Throughput optimisation in reentrant circular regular robot cells

We consider robot cells of type reentrant circular flow shop served by a single-gripper central robot having the ability to swap. The objective is to find a cyclic sequence of robot moves that minimises the cycle time of one-unit required to produce a part or, equivalently, that maximises the throughput. We analysed three-machine robot cells in-depth showing that four of the feasible one-unit cycles dominate the remaining 17 cycles. We determined the parameter regions in which each of the four cycles is optimal. In the case of m machines, we gave two new lower bounds with an emphasis on four cycles that are specific among all one-unit cycles. Initially, cycle time formulas are created for the four cycles of one-unit. In addition, we established the parameter regions where each of the cycles is best. Finally, we showed that a specific cycle provides a 3/2-approximation for the remaining unique region.