Minimizing mean flow time with release time constraint

Abstract

We consider the problem of preemptively scheduling a set of n independent tasks with release times on m identical processors with the objective of minimizing the mean flow time. For one processor, Baker gives an O( n log n) time algorithm to find an optimal schedule. Lawler asks the question whether the problem can be shown to be solvable in polynomial time or shown to be NP-hard for m⩾2. In this paper we answer this question by showing that it is NP-hard for each fixed m⩾2.