Approximation algorithms for the makespan minimization with positive tails on a single machine with a fixed non-availability interval

In this article, we consider the non–resumable case of the single machine scheduling problem with a fixed non–availability interval. We aim to minimize the makespan when every job has a positive tail. We propose a polynomial approximation algorithm with a worst–case performance ratio of 3/2 for this problem. We show that this bound is tight. We present a dynamic programming algorithm and we show that the problem has an FPTAS (Fully Polynomial Time Approximation Algorithm) by exploiting the well–known approach of Ibarra and Kim (1975). Such an FPTAS is strongly polynomial. The obtained results outperform the previous polynomial approximation algorithms for this problem.