We consider the problem of scheduling a set of jobs with different processing times and sizes on a single bounded parallel-batch machine with periodic maintenance. Because the machine is in batch-processing model and the capacity is fixed, several jobs can be processed simultaneously in a batch provided that the total size of the jobs in the batch doesn’t exceed the machine capacity. And the processing time of a batch is the largest processing time of the jobs contained in the batch. Meanwhile, the production of each batch is non-resumable, that is, if a batch cannot be completed processing before some maintenance, that batch needs to be processed anew once the machine returns available. Our goal is to minimize the makespan. We first consider two special cases where the jobs have the same sizes or the same processing times, both of which are strongly NP-hard. We present two different approximation algorithms for them and show that these two algorithms have the same tight worst-case ratio of 2. We then consider the general case where the jobs have the arbitrary processing times and arbitrary sizes, for which we propose a 17/5-approximation algorithm.

我们考虑在定期维护的一台有边界并行批处理计算机上调度一组具有不同处理时间和大小的作业的问题。由于机器处于批处理模式，并且容量是固定的，因此，只要该批次中作业的总大小不超过机器容量，就可以同时处理多个作业。并且批处理时间是该批处理中包含的作业的最大处理时间。同时，每个批次的生产都是不可恢复的，也就是说，如果某个批次在维护之前无法完成处理，则一旦机器恢复可用，就需要重新处理该批次。我们的目标是最小化制造周期。我们首先考虑两种特殊情况，即作业具有相同的大小或相同的处理时间，两者都是强烈的NP-hard。我们为它们提供了两种不同的近似算法，并表明这两种算法具有相同的严格最坏情况比率2。然后，我们考虑作业具有任意处理时间和任意大小的一般情况，为此我们建议17 / 5近似算法。