On the complexity of scheduling unrelated parallel machines with limited preemptions

We consider the problem of finding a minimum-length preemptive schedule for n jobs on m parallel machines. The problem is solvable in polynomial time, whether the machines are identical, uniform or unrelated. For identical or uniform machines, it is easy to obtain an optimal schedule in which the portion of a job that is assigned to a single machine is processed without interruption. We show that imposing this condition in the case of unrelated machines makes the problem NP-hard.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).