A note on the paper "Minimizing total tardiness on parallel machines with preemptions" by Kravchenko and Werner [2010]

TL;DR

This paper critically examines a previous study on scheduling problems, revealing errors in their proofs and leaving the complexity status of certain problems unresolved.

Contribution

It identifies errors in prior NP-hardness proofs for specific scheduling problems, challenging previous complexity classifications.

Findings

Counter-example disproves earlier NP-hardness claims

Complexity of the problems remains open

Highlights the need for revised proofs or classifications

Abstract

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.