In this paper, we study cyclic production for throughput optimization in robotic flow-shops. We are focusing on simple production cycles. Robotic cells can have a linear or a circular layout: most classical results on linear cells cannot be extended to circular cells, making it difficult to quantify the potential gain brought by the latter configuration. Moreover, though the problem of finding the best one part production cycle is polynomial for linear cells, it is NP-hard for circular cells. We consider the special case of circular balanced cells. We first consider three basic production cycles, and focus on one which is specific to circular cells, for which we establish the expression of the cycle time. Then, we provide a counter-example to a classical conjecture still open in this configuration. Finally, based on computational experiments, we make a conjecture on the dominance of a family of cycle, which could lead to a polynomial algorithm for finding the best 1-cycle for circular balanced cells.
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