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 $1+\frac{m‐1}{m‐k}$ 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 $2+\frac{k‐1}{m‐1}$ , and no polynomial time approximation algorithm with worst‐case ratio less than $\frac{m}{m‐1}$ can exist when k = m unless P = NP.