Critical Path Method, explained.
A critical path is a longest dependency path through a project network; its duration determines the earliest project completion under the schedule assumptions.
Why it happens
Tasks A–F last 3,4,2,5,3,2 days. A precedes C and D; B precedes E; C,D,E precede F. Forward and backward passes compute earliest finishes and slack. Each of three tokens shortens a task by one day, to a minimum of one.
A critical path is a longest dependency path through a project network; its duration determines the earliest project completion under the schedule assumptions.
Read the result
Zero slack identifies current timing constraints. Recompute after each token because shortening one path can make another path equally important.
A worked example
Three tokens before launch
The initial A–D–F path lasts ten days, while B–E–F lasts nine. Task C has spare time.
Spend a token shortening C and observe that the project duration stays ten, despite a real improvement to that task.
Reset and shorten D instead. Launch falls to nine days, at which point another dependency path also constrains completion.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Tasks A–F last 3,4,2,5,3,2 days. A precedes C and D; B precedes E; C,D,E precede F. Forward and backward passes compute earliest finishes and slack. Each of three tokens shortens a task by one day, to a minimum of one.
Where this idea is useful
A practical use
A team can avoid accelerating a task that already has slack while the actual launch constraint remains elsewhere.
A common misconception
“Speeding up any task makes the project finish sooner.”
A task with slack can finish earlier without changing its successors' start times. Project acceleration depends on current dependency constraints.
What this explanation leaves out
- Durations are certain, resources unlimited and dependencies finish-to-start. Real staffing constraints, uncertain durations and quality costs can change the schedule. Multiple paths may become critical after acceleration.
Can there be more than one critical path?
Yes. Equal longest paths can coexist, and shortening only one may leave the others determining the same completion date.
Which unfinished task currently determines your actual completion date rather than merely occupying attention?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.