In this note, we point out two major errors in the paper "Minimizing total tardiness on parallel machines with preemptions" by Kravchenko and Werner [2010]. More precisely, they proved that both problems P|pmtn|sum(Tj) and P|rj, pj = p, pmtn|sum(Tj) are NP-Hard. We give a counter-example to their proofs, letting the complexity of these two problems open.
@article{arxiv.1112.4396,
title = {A note on the paper "Minimizing total tardiness on parallel machines with preemptions" by Kravchenko and Werner [2010]},
author = {D. Prot and O. Bellenguez-Morineau and C. Lahlou},
journal= {arXiv preprint arXiv:1112.4396},
year = {2011}
}