Scheduling a wet station for wafer cleaning with multiple job flows and multiple wafer-handling robots

A wet station performs a cleaning process in semiconductor manufacturing. It consists of several processing baths and multiple wafer-handling robots. It simultaneously processes multiple wafer types with different processing sequences. Robot collisions and deadlocks should be prevented. There are also strict no-wait time constraints where, after a wafer is cleaned in a chemical bath, it should immediately be removed from the bath and rinsed at a water bath. We examine the scheduling problem when different jobs are repetitively processed in cyclic order. We propose a way of modelling a Petri net for the wet station operation. By examining the Petri net model, we develop conditions for preventing deadlocks and collisions. We show that the Petri net model, which is apparently an asymmetric Petri net, is behaviourally equivalent to an event graph, for which cycle time computation and many analysis methods are available. Based on these findings, we develop a mixed integer programming model for determining the robot task sequences, the jobs in progress at the baths, and a timing schedule, which are free from deadlocks and collisions, satisfy the no-wait time constraints, and minimize the cycle time. We discuss the computational results.