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There may be several critical or near critical paths. It is quite common actually. All it requires is having two or more deliverables with a sequence of events that are or are close to the longest duration.
If you are crashing or fast tracking a schedule to reduce the critical path, you may eventually get that path down to the duration of what was the second longest path.
Fully agree with @Keith comments above.
If you are looking for a specific example, here's one:
Start - A (5 days) - B (5 days) - End
Start - C (4 days) - D (5 days) - End
I add resources to A to reduce its duration from 5 to 4 days. Now both network paths are critical paths.
Hope that helps.
I don't see a problem with multiple critical paths but the more there are the greater the challenge in delivering the project within the time constraints. The risk of missing a task delivery deadline is significantly more.
My biggest concern is too many tasks being critical whether on one path of multiple path. My rule of thumb is no more than 25%. In my experience that makes the time delivery risks tolerable. Allows more flexibility with the re-planning when one or more critical tasks exceed the estimated duration.
Some may argue that maximized planning is to continue until all tasks become critical thus optimizing the delivery time. However, with that comes 100% delay risk probability and no recovery flexibility.
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