An uncertain single machine scheduling problem with periodic maintenance

This paper studies a single machine scheduling problem with periodic maintenance, in which processing time and repair time are nondeterministic. In order to deal with nondeterministic phenomena, uncertainty theory is introduced to minimize the makespan under an uncertain environment. Three uncertain programming models are proposed, which can be converted into deterministic forms based on the uncertainty inverse distribution. List scheduling (LS) and longest processing time (LPT) algorithms are employed to solve the problem. It is proved that the two algorithms have the same worst cast ratio under different confidence levels and the LPT algorithm has a better performance bound. A hybrid intelligent algorithm for the problem is designed and some numerical experiments demonstrate the effectiveness of the proposed models and algorithm.