On scheduling coupled tasks with exact delays to minimize maximum lateness

TL;DR

This paper investigates scheduling coupled tasks with exact delays on a single machine to minimize maximum lateness, providing polynomial algorithms for agreeable and disagreeable cases, while leaving the general problem's complexity open.

Contribution

It introduces polynomial time algorithms for agreeable and disagreeable cases of the scheduling problem, addressing an open question in the literature.

Findings

Polynomial algorithms for agreeable cases

Polynomial algorithms for disagreeable cases

Open complexity status for the general problem

Abstract

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.