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

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

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Article ID: iaor20132062
Volume: 7
Issue: 3
Start Page Number: 613
End Page Number: 616
Publication Date: Mar 2013
Journal: Optimization Letters
Authors:
Keywords: combinatorial optimization, scheduling
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 (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.

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