A 3/2-approximation algorithm for two-machine flow-shop sequencing subject to release dates

The two-machine flow-shop sequencing problem with arbitrary release dates of jobs and the minimum makespan criterion is considered. The problem is known to be NP-hard, and the best-known approximation algorithms are those of Potts (Math. Oper. Res. 10 (1985) 576) with a worst-case performance ratio of 5/3 and running time O(n3 log n), and a polynomial time approximation scheme of Hall (Proceedings of the 36th Annual Symposium on Foundations of Computer Science, IEEE Comput. Soc. press, Los Alamitos, 1995, pp. 82–91.) that can generate solutions arbitrary close to the optimum but with a high-time requirement. In this paper, we modify Potts’ algorithm so that its worst-case performance ratio is reduced to 3/2, but its running time remains O(n3 log n)