A question becomes "how many new employees could we handle?".
I looked at some solutions, but landed on an Excel spreadsheet with a small macro for spreadsheet setup, conditional formatting to call out an employee being allocated to 2 positions on the same shift, and a visual way to show for each operator, how long it takes to be fully trained. HR or a manager can setup training schedules by manually allocating people to training slots.
There were some constraints the business wanted (train on machine #1 before #2, do 2 days of training if you haven't already trained on _x_ machine). They would have been hard to accommodate in a way the end user could configure, so I have a notes section they can fill in (and they have to manually observe these constraints).
Totally open to other ideas people have on how to approach the proble.