I cant see a simple formula im afraid. In practice, if the number of jobs and types of employees is small i would seriously consider solving this using trial and error.

If you want a mathematical solution, You could use Linear programming - Wikipedia, the free encyclopedia. Do you know how to implement that? Your linear program would look something like this:

Define:

Groups of employees. (each group consists of all employees with the same training)

Jobs to be done (LOB A, LOB B, LOB C)

The total number of employees available in each group

The total number of employees needed to cover job j

1 if group i is trained in job j. 0 otherwise

The number of people in group i assigned to task j[/tex]

Linear Program

Minimise

Subject to: (all work must be done)

...

Subject to (cant use more than 100% of staff from each group)

...

Subject to (cant allocate negative numbers of people)

Once you have solved the linear program, you will have the minimum number of staff you need as

One advantage of this method is that it can be easily modified to find the minimumcostallocation of labour if not all your staff are paid the same