Abstract
In the paper "The complexity of mean flow time scheduling problems with release times", by Baptiste, Brucker, Chrobak, Durr, Kravchenko and Sourd, the authors claimed to prove strong $${\mathbb {NP}}$$NP-hardness of the scheduling problem $$P|{\textit{pmtn}},r_j|\sum C_j$$P|pmtn,rj|?Cj, 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 $${\mathbb {NP}}$$NP-hardness for this problem.
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