The complexity of mean flow time scheduling problems with release times

Abstract

We study the problem of preemptive scheduling of n} jobs with given release times on m identical parallel machines. The objective is to minimize the average flow time. In this paper, show that when all jobs have equal processing times then the problem can be solved in polynomial time using linear programming. Our algorithm can also be applied to the open-shop problem with release times and unit processing times. For the general case (when processing times are arbitrary), we show that the problem is unary NP-hard.