Dominance of Cyclic Solutions and Challenges in the Scheduling of Robotic Cells

We consider the problem of scheduling operations in bufferless robotic cells that produce identical parts. Maximizing the long-term average throughput of parts is an important problem in both theory and practice. We define an appropriate state space required to analyze this problem and show that cyclic schedules which repeat a fixed sequence of robot moves indefinitely are the only ones that need to be considered. For the different classes of robotic cells studied in the literature, we discuss the current state of knowledge with respect to cyclic schedules. Finally, we discuss the importance of two fundamental open problems concerning optimal cyclic schedules, special cases for which these problems have been solved, and attempts to solve the general case.