Scheduling Time-constrained Cluster Tools with Non-identical Parallel Processing Chambers

As a computer-integrated manufacturing system, cluster tools are widely used for semiconductor manufacturing. To tackle their scheduling problems with parallel processing chambers, existing studies assume that the parallel processing chambers at each step are identical. However, due to machine aging, some differences could appear among them in reality. This work represents the first one to report the scheduling problems of cluster tools with non-identical parallel processing chambers. By focusing on time-constrained single and dual-armed cluster tools with non-identical parallel processing chambers, it derives the sufficient conditions under which a system is schedulable. Based on them, it develops two algorithms to obtain the feasible and optimal schedules. It also develops two linear programming models to find the feasible and optimal ones if the sufficient conditions are violated. The experimental results based on 5400 random instances show that the proposed scheduling method can be readily used to generate schedules for both time-constrained single and dual-armed cluster tools.