A strongly polynomial algorithm for no-wait cyclic robotic flowshop scheduling

We consider the problem of cyclic scheduling of identical jobs in a re-entrant flowshop. A robot is responsible for moving each job from a machine to another. Our aim is to find a minimum length cycle of the robot's moves such that exactly one new job enters the system and exactly one completed job leaves the system during the cycle. We present a strongly polynomial algorithm for finding such a cycle.