A note on \({\mathbb {NP}}\)-hardness of preemptive mean flow-time scheduling for parallel machines
In the paper The complexity of mean flow time scheduling problems with release times, by Baptiste, Brucker, Chrobak, Drr, Kravchenko and Sourd, the authors claimed to prove strong \({\mathbb {NP}}\)-hardness of the scheduling problem \(P|{\textit{pmtn}},r_j|\sum C_j\), namely multiprocessor preemptive scheduling where the objective is to minimize the mean flow time. We point out a serious error in their proof and give a new proof of strong \({\mathbb {NP}}\)-hardness for this problem.
scheduling complexity identical machines preemptive problems