Parallel Batch Scheduling With Incompatible Job Families Via Constraint Programming

This paper addresses the incompatible case of parallel batch scheduling, where compatible jobs belong to the same family, and jobs from different families cannot be processed together in the same batch. Existing constraint programming (CP) models for this problem fail to synchronize the processing of the jobs within their batch, resulting in batch interruptions. In the context of the diffusion area in the semiconductor manufacturing process, these interrupted solutions would disrupt the thermal stability required for a uniform dopant distribution on the wafers. This paper proposes three new CP models that directly tackle these interruptions in the formulation, including two adaptions of existing models for the compatible case, and a novel Redundant Synchronized (RS) model that adds redundancy to the problem structure to improve computational performance. These existing and novel models are compared on standard test cases, demonstrating the superiority of the RS model in finding optimal or near-optimal solutions quickly.