Cyclic scheduling in 3-machine robotic flow shops

We consider a robotic flow shop model in which a single robot is responsible for the transportation of parts between machines. For reasons of simplicity, when the shop is to produce a large number of identical parts, the robot usually performs repeatedly a fixed sequence of activities. This sequence of activities is called a 1-unit cycle if each execution of the sequence results in the production of exactly one part. It has been conjectured that 1-unit cycles yield optimal production rates for 3-machine robotic flow shops. We establish the validity of this conjecture.