My total work estimate is 1056 man days Release Start time: May 10 Release End time: October 10 total Work days available: 101
1056 / 101 = 11 resource Approx.
Is this correct calculation? If not how to arrive best resource estimate.
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The only caveat I would suggest is that the formula yields 11 FTEs, not necessarily resources or actual people. If you have 11 FTEs, you may need to staff it with 13, 14, or even 15 people because we all work something less than 100% utilization on any given work day. So unproductive time needs to be accounted for. The other side of the coin is that some job families work well over an eight-hour day so utilization climbs closer to 100% again. And, finally, it does not really matter when you have a buyer-seller relationship because the seller will charge 100% of time no matter what was actually productive. So use that formula as a guide but consider these other drivers.
I think David has a very good answer. And another consideration: In many projects, you cannot have all 11 or however many, working at the same time. If the work is indeed very 'bite-sized' and independent, so all FTEs can work concurrently, then perhaps a purely mathematic answer can work. But if there are periods while only 2-3 people can be working at the same time, you must plan with a more detailed schedule.
In addition to the above from David and SGoff, you should consider any dependencies between tasks to arrive at a total duration. If this duration goes beyond the target release date, this will indicate you need to increase the number of resources for critical-path tasks.