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 ⩽ 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-1m-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-1m-1, and no polynomial time approximation algorithm with worst-case ratio less than mm-1 can exist when k = m unless P = NP.