Help creating a formula to calculate staffing

Hi All

I represent a small project team who have been tasked with creating a bespoke IT system to encompass workforce management within a contact centre. We have been able to complete most of this however we are completly stuck with an issue that requires a complicated mathematical solution!

I will try and explain.

We are attempting to create a formula that will calculate the percentage of leave available for our staff based on how many staff are available per each 30 minute slot of the day, how many calls are expected and how many different skill sets they have.

eg:

If we are forecasting the following:

LOB A: 100 calls expected

LOB B: 80 Calls expected

LOB c: 50 Calls expected

Using a simple erlang calculator we can determine how many staff are required to answer the forecasted calls within a certain service level however we are struggling to understand how we choose what staff to allocate to service the calls as they are multi skilled.

Let's say we have 300 staff who are trained as follows:

LOB A&B: 100

LOB A&C: 100

LOB B&C: 100

Is there a formula that will allow us to ratio out the number of staff required to handle the forecasted call volume thus allowing us to safely determine a non call handling percentage that can then be split into non productive time, leave etc?

Hope this makes sense and there is a possible mathematical solution!