Polynomial-time approximation schemes for two-machine open shop scheduling with nonavailability constraints

This paper addresses a two-machine open shop scheduling problem, in which the machines are not continuously available for processing. The processing of an operation affected by a non-availability interval can be interrupted and resumed later. The objective is to minimize the makespan. We present two polynomial-time approximation schemes, one of which handles the problem with one non-availability interval on each machine and the other for the problem with several non-availability intervals on one of the machines. Problems with a more general structure of the non-availability intervals are not approximable in polynomial time within a constant factor, unless P = NP. (c) 2005 Wiley Periodicals, Inc.