Single-machine scheduling with flexible and periodic maintenance

This paper deals with the problem of scheduling a single machine with periodic maintenance, where the machine is assumed to be stopped periodically to be maintained or to be reset for a constant time w during the scheduling period. Meanwhile, the maintenance period [u, v] is assumed to have been arranged previously, and the time w would not be longer than the maintenance period [u, v] (ie w <= u - v). The time u (v) is the earliest (latest) time at which the machine starts ( stops) its maintenance. The objective is to minimize the mean flow time of jobs. Four mixed binary integer programming models are developed to optimally solve this problem. Also, an efficient heuristic is proposed for solving large-sized problems.