In most cases, I have worked with the director to make the schedule. We discuss what scenes to rehearse and how long each requires. Sometimes directors write a draft and we discuss it together and check against union rules, actor availability and other schedule restraints. Sometimes they leave more of it up to me.
I don't necessarily think there is a set standard. It is best to discuss the schedule making procedure with your director before rehearsals start.
Schedule making at my current job (which is not a theater and not in the US) is really complicated. We have 62 artists, 12 coaches and 6 rehearsal spaces. Juggling all of that and outside needs (consulate visits, vaccinations, injuries), is a huge challenge. I take input from the artistic staff, coaches and our technical departments including requests, demands and constraints. I create a draft for the following week and go through it with various people a few times before publication. We also do a review of the next day's schedule each afternoon before publishing it officially.
I do most of the puzzle work (who where when) and then make adjustments based on notes from directors, etc. There is no way that a director or coach could make a schedule in this environment.