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.

我们研究了带有工作拒绝的单机调度，以及附加约束，即必须在最后期限或固定时间间隔内执行固定长度的维护活动。接受的作业的调度成本为完成时间，最大延迟，最大拖后时间，最大加权完成时间，总（加权）完成时间和延迟工作的总数（加权）。我们研究的目的是揭示接受作业的调度成本与拒绝作业的总拒绝成本之间的折衷。在证明了三个问题都是二进制NP-hard的基础上，结合文献中的已知结果，本文研究的所有问题都是二进制NP-hard的。然后，我们提出了伪多项式时间算法来解决本文研究的所有问题。