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

Damien Prot (1, 2) , Odile Bellenguez-Morineau (3) , Chams Lahlou (1, 2)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 Mines Nantes - Mines Nantes
3 SLP - Systèmes Logistiques et de Production

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 NP -Hard. We give a counter-example to their proofs, letting the complexity of these two problems open.

Domaines: Recherche opérationnelle [math.OC]

Damien Prot, Odile Bellenguez-Morineau, Chams Lahlou. A note on the paper "Minimizing total tardiness on parallel machines with preemptions" by Kravchenko and Werner (2012). Journal of Scheduling, 2013, 16 (4), pp.437-438. ⟨10.1007/s10951-012-0283-z⟩. ⟨hal-00752948⟩