This paper considers two-machine flow shop scheduling problems with machine availability constraints. When the processing of a job is interrupted by an unavailability period of a machine, we consider both the resumable scenario in which the processing can be resumed when the machine next becomes available, and the semi-resumable scenarios in which some proportion of the processing is repeated but the job is otherwise resumable. For the<br/>resumable scenario, problems with non-availability intervals on one of the machines are shown to admit fully polynomial-time approximation schemes that are based on an extended dynamic programming algorithm. For the problem with several non-availability intervals on the first machine, we present a fast 3/2-approximation algorithm. For the problem with one non-availability interval under the semi-resumable scenario, polynomial-time approximation schemes are developed
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