Complexity and approximation of single machine scheduling with an operator non-availability period to minimize total completion time

This paper considers the single machine scheduling problem with an operator non-availability period. The operator non-availability period is an open time interval in which a job may neither start nor complete. The objective is to minimize the total completion time. We prove that the problem is NP-hard, even if the length of the operator non-availability period is smaller than the processing time of any job. We also present an algorithm with a tight worst-case ratio of image.