"A 10% uplift in AHT would not return a 10% increase in net staffing when using erlang".
Absolutely correct, wasn't using erlang, hence my "Then get involved with erlang” comment. I was providing Lester with a starting point and a broad basis for planning before he got himself immersed with the whole erlang thing.
As for your suggestion, I have some observations -
52.64 FTE, Net of Shrinkage represents 65.8 employed FTE (52.64/(1-20%) based on a 37.5 hour week per employed FTE that equates to 2,467.5 employed hours (65.8 * 37.5)
The amount of work that needs to be done each week is 5,000 calls multiplied by 5 mins per call, expressed in hours (5000 * 5 / 60) = 416
Therefore the time, in your model that agents would spend handling calls as a proportion of their total employed hours would be 17% (416 / 2467.4) against my suggestion, which equates to 41% (416 / (27 * 37.5)). Even if we consider that you already have shrinkage included in your FTE figure and that an FTE works 35 hours per week then they are still only working 23% of their employed hours
Against industry norms of around 40% - 55% even my calculation looks inefficient, this is due to the final parameter of opening hours - 17 hours per day, not the opening hours you have suggested, also I have factored in that at least 2 people need to be present on the phones at any one time to ensure that the opening hours can be covered, irrespective of how low the volumes get.
So yes, increasing from 52.64 to 56.71 is a 7.3% increase in staffing, however going from 27 to 52.64 is a 95% increase to begin with.