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

**Abstract: **
We consider the problem of scheduling operations in bufferless robotic cells
that produce identical parts. Minimizing the long-term average throughput
of parts is an important problem both in 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.