Single-machine scheduling with periodic maintenance to minimize makespan

• Published in: Computers & operations research Vol. 34; no. 6; pp. 1764 - 1770
• Main Authors: Ji, Min, He, Yong, Cheng, T.C.E.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.06.2007; Elsevier Science; Pergamon Press Inc
• Subjects: Algorithms; Applied sciences; Approximation algorithm; Exact sciences and technology; Job shops; Non-approximability; Nonresumable jobs; Operational research and scientific management; Operational research. Management science; Periodic maintenance; Repair & maintenance; Scheduling algorithms; Scheduling, sequencing; Single-machine scheduling; Studies; Single-machine scheduling; Approximation algorithm; Non-approximability; Periodic maintenance; Nonresumable jobs; Polynomial approximation; Worst case method; Scheduling; Makespan; Maintenance; Polynomial method; Polynomial time; Time interval; Single machine
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2005.05.034

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 LPT algorithm is 2. Then we show that there is no polynomial time approximation algorithm with a worst-case ratio less than 2 unless P = NP , which implies that the LPT algorithm is the best possible.