Robotic cells with stochastic processing times

This article considers the scheduling of flow shops with a common server that performs all material handling, including the transfer of parts between machines, in the context of robotic cell flow shops. Specifically, the first analytic study of the operations of a robotic cell in which one process has a stochastic processing time, which is common in the microlithography portion of semiconductor manufacturing, is presented. How to measure throughput in such cells is defined and then how the proximity of the stochastic process to the bottleneck process affects throughput is demonstrated. The distribution function of the robot's sequence time is found and verified with simulation results. This yields formulas for the cell's expected throughput. On-line scheduling schemes to improve throughput are presented.