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CPM is the longest path and its duration is the shortest duration to complete the project
People often get confused with the statement:
"Critical Path is the longest path through the project network diagram, and it is an estimate of the minimum (shortest) project duration."
On first impression, the statement sounds ambiguous or outright wrong. How can a Critical Path be the longest path and its duration the shortest duration to complete the project?
Let's break it down.
Critical Path is the longest path through the project because that's the only path with no (positive) float / wiggle room. Other (non-critical) paths on the schedule network diagram have (positive) float / wiggle room.
Critical Path duration is also an estimate of the minimum (shortest) duration to complete the project because it's the only path that runs continuously from start to end of the project i.e. it has no float / wiggle room to cut down. Other paths have float / wiggle room, but shortening the other paths will not shorten your project schedule.
The only way to shorten the project schedule is to shorten the Critical Path and that can be done using schedule compression techniques such as Fast-tracking and Crashing.
Hope this brief explanation helps make some sense of the statement.