This is the Pre-Published Version. We consider a single-machine scheduling problem with periodic maintenance activities. Although the scheduling problem with maintenance has attracted researchers' attention, most of past studies considered only one maintenance period. In this research several maintenance periods are considered where each maintenance activity is scheduled after a periodic time interval. The objective is to find a schedule that minimizes the makespan, subject to periodic maintenance and nonresumable jobs. We first prove that the worst-case ratio of the classical LP T algorithm is 2. Then we show that there is no polynomial time approximation algorithm with a worst-case ratio less than 2 unless P = N P , which implies that the LP T algorithm is the best possible.
Ji et al. REF dealt with single-machine scheduling with periodical maintenance to minimize makespan.
Single-machine scheduling with periodic maintenance to minimize makespan
Comput. Oper. Res.
Comput. Oper. Res.
Computer Science Mathematics