What is Critical path method (CPM)?

A scheduling technique that uses the durations of a project's activities and the order relations between them to find each activity's earliest and latest start and its float, and then finds the longest path connecting activities with zero float (the critical path) and the total project duration. A delay in any activity on the critical path delays the whole project.

Japanese name: クリティカルパス法(CPM)

Critical path method (CPM) appears in 1 practice question across 1 topic, including Software Development and Project Management.

Field: Software Development and Project Management

Earliest start and latest start

Working forward, the earliest start of each activity is the latest finish among all its predecessors, and the earliest finish of the last activity is the total project duration. Then, working backward, the latest start is the latest day an activity can begin without extending the project. The latest start minus the earliest start is the activity's total float, and the path connecting activities with zero total float is the critical path. For example, if A (6 days) → D (4 days) → F (3 days) is the longest path at 13 days, a one-day delay in any of A, D or F delays the whole project by one day.

Arrow diagrams and dummy activities

Japanese IT engineer examinations often use arrow diagrams (PERT charts), which show activities as arrows and the points between them as nodes (circles). Order relations that arrows alone cannot express are shown with dummy activities of zero duration (dotted arrows). For example, when activity D cannot start until A as well as B has finished, a dummy activity is drawn from the end of A to the start of D. Overlooking a dummy activity gives a total duration shorter than the real one, so care is needed.

Ways to shorten the schedule

To shorten the project, activities on the critical path must be shortened; shortening activities that are not on it does not change the total. Shortening activities by adding people or money is called crashing, and overlapping activities that were planned to run in sequence is called fast tracking. In crashing, the activity on the critical path that is cheapest to shorten by one day is shortened first. After shortening, another path may become the new critical path, so the calculation is repeated each time.

Try it: questions about Critical path method (CPM)

A project has the following activities, durations and predecessors: A: 4 days (no predecessor); B: 2 days (none); C: 3 days (A); D: 2 days (B); E: 5 days (C); F: 4 days (C and D); G: 2 days (F). If all other activities start as early as possible, what is the maximum number of days by which the start of activity B can be delayed without extending the total project duration?

A0 days
B1 day
C3 days

Show answer and explanation

Answer: C. 3 days

The earliest start is day 4 for C, day 7 for E and F (for F, the later of day 7 when C ends and day 4 when D ends) and day 11 for G, so the whole project takes A → C → F → G = 4 + 3 + 4 + 2 = 13 days. Working backward for the latest starts gives day 11 for G, day 7 for F, 7 − 2 = day 5 for D and 5 − 2 = day 3 for B, so B's total float is 3 − 0 = 3 days. Delaying B also delays the start of D, but D has the same float, so up to 3 days does not extend the project. 0 days is B's free float (the delay possible without delaying the earliest start of its successor D), and 1 day is E's float. In the critical path method (CPM), the floats are found in this way, and the path connecting activities with zero float is the critical path.

FAQ

Is there only one critical path?

There can be several. If two longest paths have the same duration, both are critical paths, and both must be shortened to shorten the project.

What is the difference between total float and free float?

Total float is the number of days an activity can be delayed without extending the total project duration. Free float is the number of days it can be delayed without delaying the earliest start of any successor, and it is never larger than the total float. When an activity shares float with its successor, its free float can be 0 while its total float is positive.

Critical path method (CPM) in the explanations

In the critical path method (CPM), the floats are found in this way, and the path connecting activities with zero float is the critical path.
A project has the following activities, durations and prede…