This paper studies the optimal behavior of a flexible manufacturing cell with parallel identical machines. We present our new approach, which is applied to a real manufacturing system, drawn from Sikorsky Aircraft Corporation. The approach states the scheduling problem in the form of an optimal control problem with different production constraints: precedence constraints, setup effects, and fixture inspections. The objective is to find the schedule with minimal surplus/backlog costs subject to a given demand profile. Applying the maximum principle to the problem allows an effective numerical scheduling method to be constructed. The method is able to obtain near-optimal results for large-scale systems. The paper considers two modifications of a cell with parallel identical machines: with and without fixture inspections, and presents examples for both cases.