In this paper we study a single batch-processing machine scheduling model. In our model, a set of jobs having different release dates needs to be scheduled onto a single machine that can process a batch of jobs simultaneously at a time. Each batch incurs a fixed setup time and a fixed setup cost. The decision maker may reject some of the jobs by paying penalty cost so as to achieve a tight makespan, but the total rejection penalty cost is required to be no greater than a given value. Our model extends several existing batch-processing machine scheduling models in the literature. We present efficient approximation algorithms with near-linear-time complexities.

中文翻译：

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用于调度具有设置和作业拒绝的批处理机器的近线性时间近似算法

在本文中，我们研究了单个批处理机器的调度模型。在我们的模型中，需要将一组具有不同发布日期的作业安排到一台可以同时处理一批作业的机器上。每个批次都会产生固定的设置时间和固定的设置成本。决策者可以通过支付惩罚成本来拒绝一些工作，以实现严格的完工时间，但要求总拒绝惩罚成本不大于给定值。我们的模型扩展了文献中几个现有的批处理机器调度模型。我们提出了具有近线性时间复杂度的有效逼近算法。