A PTAS for non-resumable open shop scheduling with an availability constraint

Shop scheduling problem is one of the most classical problems in combinatorial optimization. In this paper, we study two-machine open shop scheduling problem, provided that one machine is subject to maintenance period which has to be performed in a fixed time interval. The target is to minimize the makespan. This paper considers non-resumable scenario, i.e., if a job which starts before the maintenance period cannot be completed before the maintenance period, then it must be restarted after the interval from scratch. We only discuss the case that the maintenance period is performed on the first machine, while the case of the maintenance period on the second machine is symmetric. We obtain a polynomial time approximation scheme, which is better than the best previous result $$\frac{4}{3}$$ .