I've thought a lot about Time & Attendance Systems (TAS) or Workforce Management Systems (WFMS) over the last 18 months. I was recently asked for a recommendation, with some requirements that were heavily focused on optimal staffing levels.
Ensuring the right number of people are working is of course a key concern. Too many staff is expensive, and being understaffed means you won't capture all the revenue you could. Getting it wrong hurts the bottom line.
That said: I just don't think the pay-off is there to hyper-optimize a schedule. The returns diminish quickly. Keep it simple.
Lofty optimization goals give me midtwit vibes. Over-thinking this means you're going to work really hard and stress out a lot to make little impact.
Perhaps the AI-revolution we're currently speed-running could change all of this. However today, I just don't think the ROI is there unless you have enormous scale and can tailor a solution to your business and customer base habits.
In my opinion, the most effective thing you can actually do is improve retention. Nickel-and-diming the minutes leads to employees resenting the hours, and finding new jobs. Focus on keeping great staff. Experienced people are more productive, meaning you need fewer of them. They're happier. Ask them what they need to be more productive. Give it to them! Spend the time and money here.