Robots and Manufacturing Automation
Robots and Manufacturing Automation
Complexity of one-cycle robotic flow-shops
Journal of Scheduling
Sequencing and Scheduling in Robotic Cells: Recent Developments
Journal of Scheduling
Scheduling in a three-machine robotic flexible manufacturing cell
Computers and Operations Research
Identical part production in cyclic robotic cells: Concepts, overview and open questions
Discrete Applied Mathematics
Pure cycles in flexible robotic cells
Computers and Operations Research
Parametric algorithms for 2-cyclic robot scheduling with interval processing times
Journal of Scheduling
Two-machine robotic cell scheduling problem with sequence-dependent setup times
Computers and Operations Research
Hi-index | 0.98 |
We consider a robotic cell, consisting of a flow-shop in which the machines are served by a single central robot. We concentrate on the case where only one part type is produced and analyze the validity of the so-called one-cycle conjecture by Sethi, Sriskandarajah, Sorger, Blazewicz and Kubiak. This conjecture claims that the repetition of the best one-unit production cycle will yield the maximum throughput rate in the set of all possible cyclic robot moves. We present a new algebraic approach, unifying the former rather tedious proofs for the known results on pyramidal one-cycles and two- and three-machine cells. In this framework, counterexamples will be constructed, showing that the conjecture is not valid for four and more machines. We first present examples for a general four-machine cell, for which the two-unit production cycles dominate the one-unit cycles. Then we consider in particular the so-called regular cells, where all machines are equidistant, since the one-cycle conjecture has originally been formulated for this case. Here, we prove that for four-machine cells, two-unit production cycles are still dominated by one-unit production cycles. Then we describe a counterexample with a three-unit production cycle, thus, settling completely the one-cycle conjecture.