A first Fit type algorithm for the coupled task scheduling problem with unit execution time and two exact delays

Abstract The considered coupled task problem (CTP) is to schedule n jobs, each consisting of two (sub)tasks, on a single machine. Exact delay times are between the subtasks of a job and the makespan has to be minimized. It has been proven that the problem is strongly NP -hard in general case (see Orman and Potts (1997)), even if the lengths of the subtasks are identical. This paper considers a special case of CTP where there are jobs with two different delay times only. The complexity status of this problem is unknown. We will present an algorithm – called First Fit Decreasing (FFD) – and we will prove that its approximation ratio is in the interval ( 1.57894 , 1.57916 ) .