Adding shrinkage to workload FTE

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Hi all

We've recently discovered that a former WFP has been adding shrinkage to workload FTE incorrectly in long term budget forecasts. In short, they were adding the shrinkage to the workload FTE using the formula FTE*(1+% fraction) which left us with a 'supposed' required FTE but after further investigation we found when subtracting the shrinkage from this required FTE (assuming your forecast ended up being your actual) you were left with a number lower than forecast workload FTE as it was subtracting a % from the new whole number. I loosely understand what's happening here but wondering if anyone can explain in a little more details so I can confidently explain to MGMT what's been going on and why our revised budget forecast FTE is higher than previous. Any maths whiz that can better explain would be greatly appreciated.

PS please note in case you are wondering that after adding shrinkage we are also adding a factor for occupancy (target 90%) and schedule efficiency (10% inneficiency) which also wasn't done previously and again contributed to the higher than previous forecasts.


Helper

Call Centre Helper


I think that the formula should be FTE / (1 - %Shrinkage)

So with

15% shrinkage you would need 17% more staff.

50% shrinkage you would need 2 times the number of staff.

The analogy for Management is the difference between percentage margin and percentage mark up.

If you add 20% (mark up) to £100 you end up with £120. If you take 20% off (margin) from £120 you end up with £96! Which is not where you started. I hope that this makes sense.


Algebra
Joining this late but adding in case it helps. This comes up OFTEN. This is a simple algebra calcultion to find a missing variable. If you need 100 FTE after losing 30% shrink the formula is: (100 = X*.7). To solve for X you divide both sides by .7 or 100/.7=X, the answer is 142.8571 headcount required. The 90% occupancy you are adding and 10% inflex for scheduling efficiency should be in the 100 FTE number in my example.

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