Scheduling in Reentrant Robotic Cells: Algorithms and Complexity

We study the scheduling of m-machine reentrant robotic cells, in which parts need to reenter machines several times before they are finished. The problem is to find the sequence of 1-unit robot move cycles and the part processing sequence which jointly minimize the cycle time or the makespan. When m = 2, we show that both the cycle time and the makespan minimization problems are polynomially solvable. When m = 3, we examine a special class of reentrant robotic cells with the cycle time objective. We show that in a three-machine loop-reentrant robotic cell, the part sequencing problem under three out of the four possible robot move cycles for producing one unit is strongly НП-hard. The part sequencing problem under the remaining robot move cycle can be solved easily. Finally, we prove that the general problem, without restriction to any robot move cycle, is also intractable.