This paper studies scheduling coupled tasks with exact delays to minimize maximum lateness. The first task has processing time $p>0$ and the second $b_i\geq 0$, also the second needs to start exactly $p$ units of time after the completion of the first. The couple has due date $d_i$. The tasks are scheduled on a single machine to minimize maximum lateness. The problem has been left open in the literature which offer hardly any results on scheduling coupled tasks with exact delays to minimize maximum lateness. The paper shows polynomial time algorithms for \emph{agreeable} ($d_i\geq d_j$ implies $b_i\geq b_j$) and \emph{disagreeable} ($d_i\geq d_j$ implies $b_i\leq b_j$) cases. The complexity of the general problem remains open.

翻译：本文研究调度具有精确延迟的耦合任务以最小化最大延迟的问题。每个耦合任务包含两个子任务：第一个子任务处理时间为 $p>0$，第二个子任务处理时间为 $b_i\geq 0$，且第二个子任务必须在第一个子任务完成后恰好 $p$ 个单位时间开始执行。每个耦合任务具有一个截止日期 $d_i$。所有任务在一台机器上调度，目标是最小化最大延迟。现有文献中关于调度具有精确延迟的耦合任务以最小化最大延迟的研究极少，该问题此前尚未解决。本文针对**一致型**（$d_i\geq d_j$ 蕴含 $b_i\geq b_j$）和**非一致型**（$d_i\geq d_j$ 蕴含 $b_i\leq b_j$）两种情况提出了多项式时间算法。一般性问题的计算复杂度仍待研究。