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-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. (C) 2011 Elsevier B.V. All rights reserved.