An efficient time algorithm for makespan objectives

This paper focuses on a single machine scheduling subject to machine deterioration with rate-modifying activities (RMA). The motivation for this study stems from the automatic-production line problem with one machine. The main question is to find the sequence in which jobs should be scheduled, how many maintenance activity (RMA) to use, if any, and where to insert them in the schedule during the time interval with optimal makespan objective. This problem is known to be NP-hard and we give concise analyses of the problem and provide polynomial time algorithms to solve the makespan problem. We also propose an algorithm which can be applied to some scheduling problems with the actual processing time of job nonlinearly based on its position.