This paper addresses the production control problems created in the scheduling of a flexible manufacturing cell consisting of groups of identical machines. An actual manufacturing system, drawn from Sikorsky Aircraft Corporation, was used as a prototype for modeling the cell to study its optimal behavior. The model, stated in the form of optimal production flow control combines classical machine-part scheduling and scheduling of part fixtures. Such an extension induces three problem formulations comprising practical production issues important for many modern plants other than Sikorsky. These formulations are related to three production cases covering different degrees of fixture availability. With the aid of the maximum principle, a numerical scheduling method is constructed for all three problem formulations, and case studies are presented.