Single machine scheduling problems involving job-dependent step-deterioration dates and job rejection

This research focuses on scheduling problems with step-deteriorating job processing times. This phenomenon reflects various real-life settings where the processing time of the jobs, processed after their pre-determined and job-dependent deterioration date, is defined by a step function. A single machine setting is assumed, and optional job rejection is considered. The scheduling measure focused on in this study is makespan, and three variants of the basic problem are considered: (i) minimizing the sum of the scheduling measure and total rejection cost; (ii) minimizing the scheduling criterion, given an upper bound on the total rejection cost; and (iii) minimizing the total rejection cost, subject to a constraint on the scheduling measure. As minimizing the makespan on a single machine with step deterioration is known to be ordinary NP-hard, even if all jobs share a common deterioration date, all presented problems are NP-hard. For all problems, pseudo-polynomial time dynamic-programming (DP) algorithms are presented, establishing that they remain ordinary NP-hard. Furthermore, an extensive experimental study was conducted to determine the efficiency of the proposed algorithms.