Minimizing cycle time in large robotic cells

We solve scheduling problems for a Texas-based company called FSI International Inc. that designs and manufactures robotic cells for semiconductor wafer fabrication companies. A robotic cell contains several processing stations served by a robot, repetitively producing a set of identical parts. Processing constraints define the cell to be an m-stage flowshop, i.e., each part is processed in it through an identical sequence of m processing stages. The robot acts as a material handling device transferring parts between stages. The objective is to find a robot moves sequence that minimizes the average time to produce a part. We study three robotic cell configurations that are used by FSI and other designers of robotic cells. It is shown that a well known cyclic solution, referred to as downhill permutation achieves optimal solutions for practically relevant problem instances of the simplest robotic cell configuration. For other configurations, we define a new class of cyclic schedule of robot moves called Least Common Multiple (LCM) cycles that are simple and easy to understand and implement. Metaheuristic algorithms are then devised to find the best LCM-cycle, where each cyclic schedule is evaluated through linear programming. These algorithms are considerably superior to the heuristic currently being used at FSI and improvements could amount to several million dollars per year for FSI's clients. We also establish theoretical lower bounds on the average time to produce a part. Subsequently, through extensive computational experiments, we show that the proposed metaheuristic solutions are very close to optimal solutions.