Random Auto Populate Staff Schedule

Hello everyone,

I have not been able to find a clean solution (or even a hint at one).
Perhaps VBA is not the right way of going about this?

I want to auto randomly populate a schedule for staff according to pre determined conditions:
i.e. Anna is available all day but not on Sturdays and Sundays
Susanne is available from 15:00 - 18:30 on some days
etc etc etc

Then I want to click on a button and auto populate a schedule, so that the above conditons are met AND so that each staff member has a roughly euqal number of shifts in each time slot.

Any ideas?

Thanks in advance for your time and help,