Yes, my scheduling software has those, or equivalents. iCalendar export, a way to email everybody if you get sick, et cetera. It works on the honour system: anybody with a login can schedule anybody else for a particular shift. The presumption is that the other party has agreed to the change, and that assumption hasn't been violated for the 5 years they've used the software. If that presumption ever gets violated I suppose I may be asked to put in more verification, but I suspect that the response likely would be to remove the offender from the group.

In retrospect, that's perhaps all I should have built. But the schedule optimization part was the "fun" part. The rest is pretty standard CRUD + email webapp.