PMP Critical Path and Schedule Compression: A Worked Network

Where schedule math sits on the 2026 PMP

Scheduling is Process task 8 in PMI's 2026 Exam Content Outline (revised August 11, 2026, as checked on October 27, 2026). It expects a schedule that suits the delivery approach, estimates grounded in dependencies or story points and in past data, a baseline, and analysis when reality drifts from it. The outline names no formulas, so the method below follows the U.S. Government Accountability Office's Schedule Assessment Guide (GAO-16-89G), a public reference on critical path scheduling.

GAO defines the critical path as the longest continuous sequence of activities in a schedule. It sets the program's earliest completion date, and when no date constraints are imposed, critical activities have zero float, so a one-day slip on them moves the finish by one day.

The six-activity PMP practice network

The network is invented. Northgate Library, a fictional city library, is rolling out self-checkout kiosks. Durations are in working days, and every link is finish-to-start.

This page counts from day 0, so early finish = early start + duration. Some courses count from day 1 and subtract 1. Both conventions produce the same float and the same critical path.

Forward pass: early start and early finish

GAO describes the forward pass as adding durations through the network from the first day. Each activity's early start is the latest early finish among its predecessors.

1. A starts at 0 and finishes at 4.
2. B and C both start at 4. B finishes at 10 and C at 7.
3. D starts at 10 and finishes at 18. E starts at 7 and finishes at 14.
4. F needs both D and E, so it waits for the later one: early start 18, early finish 22.

The project takes 22 days.

Backward pass: late start, late finish, and float

The backward pass runs the other way. Start F with a late finish of 22 and subtract durations. Where an activity has two successors, its late finish is the earlier of their late starts. That rule matters for A, which feeds both B (late start 4) and C (late start 8), so A's late finish is 4.

Reading the critical path and float on the PMP

Two paths run through the network:

• A–B–D–F: 4 + 6 + 8 + 4 = 22 days, zero float, the critical path
• A–C–E–F: 4 + 3 + 7 + 4 = 18 days, 4 days of float

C and E share the same 4 days of total float, but their free float differs. GAO defines total float as how long an activity can slip before the program finish date moves, and free float as how long it can slip before its immediate successor moves. If C slips 2 days, E starts 2 days late (C has zero free float), but the project still finishes on day 22. If E slips 2 days, nothing downstream moves until the slip passes 4 days. GAO also notes that total float can be negative when a constraint date is earlier than the logic allows, which means time has to be recovered.

A common mistake is to treat "float" on one activity as if it belonged to that activity alone. C and E sit on the same path, so if C uses all 4 days, E has none left.

After you can rebuild this table from the activity list alone, change two durations and work it again to check that the method holds when the numbers change. Network math rewards repetition, and full PMP prep, still being built, plans a Redemption challenge that brings back the questions you missed.

Crashing vs fast tracking the PMP network

Now suppose the library board needs the kiosks live in 19 days, three days sooner. GAO's table of recovery techniques describes the two classic options. Crashing adds resources to finish activities faster, which raises cost and can lower quality. Fast tracking turns sequential work into partly parallel work, for example finish-to-start into start-to-start, which can overload people and adds risk.

Crashing options for Northgate (invented costs):

The crashing answer. Crash only critical activities, cheapest first. E is cheapest but has float, so money spent there buys no time. Crashing D by 3 days costs 3 × $1,500 = $4,500 and brings A–B–D–F to 4 + 6 + 5 + 4 = 19 days. The other path is 18 days, so C and E now have only 1 day of float.

Going one more day, to 18, would cost the next cheapest critical option: 1 day of B for $2,000, a total of $6,500. Both paths would then be 18 days long and both would be critical, so any slip anywhere delays the finish. A good answer mentions that rise in risk, not only the cost.

The fast-tracking answer. Instead of paying, the team could start the catalog integration (D) 3 days before the database configuration (B) is finished. A–B–D–F becomes 22 − 3 = 19 days with no added labor cost. The price is rework risk: if the database design changes during those 3 days, part of D has to be redone.

Which one a question expects depends on the constraint in the stem. A fixed budget with some appetite for risk points to fast tracking. A fixed date with funding available and little tolerance for rework points to crashing. Either way, GAO treats the critical path as the guide to which activities deserve management attention, and shortening an activity off that path does not move the finish date. One of the 20 free PMP practice questions asks you to crash a small network, so you can test this right away. For volume later, the PMP page lists the Process bank of more than 1,100 questions planned for launch.

Agile counterparts: velocity and a release burn-up

In adaptive work the same question, "when will we finish?", is answered from velocity rather than a network. Task 8 explicitly includes story points as an estimating unit.

Suppose a team's last three two-week iterations delivered 18, 22 and 20 story points, an average of 20, with 120 points left in the release backlog. At 20 points per iteration that is 120 ÷ 20 = 6 iterations, about 12 weeks. Using the slowest recent iteration (18 points) gives 6.7, so 7 iterations. A sound forecast gives the range, 6 to 7 iterations, rather than one date.

A release burn-up chart shows the same picture with two lines: completed points climbing toward a scope line. When the scope line rises because stakeholders added work, the gap widens even though the team is delivering, which is the agile equivalent of a schedule variance caused by scope growth.

For questions that mix a fixed milestone with iterative delivery, see how the PMP frames agile and hybrid questions. Cost-side tracking of the same project is in the PMP earned value guide, and the full set of planning and control tasks is in the PMP Process domain overview. When crashing vs fast tracking feels automatic, check your speed in context, since schedule items on the exam sit among questions from every domain. The PMP page describes a full-length mock, planned for launch, that follows practice in all three domains, and any long mixed set does the same job meanwhile.