Single machine scheduling with general job-dependent aging effect and maintenance activities to minimize makespan

This paper considers single machine scheduling with an aging effect in which the processing time of a job depends on its position in a sequence. It is assumed that aging ratios are job-dependent and machine can be maintained some times in a schedule. After a maintenance activity, machine will be restored to its initial condition. The processing of jobs and the maintenance activities of machine are scheduled simultaneously. The objective is to schedule the jobs and the maintenance activities, so as to minimize the makespan. We provide a polynomial time algorithm to solve the problem.