Cyclic part scheduling in a robotic cell

This paper considers scheduling problems in robotic cells which cyclically produce a set of parts of different types. The transportation of parts between machines are carried out by a robot. We study the part sequencing problem in a cell in order to minimize the production cycle time when the sequence of the robot moves is given. This problem is NP-hard in general. We first give a mathematical formulation to the problem, and then propose a branch-and-bound algorithm to solve it. The bounding scheme is based on relaxing, for all of the machines except two, the constraints that a part should stay on a machine for a period at least as long as its processing time. It turns out that the lower bound obtained in this way is tight. The lower bound can be computed using the algorithm of Gilmore and Gomory (1964). Computational experiments on part sequencing problems in three-machine robotic cells are given