Single-Machine Scheduling with Job Rejection, Deteriorating Effects, and Deteriorating Maintenance Activities

This paper addresses the single-machine scheduling problems with simultaneous considerations of job rejection, deterioration effects, and deteriorating multimaintenance activities. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on the single machine. Three deterioration effect models are investigated, and it is assumed that each machine may be subject to several maintenance activities over the scheduling horizon, and the duration of the maintenance depends on its running time. Moreover, due to the restriction of the budget of maintenance, the upper bound of the total maintenance frequencies on the machine is assumed to be known in advance. The objective is to find jointly the optimal accepted job set, the optimal maintenance frequencies, the optimal maintenance positions, and the optimal accepted job sequence such that the cost function based on the total completion time and rejection penalty is minimized. It is shown that all the versions of the problem under study are polynomial time solutions.