Bicriterion Pareto‐scheduling of equal‐length jobs on a single machine related to the total weighted late work

In this article, we study bicriterion Pareto-scheduling on a single machine of equal-length jobs, where one of the criteria is the total weighted late work. Motivated by two Pareto-scheduling open problems where one criterion is the total (weighted) late work and the other criterion is the weighted number of tardy jobs, we show that 12 constrained scheduling problems unaddressed in the literature are binary NP $$ NP $$ -hard, implying that the Pareto-scheduling versions of these problems are also binary NP $$ NP $$ -hard. Moreover, we introduce the concept of dummy due dates (DDD) for equal-length jobs to be scheduled in equal-length intervals. Intriguingly, we find that a DDD-based technique outperforms the existing solution methods and improves the known time complexities of the related problems. In addition, we extend our research to the two-agent scheduling model under the assumption of equal-length or partially equal-length jobs by including the total weighted late work as the criterion of one agent. For these problems, our results also improve the known time complexity results.