Abstract
We study the single-machine scheduling with job rejection and the additional constraint that a maintenance activity of fixed length must be performed either by a deadline or in a fixed time interval. The scheduling costs of the accepted jobs are the makespan, maximum lateness, maximum tardiness, maximum weighted completion time, total (weighted) completion time, and total (weighted) number of tardy jobs. The objective of our research is to reveal the tradeoff between the scheduling cost of the accepted jobs and the total rejection cost of the rejected jobs. After showing that three problems are binary NP-hard, combining the known results in the literature, all the problems studied in this paper are binary NP-hard. Then we present pseudo-polynomial-time algorithms for solving all the problems studied in this paper. The distinctive feature of our research is that we always obtain time-complexity results by studying some related auxiliary Pareto scheduling problems.
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