When should a faculty candidate notify schools about a competing offer?
I think it depends on the deadline the offering school gave you. If it's after you expect to hear from the other schools, maybe waiting will be OK. If it's before, then you may have to light a fire under the slower schools. Also, there's a big difference between being "notified that she is going to receive an offer from" the first school and actually receiving it. I wouldn't do anything until you have the first offer in hand (or email).