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.
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References
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This work was financially supported by the Polish Ministry of Science and Higher Education.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Rudek, R. A note on proving the strong NP-hardness of a scheduling problem with position dependent job processing times. Optim Lett 7, 613–616 (2013). https://doi.org/10.1007/s11590-012-0445-0
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DOI: https://doi.org/10.1007/s11590-012-0445-0