Scheduling large robotic cells without buffers

A robotic cell is a manufacturing system that is widely used in industry. A robotic cell contains two or more robot-served machines, repetitively producing a family of similar parts, in a steady state. There are no buffers at or between the machines. Both the robot move cycle and the sequence of parts to produce are chosen in order to minimize the cycle time needed to produce a given set of parts. This objective is also equivalent to throughput rate maximization. In practice, simple robot move cycles that produce one unit are preferred by industry. In an m machine cell for m >= 2, there are m! such cycles that are potentially optimal. Choosing any one of these cycles reduces the cycle time minimization problem to a unique part sequencing problem. We prove the following results in an m machine cell, for any m >= 2. The part sequencing problems associated with these robot move cycles are classified into the following categories: (i) sequence independent; (ii) capable of formulation as a traveling salesman problem (TSP), but polynomially solvable; (iii) capable of formulation as a TSP and unary NP-hard; and (iv) unary NP-hard, but not having TSP structure. As a consequence of this classification, we prove that the part sequencing problems associated with exactly 2m-2 of the m! available robot cycles are polynomially solvable. The remaining cycles have associated part sequencing problems which are unary NP-hard.