Critical Path Method & PERT
The longest path sets the shortest time — and PERT is a probability, not a date
The Critical Path Method finds the longest chain of dependent activities — whose length is the shortest possible project time. A forward pass gives earliest times, a backward pass gives latest times, and their difference is the float; activities with zero float are critical. PERT handles uncertain work with three estimates, giving an expected time and a probability — not a guaranteed date. CPM is deterministic (1957, DuPont); PERT is probabilistic (1958, US Navy, Polaris).
Learning objectives
By the end of this lesson, you will be able to — mapped to the course outcomes for Project Management in Interior Design:
Run a forward and backward pass to find ES, EF, LS, LF, float and the critical path.
Explain PERT's three estimates, expected time and its probabilistic answer.
Distinguish CPM (deterministic) from PERT (probabilistic) and choose between them.
The critical path, and the two passes
The critical path is the longest chain of dependent activities — its length is the shortest possible project time. A forward pass (add durations) finds the earliest start and finish; a backward pass (subtract) finds the latest; their difference is the float, and zero float means critical.[1]
The longest chain rules the finish
The CRITICAL PATH METHOD (CPM) finds, in a network, the LONGEST chain of dependent activities from start to finish. That length is the SHORTEST possible time in which the whole project can be done — because every activity on it must happen in sequence, with no slack. This chain is the CRITICAL PATH, and its activities are CRITICAL: delay any one of them, and the whole project finishes late. Everything else in the project has some spare time. So managing a project is, above all, managing its critical path — protecting it, watching it, and knowing that time lost there is lost for the whole job. 'Longest path = shortest project time' is the paradox at the heart of scheduling.[1, 2]
Critical-path explorer · the longest chain sets the shortest time
A six-task interior fit-out. Change any duration (days) and watch the critical path and finish date shift.
Activity durations (days)
Project duration
14 days
Critical path: A → B → D → F — the longest chain, with zero float. Delay any of these and the whole project slips.
Float on the other work
- C Procure materials — 4 days float
- E Joinery & furniture — 4 days float
Float is flexibility — but spend a path’s float and it can turn critical.
Try it: push a non-critical task’s duration up until its float hits zero — the critical path jumps to it.
Float, honestly
Float (slack) is the spare time a non-critical activity has — legitimate flexibility, not wasted time. But float is a budget: spend a path’s float and it is gone, and consuming it can turn that path critical. Knowing where the float is, and where it is not, is knowing where a project is fragile.[1]
Flexibility, spent deliberately
FLOAT (or slack) is the spare time a non-critical activity has — how long it can be delayed without delaying the project (total float) or the next activity (free float). It is not WASTED time and it is not a mistake; it is legitimate scheduling FLEXIBILITY, and a manager uses it to shift work, smooth resources and absorb small delays. But float is a budget: SPEND it and it is gone, and consuming a path's float can turn that path CRITICAL, creating a new constraint. So float is real and useful, but it must be spent DELIBERATELY, with the knowledge that a delayed non-critical activity is quietly eating its own safety margin. Knowing where the float is, and where it is not, is knowing where a project is fragile.[1]
PERT — three estimates, a probability
Where durations are uncertain, PERT uses three estimates — optimistic, most likely, pessimistic — so expected time te = (o + 4m + p) / 6, with a variance. Its answer is a probability of finishing by a date, not a guaranteed date. CPM is deterministic (known work); PERT is probabilistic (uncertain work).[2, 3]
Three estimates, not one
CPM assumes you KNOW each activity's duration. Often you do not — the work is novel, or uncertain. PERT (Program Evaluation and Review Technique) handles this HONESTLY, with THREE estimates per activity: OPTIMISTIC (o, all goes well), MOST LIKELY (m), and PESSIMISTIC (p, all goes badly). From these it computes an EXPECTED time, te = (o + 4m + p) / 6 — a weighted average leaning on the most likely — and a VARIANCE, ((p − o) / 6)², that measures the UNCERTAINTY. PERT was built in 1958 for the US Navy's Polaris programme, where thousands of never-done-before tasks made single estimates meaningless. Its whole point is to face uncertainty rather than pretend it away.[2, 3]
At a glance
| Aspect | The fact | The folklore |
|---|---|---|
| The critical path is | The LONGEST chain — its length is the shortest project time | The most important or costly part |
| The forward pass finds | Earliest start/finish (ES, EF) — the soonest | The cost |
| The backward pass finds | Latest start/finish (LS, LF) — the last safe moment | The duration |
| Float is | LS − ES — spare time; zero float = critical | Wasted time to cut |
| CPM | Deterministic — one estimate; known, repetitive work | Probabilistic guessing |
| PERT | Probabilistic — three estimates, a probability, not a date | An exact guaranteed finish date |
Key terms
The longest chain of dependent activities in a network, with zero float — its length is the shortest possible project duration; delaying any critical activity delays the project.
