We consider non-preemptive scheduling problems on parallel identical machines where machines change their status from being available to being unavailable and vice versa along the time horizon. The particular form of unavailability we consider is when the starting time of each downtime depends upon the cardinality of the job subset processed on that machine since the previous downtime. We consider the problem of minimizing the makespan in such scenarios as well as its dual problem where we have a fixed common deadline of 1 and the goal is to minimize the number of machines for which there is a feasible schedule. We develop an EPTAS for the first variant and an AFPTAS for the second variant.

中文翻译：

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使用基数相关的不可用期进行调度

我们考虑并行相同机器上的非抢占式调度问题，其中机器在时间范围内将其状态从可用更改为不可用，反之亦然。我们考虑的不可用性的特定形式是每次停机的开始时间取决于自上次停机以来该机器上处理的作业子集的基数。我们考虑在这种情况下最小化完工时间的问题及其对偶问题，其中我们有一个固定的公共截止日期为 1，目标是最小化有可行计划的机器数量。我们为第一个变体开发了 EPTAS，为第二个变体开发了 AFTAS。