In this paper, we deal with the problem of sequencing parts and robot moves in a robotic cell where the robot is used to feed machines in the cell. The robotic cell, which produces a set of parts of the same or different types, is a flow-line manufacturing system. Our objective is to maximize the long-run average throughput of the system subject to the constraint that the parts are to be produced in proportion of their demand. The cycle time formulas are developed and analyzed in order to find the optimal sequences of robot moves in cells producing a single part using two or three machines. A state space approach is used to address the problem. Both necessary and sufficient conditions are obtained for various cycles to be optimal. The situation with two machines is also formulated as a Petri net to illustrate an alternative methodology. Finally, in the case of many part types, the problem of scheduling of parts for a specific sequence of robot moves in a two machine cell is formulated as a solvable case of the traveling salesman problem.