We consider a general model for scheduling jobs on unrelated parallel-machines with maintenance interventions. The processing times are deteriorating with their position in the production sequence and the goal of the maintenance is to help to restore good processing conditions. The maintenance duration is depending on the time elapsed since the last maintenance intervention. Several performance criteria and different maintenance systems have been proposed in the literature, leading basically to assignment problems as the underlying model. We shall inverse the approach and start first to set up the matrix for the assignment problems, which catches all the information for the production-maintenance system. This can be done for very general processing times and maintenance durations. The solutions to the assignment problems are determined first. They define the order in which the jobs are to be processed on the various machines and only then the vital informations about the schedule are retrieved, like completion and maintenance times. It will be shown that these matrices are easily obtained, and this approach does not necessitate any complex calculations. 
Parallel-machine scheduling with maintenance: Praising the assignment problem