On single-machine scheduling with flexible maintenance activities

This paper addresses a single-machine scheduling problem with nonresumable jobs and flexible maintenance activities (SJM) and its online version SJMO. It is showed that the competitive ratio of the classical list scheduling (LS) algorithm is 2 for SJMO, and it is the best possible polynomial time approximation algorithm for SJMO from both the competitive ratio point of view unless P = NP and the computational time complexity point of view. Based on the relationship between SJM and SJMO, it is showed that the LS algorithm is the best possible polynomial time approximation algorithm for SJM from both the worst-case ratio point of view unless P = NP and the computational time complexity point of view, which is a significant improvement of some of the existing results on SJM and its special case in the literature. Note that the worst-case ratio of the classical longest processing time first (LPT) algorithm is also 2 for SJM. In order to show which algorithm is better for SJM on average, numerical experiments are conducted. Computational results show that the LPT algorithm performs better than the LS algorithm in all combinations from an average-case error point of view.