Forward: add durations start-to-finish for earliest start/finish (ES, EF). Backward: subtract finish-to-start for latest start/finish (LS, LF). Their difference is float.
The spare time a non-critical activity has (total float = LS − ES). Legitimate flexibility, not waste — but spending a path's float can make it critical.
Critical Path Method — a deterministic network technique using one time estimate per activity; suits known, repetitive work. Developed 1957 (DuPont).
Program Evaluation and Review Technique — uses three estimates (o, m, p) so expected time te = (o + 4m + p)/6, with a variance; probabilistic, for uncertain work. Developed 1958 (US Navy, Polaris).
PERT's weighted-average duration te = (o + 4m + p)/6 and its uncertainty ((p − o)/6)² — giving a probability of finishing by a date, not a guaranteed date.
Study task
Open the critical-path explorer above. Note the starting critical path and the project duration, and see which activities have float. Now increase a non-critical activity’s duration one day at a time and watch its float shrink — keep going until the critical path jumps to it. That is float being spent until a new path becomes critical. Then, for one activity where you were unsure of the duration, write three PERT estimates (optimistic, most likely, pessimistic) and compute te = (o + 4m + p) / 6 — and say honestly whether this activity is really CPM (you know the time) or PERT (you are guessing) work. The goal is to feel, in your hands, that the longest chain rules the finish, and that a single date can be false precision.
Self-assessment
1. What is the critical path, precisely?
2. How is float calculated, and what does zero float mean?
3. What does PERT actually give you?
4. When do you use CPM versus PERT?
Recap
References & further reading
- [1]B. C. Punmia & K. K. Khandelwal, Project Planning and Control with PERT and CPM — the critical path, forward and backward pass, float, and computing project time. https://www.laxmipublications.com/
- [2]Jerome D. Wiest & Ferdinand K. Levy, A Management Guide to PERT/CPM, Prentice-Hall of India — CPM and PERT analysis and network performance. https://www.phindia.com/
- [3]Critical Path Method (CPM, 1957, M. Walker of DuPont & J. Kelley of Remington Rand, deterministic) and PERT (1958, US Navy Special Projects Office with Booz Allen Hamilton for the Polaris programme, probabilistic) — origins and the deterministic-vs-probabilistic distinction. https://www.pmi.org/
Further reading
- B. C. Punmia & K. K. Khandelwal, Project Planning and Control with PERT and CPM.
- Jerome D. Wiest & Ferdinand K. Levy, A Management Guide to PERT/CPM.
- Punmia / Wiest & Levy on the origins and comparison of CPM and PERT.
Sources gathered and fact-checked June 2026. Published values vary by source, sample and method — treat as indicative and confirm against the cited standard before structural use.
The author
Amogh N P
Architect, interior designer, and creative polymath. Studio Matrx began in his notebooks — his vision of design made honest, useful, and open to everyone. Its Academy is written and taught in his memory, and free, forever.
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