Flexible job shop scheduling problem with parallel batch processing machine

A flexible job-shop scheduling problem (FJSP) with parallel batch processing machine (PBM) is studied. First, mixed integer programming (MIP) formulation is proposed. In order to address a NP-hard structure of this problem, we relax the model to selectively include jobs into the model. There are thousands of jobs in a floor, but we are mostly interested in priority jobs because special customers promise a significant amount of financial compensation in exchange of an expedited delivery. This relaxation could allow non-priority jobs remain unscheduled, but it expedites the discovery of solutions. We then turn job-dependent processing time into machine-dependent by assuming a machine has an equal processing time on different jobs. This assumption is acceptable for the sake of the reduced computational time. This further relaxed model significantly reduces a computational time compared to the original one when tested on a set of common problem instances from a paper in the literature.