Scheduling on parallel machines with time constraints and Equipment Health Factors

In this paper, we are interested in the integration of scheduling and Advanced Process Control (APC) in semiconductor manufacturing. We consider the problem of scheduling jobs of different families on non-identical parallel machines. A special time constraint, associated to each job family, must be satisfied for a machine to remain qualified to process the job family. In addition, we introduce the notion of the risk, modeled as the expected yield resulting from assigning a job to a machine. The objective is to schedule jobs to minimize the combination of three criteria: The sum of completion times, the number of machine disqualification and the sum of expected yield. We propose an integer linear programming model and heuristics to solve this problem. Numerical experiments are reported.