Abstract
In this paper, we show that the strong NP-hardness proofs of some scheduling problems with start time dependent job processing times presented in Gawiejnowicz (Eur J Oper Res 180:472–478, 2007) and Zhao and Tang (Optim Lett 5:183–190, 2011) are incorrect. Namely, the applied transformations from 4-Product problem to the considered scheduling problems are polynomial not pseudopolynomial. Thus, the related problems are NP-hard, but their complete computational status is still an open issue: ordinary or strongly NP-hard?
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References
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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 some scheduling problems with start time dependent job processing times. Optim Lett 6, 1021–1025 (2012). https://doi.org/10.1007/s11590-011-0330-2
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DOI: https://doi.org/10.1007/s11590-011-0330-2