Optimal cyclic scheduling of a robotic flowshop with multiple part types and flexible processing times

This paper proposes a branch-and-bound algorithm for cyclic scheduling of a robotic flowshop with multiple part types in which the processing times of parts can vary within their given time windows. The problem consists of two types of sequencing issues: part input sequencing and robot move sequencing. We give a formulation for the problem and propose a branch-and-bound algorithm based on the properties of the developed model. The proposed branch-and-bound algorithm consists of three nested procedures, called procedures A, B and C, respectively. Procedures A and B are mainly designed for enumerating part input sequences, while procedure C is responsible for enumerating robot move sequences. To reduce the solution space and speed up the algorithm, we derive the upper bound of the number of parts that can be serviced by the robot within a cycle. Computational results on both benchmark and randomly generated instances are reported.