In this paper, we study classical single machine scheduling problems with the additional constraint that a set of special jobs must be scheduled at certain positions in the job sequence. In other words, a special job must start when a certain number of jobs have finished on the machine. We analyze several classical objective functions for this more general setting with the additional constraint of fixed positioned jobs. We show that for some of them they are still polynomially solvable. Then, we focus on the objective of minimizing the number of tardy jobs. Considering the case of just one special job, this allows for a polynomial-time algorithm.

中文翻译：

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固定岗位工作安排


在本文中，我们研究经典的单机调度问题，附加约束是一组特殊作业必须调度在作业序列中的某些位置。换句话说，当机器上完成一定数量的作业时，必须开始一项特殊作业。我们分析了这种更一般设置的几个经典目标函数，并附加了固定职位工作的额外约束。我们证明，对于其中一些问题，它们仍然是多项式可解的。然后，我们重点关注最大限度减少迟到工作数量的目标。考虑到只有一项特殊作业的情况，这允许使用多项式时间算法。