Scheduling Recommendation

Hey folks,

I'm looking for a (perhaps) unique way to schedule for up to roughly 20 employees. This is a healthcare setting with 24/7 needs. My employees are required to work 12 shifts per month. I'd like the following:

1) Staff start by "x"ing out days that they do not want to work. This is not PTO, but a limited number of "x"s that the staff put in to avoid working on those days. This is how we currently do it, but with our scheduler. Currently, we can't have more than 4 people putting an "x" on one day. First come, first serve.

If you put more than 4 "x"s in a row, then you have to use a day of PTO, and that continues every other day. Like so: X X X X (PTO) X (PTO) X

2) Randomized, automated completion of the rest of the days. We need 4 employees working every day. Equity is an issue with the scheduler now, so randomized shifts will help that.

One further complication is that, in this line of work, continuity really helps, so having people work in blocks (like 2 or 3 days in a row) is necessary. 4-day blocks leads to burnout, though, so I'm looking to have the option to keep those blocks to 1, 2, or 3 days.

Reading this back, it seems complicated, but I'm essentially looking for a software that allows off-days to be prioritized and the schedule to be built around those.

Thank you for any insight or recommendations.
 
@marilynliddell It's not exactly the medical you're thinking of. I don't want to say too much, but these are not nurses, but people who work a nurse-like schedule.

***I didn't clarify above: these are 24-hour on-call shifts. So not randomized by time-of-day, but randomized by day-of-the-week. Apologies for the confusion.
 
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