A simple heuristic for the coupled task scheduling problem

Abstract

The coupled task scheduling problem deals with the problem of scheduling a set of jobs to be processed on a single machine. Each job consists of two separated tasks where the second task of a job must be started after the completion of its first task plus a predefined exact delay ti me. We study the coupled task scheduling problem with the objective of minimising the maximum completion time, i.e., the makespan. The problem is known to be strongly NP-hard. We propose a simple heuristic for the problem. The heuristic sets the midpoint of given lower and upper bounds as a makespan and solves a feasibility problem. Upon solving the feasibility problem the upper bound is updated to the midpoint. Otherwise, the lower bound is updated to the midpoint. The algorithm keeps iterating until the bound interval is zero. Computational experiments indicate that the proposed heuristic outperforms the exact solver.