A note on the paper ‘Minimizing total tardiness on parallel machines with preemptions’ by Kravchenko and Werner (2012)

In this note, we point out two major errors in the paper ‘Minimizing total tardiness on parallel machines with preemptions’ by Kravchenko and Werner (2012). More precisely, they claimed to have proved that both problems P|pmtn|∑T j and P|r j ,p j =p,pmtn|∑T j are $\mathrm{𝒩𝒫}$ ‐Hard. We give a counter‐example to their proofs, letting the complexity of these two problems open.