A note on proving the strong NP-hardness of a scheduling problem with position dependent job processing times
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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.
KeywordsComputational analysis Strong NP-hardness Scheduling Learning effect Position-dependent processing time
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