I used to be drawn to this kind of (over)-optimization of operational efficiencies, I think it's kind of natural for programmers.

The reality though is that for most businesses, the hard part is customer acquisition, marketing, logistics - for a restaurant, site selection, decor, etc... if you get that right, you can probably solve your staffing problems pretty easily by just being 50% overstaffed, and using a whiteboard and post-it notes. If you _don't_ get that right, then no amount of efficient shift scheduling can save you.