Throughput optimization in dual-gripper interval robotic cells

Interval robotic cells with several processing stages (chambers) have been increasingly used for diverse wafer fabrication processes in semiconductor manufacturing. Processes such as low-pressure chemical vapor deposition, etching, cleaning and chemical-mechanical planarization, require strict time control for each processing stage. A wafer treated in a processing chamber must leave that chamber within a specified time limit; otherwise the wafer is exposed to residual gases and heat, resulting in quality problems. Interval robotic cells are also widely used in the manufacture of printed circuit boards. The problem of scheduling operations in dual-gripper interval robotic cells that produce identical wafers (or parts) is considered in this paper. The objective is to find a 1-unit cyclic sequence of robot moves that minimizes the long-run average time to produce a part or, equivalently, maximizes the throughput. Initially two extreme cases are considered, namely no-wait cells and free-pickup cells; for no-wait cells (resp., free-pickup cells), an optimal (resp., asymptotically optimal) solution is obtained in polynomial time. It is then proved that the problem is strongly NP-hard for a general interval cell. Finally, results of an extensive computational study aimed at analyzing the improvement in throughput realized by using a dual-gripper robot instead of a single-gripper robot are presented. It is shown that employing a dual-gripper robot can lead to a significant gain in productivity. Operations managers can compare the resulting increase in revenue with the additional costs of acquiring and maintaining a dual-gripper robot to determine the circumstances under which such an investment is appropriate.