. Float describes scheduling flexibility. Crashing evaluates extra cost against feasible time savings. Fast tracking overlaps work that was planned in sequence. Start with the network before choosing a recovery technique.
A five-day delay does not automatically cause a five-day project delay. First check the affected path, available float, dependencies and remaining work. A task with an important-sounding name is not necessarily critical; the calculation, not its label, establishes its schedule effect. Resource limits and imposed dates can also change the result.
Worked example: preparing an internal application release
This is an illustrative learning example, not a claimed customer incident. Assume finish-to-start dependencies, zero lag, one working calendar, unlimited resources and no imposed finish constraint. Times start at zero: a two-day activity beginning at time 0 finishes at time 2. Do not mix this convention with inclusive day-number calculations.
| Path | Duration | Result |
|---|---|---|
| A → B → D → F | 2 + 5 + 4 + 2 = 13 days | Critical path |
| A → C → E → F | 2 + 3 + 4 + 2 = 11 days | Two days shorter |
The earliest finish is 13 days, not 11. Both branches must be ready before F can begin. The training branch finishing sooner does not allow the release to bypass unfinished integration testing.
Calculate early dates, then late dates
- Forward pass: early start (ES) is the latest early finish among immediate predecessors. Early finish (EF) equals ES plus duration. F therefore starts at max(11, 9) = 11.
- Backward pass: start from the calculated project finish. Late start (LS) equals late finish (LF) minus duration. For a predecessor with several successors, use the earliest successor LS as its LF.
- Total float: calculate LS − ES, equivalently LF − EF under these assumptions.
- Free float: for this zero-lag network, use the earliest successor ES minus the activity EF. The terminal activity is measured against the finish milestone.
| Activity | Work | After | Days | ES | EF | LS | LF | TF | FF |
|---|---|---|---|---|---|---|---|---|---|
| A | Confirm requirements | Start | 2 | 0 | 2 | 0 | 2 | 0 | 0 |
| B | Build integration | A | 5 | 2 | 7 | 2 | 7 | 0 | 0 |
| C | Prepare training | A | 3 | 2 | 5 | 4 | 7 | 2 | 0 |
| D | Test integration | B | 4 | 7 | 11 | 7 | 11 | 0 | 0 |
| E | Review training | C | 4 | 5 | 9 | 7 | 11 | 2 | 2 |
| F | Release readiness | D, E | 2 | 11 | 13 | 11 | 13 | 0 | 0 |
Read row C carefully: ES 2, EF 5, LS 4 and LF 7. C can move two days later without changing the finish milestone, provided downstream work shifts within that same allowance. This is not two spare days for C plus another two spare days for E.
Total float protects the finish; free float protects the successor
C has total float 2 and free float 0. If C slips one day, E must start one day later. E then finishes at time 10, still before D finishes at 11, so F can retain its start at 11. The project finish is unchanged, but the training-review team needs a revised handoff.
E has free float 2 because it can finish at 11 instead of 9 without moving the early start of F. Float belongs to the connected project logic: consuming it can reduce flexibility available elsewhere. Discuss the effect with affected owners rather than treating it as personal spare time.
Zero total float identifies the critical activities in this unconstrained example. Real schedules may show negative float because of imposed dates, or use different calendar and criticality settings. Investigate the logic and constraints before interpreting every software flag as the same thing.
Crashing vs fast tracking: compare the trade-off
| Technique | Change | Watch for |
|---|---|---|
| Crashing | Pay for a feasible shorter duration | Cost, skill availability, coordination and diminishing returns |
| Fast tracking | Overlap work previously planned in sequence | Dependency limits, rework and quality risk |
A simple crashing calculation
Suppose B can reduce from five days at $5,000 to three days at $6,600. With a linear cost assumption, the incremental cost per day saved is ($6,600 − $5,000) ÷ (5 − 3) = $800/day. These are illustrative figures, not training fees or a project quotation.
Reducing B by two days makes its path 11 days. The other path is also 11 days, so there are now two critical paths. Shortening B again alone would not move the project finish: the training branch would still control it. Recalculate after each change. Consider work shared by both paths, or feasible changes on both branches, before spending more.
When overlap may help
In a different recovery option, the team might test a stable integration component while a separate component is still being built. This is fast tracking only if the partial handoff and dependency logic permit it. Starting testing against unstable interfaces can create repeated retesting. Document assumptions, quality gates and the effect on the finish date.
Adding people to work that cannot be divided may not shorten it. Skipping required testing is not a sound substitute for compression. Removing scope is a separate governance decision, not crashing or fast tracking.
A practical recovery decision sequence
- Validate status: confirm actual progress, remaining duration and the cause of the delay.
- Recalculate: identify critical and near-critical paths, float and resource conflicts.
- Compare options: estimate time saved, additional cost, rework exposure and effects on benefits or compliance.
- Get the right decision: follow agreed authority for spending, contractual commitments and baseline changes.
- Verify: check that the accepted option actually changes the forecast and monitor the new constraints.
Use the change-control guide when recovery changes controlled commitments. Use CPI, SPI and forecasting for complementary performance evidence; SPI alone does not tell you the exact calendar delay.
Four original practice questions—with reasoning
C has two days of total float. If C slips one day, is communication unnecessary?
No. C has zero free float, so E must start later even though the final finish remains unchanged. Coordinate the new handoff and confirm resource availability. The wrong assumption is that unchanged project finish means nobody else is affected.
A sponsor wants a one-day earlier finish. Should the team crash E because it is cheapest?
Not in the original network. E is not on the controlling path. Shortening E alone will not reduce the 13-day finish. First identify feasible changes on A–B–D–F, then compare their full trade-offs.
After B is reduced to three days, how much earlier does another one-day reduction to B finish the project?
Zero days in this network. A–C–E–F still lasts 11 days. Both paths must be addressed, or suitable shared work shortened, to finish earlier.
A team starts testing stable modules before all development finishes. Which technique is this?
Fast tracking. The work overlaps instead of waiting for the full predecessor activity. Check partial dependency validity and rework risk. Merely paying overtime without overlap would be a different option.
For broader preparation, continue to the detailed PMP course material, then use a free full-length PMP mock exam. These examples are independent learning exercises, not actual or recalled PMI exam questions.
Frequently asked questions
Is the critical path the longest or shortest path?
It is the longest-duration dependency path in the schedule network, establishing the earliest possible finish under the stated assumptions. It is not the path with the greatest number of activities.
Can total float be positive while free float is zero?
Yes. In the example, C has two days of total float but zero free float: delaying it moves the early start of E before it moves the project finish.
Does crashing always mean hiring more people?
No. It means evaluating feasible time–cost trade-offs to shorten the schedule. Extra skilled capacity, overtime or a faster supplier may be options, but only if they actually reduce the duration of work controlling completion.
Is fast tracking free?
Not necessarily. Overlapping work may avoid an immediate resource purchase, but it can introduce rework, coordination costs and quality risk. Compare the full effect rather than assuming it costs nothing.
Use the current exam outline, not a list of memorized formulas
PMI updated the PMP exam in July 2026. Use its current outline to define your preparation scope. This guide supports predictive schedule reasoning; it does not replace study of people, business value, agile or hybrid delivery, and no particular question is promised to appear.
Want guided preparation? Review PMP certification training or return to the PMP preparation hub to choose your next topic.
References
The calculation and practice scenarios above were created for this guide. The PMI scheduling library articles explain established methods; use the current PMI exam page for current exam requirements.