Unrelated parallel machines scheduling under machine availability and eligibility constraints

In the literature of the parallel machines scheduling, it is generally assumed that all machines are continuously available for processing jobs and each job can be processed by any machine. However, these assumptions become unrealistic in some industrial environments. In this study, we consider the problem of scheduling n independent jobs on m unrelated parallel machines subject to machine availability and eligibility constraints, given the maximum continuous working time before the maintenance of each machine and the maintenance time. Our objective is to minimize the makespan, which is the time to complete the processing of all jobs. We consider both resumable and non-resumable jobs, and develop mathematical models and heuristic algorithm that obtain exact and near-optimal solutions, respectively, for both cases with multiple machine unavailability periods. Computational experiments are done to evaluate the performance of our solution methods in terms of both quality and time. The results show that the proposed heuristic algorithm finds near-optimal solutions in very short time.