We study scheduling problems with periodic availability constraints. Each machine is periodically unavailable due to routine arrangements or regular maintenance. The availability periods and unavailability periods, each with the same duration, appear alternately on each machine. All jobs are available at time zero, and no job preemption is allowed. The objective is to minimize the makespan. We conduct the worst-case analysis of two algorithms, SFFD and DFFD, with respect to parameter \(\beta \), the ratio between the length of an unavailability period and an availability period. For the single machine problem, the worst-case ratio of the algorithm SFFD is given, and the bound is tight when \(\beta >0.1022\). An algorithm with a worst-case ratio arbitrarily close to \(\frac{2\beta +2}{\beta +2}\) is also presented. For the two machines problem, we propose a new algorithm DFFD and show its tight worst-case ratio.

我们研究具有周期性可用性约束的调度问题。由于日常安排或定期维护，每台机器都会定期不可用。可用期和不可用期的持续时间相同，并且在每台计算机上交替出现。所有作业在零时间都可用，并且不允许作业抢占。目标是最大限度地缩短完工时间。我们对 SFFD 和 DFFD 两种算法的参数\(\beta \)（不可用期长度与可用期长度之间的比率）进行了最坏情况分析。对于单机问题，给出了算法 SFFD 的最坏情况比率，并且当\(\beta >0.1022\)时界限是紧的。最坏情况比率任意接近的算法\(\frac{2\beta +2}{\beta +2}\)也被提出。对于两台机器问题，我们提出了一种新算法 DFFD 并展示了其严格的最坏情况比率。