Sequencing of parts in robotic cells

This paper considers scheduling problems in robotic cells that produce a set of part types on several machines served by one robot. We study the problem of sequencing parts of different types in a cell to minimize the production cycle time when the sequence of the robot moves is given. This problem is NP-hard for most of the one-unit robot move cycles in a robotic cell with more than two machines and producing more than two part types. We first give a mathematical formulation to the problem, and then propose a brand-and-bound algorithm to solve it. The bounding scheme of this algorithm is based on relaxing, for all of the machines except two, the constraints that a machine should be occupied by a part for a period at least as long as the processing time of the part. The lower bound obtained in this way is tight. This relaxation allows us to overcome the complexity of the problem. The lower bound can be computed using the algorithm of Gilmore and Gomory. Computational experiments on part sequencing problems in three-machine robotic cells are given.