When I talked to Qgenda, they claimed it could be done ... part of the custom setup which we'd be paying $10K for. They even said they could have it pull data from our surgery scheduling system (though they admitted they were unfamiliar with that software, which was itself non-commercial). The demo didn't make it clear that their system would be ideal for daily assignments, just that it could be done. I didn't look into it more carefully because even the government discounted rates per person per month were too high.
I looked at a number of physician scheduling programs and most looked fine for making monthly schedules that were fairly well defined and static. Got a clinic or a call schedule to make? All of them could do it. For daily assignments for an anesthesia department, not so much. There's just too much variability in what locations we cover each day, what kind of person needs to be put in each location each day, the last-minute nature of our daily scheduling, and the way department's needs (ORs, preop, sedation services, etc) intersect with individuals' needs (meetings, research, academics). All of that stuff on separate calendars. It seemed like all of those commercial options were made for not-anesthesia groups that just work in one clinic or ward and have simple call requirements.
When I made the daily schedule, I wanted (on one screen) every location that needs a body, the procedures to be done at that location (and who's doing them), and a list of available people with annotations of their subspecialty qualifications (if any), their recent assignments, requests, non-clinical duties that day, call obligations, all of it.
They use Qgenda where I'm a fellow. I'm not privy to the complete daily assignment process but it sure looks like they're doing it the hard way, manually looking at Calendar A to see which ORs need people every day and picking someone from Calendar B and entering it into Calendar C. The Qgenda calendar has a list of names assigned to things like "Cardiac OR 1" and "Peds OR 1" for faculty but someone's still got to take that info and enter it into the surgery schedule for actual ORs, and add a fellow or resident (who aren't in Qgenda system at all, as far as I can tell). I just assumed that they're not using Qgenda to its full potential for some reason. Or maybe the sales rep just says "yeah it can do that" to every question ...