Optimization Letters

, Volume 7, Issue 3, pp 613–616

A note on proving the strong NP-hardness of a scheduling problem with position dependent job processing times

Open AccessShort Communication

DOI: 10.1007/s11590-012-0445-0

Cite this article as:
Rudek, R. Optim Lett (2013) 7: 613. doi:10.1007/s11590-012-0445-0

Abstract

In this paper, we show that the strong NP-hardness proof of the single machine makespan minimization problem with ready times and job processing times described by a non-increasing power function dependent on a job position in a sequence presented in Bachman and Janiak (J Oper Res Soc 55:257–264, 2004) is incorrect. Namely, the applied transformation from 3- Partition problem to the considered scheduling problem is polynomial not pseudopolynomial. Thus, the related problem is NP-hard, but it is not proved to be strongly NP-hard.

Keywords

Computational analysisStrong NP-hardnessSchedulingLearning effectPosition-dependent processing time
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© The Author(s) 2012

Authors and Affiliations

  1. 1.Wrocław University of EconomicsWrocławPoland