Abstract
This paper considers a parallel-machine scheduling problem with machine maintenance. There are unavailable periods on each of the first k machines, and the remaining m − k machines are always available, where 1 ⩽ k ⩽ m is an integer. The objective is to minimize the total completion time of all jobs. We show the classical SPT algorithm has a worst-case ratio of at most 1 + m - 1 m - k when k < m. If there is exactly one unavailable period on each of the first k machines, and the unavailable periods do not overlap, the worst-case ratio of SPT is at most 2 + k - 1 m - 1 , and no polynomial time approximation algorithm with worst-case ratio less than m m - 1 can exist when k = m unless P = NP.
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