Computational complexity of the single processor makespan minimization problem with release dates and job-dependent learning

Abstract

In this paper, we analyse the single processor maximum completion time (makespan) minimization problem with distinct release dates of jobs and the sum-of-processing time-based learning effect. We prove that the considered problem is strongly NP-hard, if, in addition to jobs with the same learning ratio, there are jobs with constant job processing times. Such jobs are not affected by learning and model, for instance, required system upgrades or training courses.