On scheduling coupled tasks with exact delays to minimize maximum lateness

This paper studies scheduling coupled tasks with exact delays to minimize maximum lateness. The first task has processing time $p>0$ and the second $b_i\ge 0$, 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} ($d_i\ge d_j$ implies $b_i\ge b_j$) and \emph{disagreeable} ($d_i\ge d_j$ implies $b_i\le b_j$) cases. The complexity of the general problem remains open.