An improved approximation algorithm for two-machine flow shop scheduling with an availability constraint

We study the problem of scheduling n jobs in a two-machine flow shop where the second machine is not available for processing during a given time interval. A resumable scenario is assumed, i.e if a job cannot be finished before the down period it is continued after the machine becomes available again. The objective is to minimize the makespan. The best fast approximation algorithm for this problem guarantees a relative worst-case error bound of 4/3. We present an improved algorithm with a relative worst-case error bound of 5/4.