Why is it important to focus on the critical path?
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As the critical path determines the finish date of the project, this is where the main focus for the project manager/planner should be. For instance, the critical path should be free from any (unrealistic) resource overallocation. If these tasks can only be performed by one resource, the actual critical path will be longer as this limited resource problem does affect the end date as well.
Managing the critical path
This can be done in several ways, among which:
Work overtime
Reassign to other resources with more availability
Align on the specs before you start, to avoid rework
FastTracking: Have tasks run in parallel to shorten the total duration
Crashing: Add resources to tasks on the critical path so the duration of these tasks decreases