A 3/2-approximation for the proportionate two-machine flow shop scheduling with minimum delays

Abstract

We study the two-machine flow shop problem with minimum delays. The problem is known to be strongly NP-hard even in the case of unit processing times and to be approximable within a factor of 2 of the length of an optimal schedule in the general case. The question whether there exists a polynomial-time algorithm with a better approximation ratio has been posed by several researchers but still remains open. In this paper we improve the above bound to for the special case of the problem when both operations of each job have equal processing times (this case of flow shop is known as the proportionate flow shop). Our analysis of the algorithm relies upon a nontrivial generalization of the lower bound established by Yu for the case of unit processing times. © 2008 Springer-Verlag Berlin Heidelberg.