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 \(\frac{4}{3}\).

车间调度问题是组合优化中最经典的问题之一。在本文中，我们研究了两台机器开放车间调度问题，前提是一台机器必须在固定的时间间隔内进行维护。目标是最小化完工时间。本文考虑不可恢复的场景，即如果在维护期之前开始的作业在维护期之前无法完成，则必须在间隔后从头开始重新启动。我们只讨论第一台机器维护周期的情况，而第二台机器维护周期的情况是对称的。我们获得了多项式时间近似方案，该方案优于先前的最佳结果\(\frac{4}{3}\)。