Parallel machines scheduling with machine maintenance for minsum criteria

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 [less-than-or-equals, slant] k [less-than-or-equals, slant] 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 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 , and no polynomial time approximation algorithm with worst-case ratio less than can exist when k = m unless P = NP.