Is CPM the same as a Gantt chart?

No. A Gantt chart displays a schedule; CPM calculates relationships and dates that may be shown on it.

Does CPM require special software?

Small networks can be calculated manually, although software helps manage larger ones.

Can CPM show more than one critical path?

Yes. Several dependent chains can tie for the controlling duration.

AI Glossary / Graphs and symbolic AI / Intermediate

Critical path method

Definition

The critical path method, or CPM, is a scheduling technique that uses activity durations and dependencies to calculate early and late start and finish times, available float and the chains controlling project completion. Its basic form assumes known durations and a feasible precedence network.

What it means

CPM turns a list of tasks into a model of when work can occur. The critical path is an output of that model; the method includes the calculations and assumptions used to find it.

Early dates show when activities can occur if their predecessors finish as soon as the model allows. Late dates show how far activities can move without violating the selected completion target and model constraints. Their difference helps identify schedule flexibility.

This flexibility is not spare labor or a guarantee against delay. Float belongs to the dependency structure. Two activities on the same noncritical chain may share the same available allowance, so each cannot necessarily use its displayed float independently.

CPM is useful for understanding deterministic schedule relationships. It does not automatically model uncertainty, resource scarcity or the probability of meeting a promised date.

How it works

Define activities, durations and dependency relationships. In a simple finish-to-start network, an activity can begin only after every predecessor is complete. Check that the network has no impossible circular dependency and that all required work connects appropriately to completion.

The forward pass computes early dates. An activity's early start is the maximum early finish of its predecessors, and its early finish is early start plus duration.

The backward pass begins from the chosen project finish. An activity's late finish is the minimum late start among its successors, and its late start is late finish minus duration. Multiple terminal activities can connect to a common finish milestone.

For this simple model, total float is late start minus early start, equivalently late finish minus early finish. Free float concerns delay that does not postpone a successor's early start and can be smaller.

Calendars, lags and other relationship types require corresponding calculation rules. Resource leveling can add practical sequencing or change dates.

Three practical examples

A product team computes how late a documentation task can start without changing a release milestone.
A facilities planner compares two proposed work sequences and identifies which dependencies create the longest completion chain.
A reporting team checks whether a delay in data preparation can be absorbed before final review or shifts the report's availability.

Think of it this way

Think of arranging a relay of dependent jobs, with some parallel teams joining at common handoffs. A forward pass finds the earliest each handoff can happen; a backward pass finds the latest it can happen while preserving the finish.

The analogy assumes the teams and equipment are actually available. A paper handoff schedule cannot create resources or remove uncertainty in how long work takes.

Worked example

Calculating early, late and float values

Use elapsed days from 0. Activity A takes 3 days. After A, B takes 4 days and C takes 2 days. D takes 3 days and requires both B and C. Assume finish-to-start links, continuous working time and adequate resources.

Forward pass: A has ES 0 and EF 3. B has ES 3 and EF 7. C has ES 3 and EF 5. D must wait for both, so ES is max(7, 5) = 7 and EF is 10.

Set the backward-pass finish to day 10. D has LF 10 and LS 7. B has LF 7 and LS 3. C has LF 7 and LS 5. A must finish before either successor's late start, so LF is min(3, 5) = 3 and LS is 0.

Total float is 0 for A, 0 for B, 2 for C and 0 for D. The critical chain is A-B-D, totaling 10 days. C can start on day 5 rather than day 3 and still finish before D starts on day 7.

If a required finish of day 9 is imposed without changing durations, the backward pass exposes a one-day shortfall on the controlling chain. It does not make the network physically finish sooner; negative float is a signal to reconcile the target and plan.

Illustrative case study

Fictional case: Larch Publishing imports tasks into scheduling software and accepts its displayed completion date. A review finds that two review activities lack predecessor links, allowing them to appear at the project start even though their inputs are not yet available.

The team corrects the dependencies, performs a small manual forward and backward check and compares the revised finish with the requested launch date. It then addresses resource conflicts separately.

The lesson is that CPM calculates the implications of a network.

Common misconceptions and mistakes

CPM predicts a certain completion date. Its dates depend on modeled durations and constraints.
Early and late dates are automatically contractual commitments. They are calculated schedule quantities unless adopted as commitments.
Total float and free float are identical. They refer to different limits on delay.
Every task may independently consume all displayed float. Activities can share the same path allowance.
Adding a deadline shortens the work. It can instead reveal that the current plan cannot meet the target.

Business use

CPM supports discussions about sequencing, delay impact and possible acceleration.

Before using its results, check task completeness, duration units, calendars, dependencies and external constraints. Keep baseline and current schedules distinguishable so changes can be explained. When considering faster completion, model the actual intervention and recalculate the whole network; another path may become controlling. Add uncertainty and resource analysis when the decision depends on them.

Check your understanding

An activity has early start 4 and late start 7 in the stated simple model. What is its total float?

Answer: Three days. Using that allowance must still be assessed with the rest of the network and any shared constraints.

Related terms

Critical path
forward pass
backward pass
early start
late finish
total float
free float
resource levelling

Learn next

Recalculate the worked network with C increased to 5 days. Find every early and late date again, then compare the new controlling chain. Explain why changing one duration can affect dates on activities whose own durations stayed constant.

Sources

Kramer and Jenkins, primary PMI conference paper explaining CPM terminology and forward/backward calculations: https://www.pmi.org/learning/library/critical-path-method-calculations-scheduling-8040

Primary PMI conference discussion of resource levelling and scheduling: https://www.pmi.org/learning/library/scheduling-resource-leveling-project-progression-8006

The four-activity network and publishing case are original examples with explicit simplifying assumptions.

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