We have a job to do. We, like the designers, have to work as a team. Scheduling the entire process comes down to one person. This person's title depends on your companies roster. The Production Manager is just that, the manager of the entire production.
Some companies have a company manager.
The company mgr. Usually, the TD is in charge of everything technical that goes on during that time before those actors show up. The stage manager deals with everything technical that may come into contact with an actor during the show. Many theater have the TD be responsible for everything regarding the set. The master electrician will be in charge of everything that can give you a shock.