Short Communication

Optimization Letters

, Volume 7, Issue 3, pp 613-616

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

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


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.


Computational analysis Strong NP-hardness Scheduling Learning effect Position-dependent processing time