Unrelated parallel-machine scheduling with deterioration effects and deteriorating multi-maintenance activities for minimizing the total completion time

This paper investigates scheduling problems with simultaneous considerations of deterioration effects and deteriorating multi-maintenance activities on unrelated parallel machines. We examine two models of scheduling with the deterioration effect, namely the job-dependent and position-dependent deterioration model and the time-dependent deterioration model. We assume that each machine may be subject to several maintenance activities over the scheduling horizon, and the duration of maintenance on a machine depends on its running time. Moreover, due to the restriction of the budget of maintenance, the upper bound of the total maintenance frequencies on all the machines is assumed to be known in advance. The objective is to find jointly the optimal maintenance frequencies, the optimal maintenance positions, and the optimal job sequences such that the total completion time is minimized. If the number of machines is fixed, we introduce polynomial time solutions for all the versions of the problem under study.