Abstract We study a novel rescheduling problem in which a set of jobs has been assigned an original schedule to minimize the total weighted completion time on a single machine, with the assumption but not with 100% certainty that all of them will be available when the planned processing begins. The need for rescheduling arises due to some jobs could not arrive in time; the decision-maker has to adjust the original schedule to account for the delayed jobs without causing excessive time disruption to the original schedule and to minimize their operational cost. While the decision-maker can choose to reject any of the delayed or non-delayed jobs, the total rejection cost and the tardiness of each accepted job in the adjusted schedule are strictly upper bounded by given thresholds, respectively. The total operational cost includes three components: the total weighted completion time of the accepted jobs, the total rejection cost of the rejected jobs, and the penalty on the maximum tardiness for the accepted jobs. We study this novel rescheduling problem from approximation algorithm perspective, as it generalizes several classic NP-hard scheduling problems; we design a pseudo-polynomial time dynamic programming exact algorithm and, when the total rejection cost is unbounded, we develop the exact algorithm into a fully polynomial time approximation scheme.

中文翻译：

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拒绝允许的单机重新调度的近似方案

摘要 我们研究了一个新的重新调度问题，其中一组作业被分配了一个原始调度以最小化单台机器上的总加权完成时间，假设但不是 100% 确定所有这些都将在计划时可用。处理开始。部分工作不能及时到达，需要重新安排；决策者必须调整原定时间表以考虑延迟的工作，同时又不会对原定时间表造成过多的时间中断，并尽量减少其运营成本。虽然决策者可以选择拒绝任何延迟或未延迟的作业，但调整后的时间表中每个接受作业的总拒绝成本和延迟分别受到给定阈值的严格上限。总运营成本包括三个组成部分：接受作业的总加权完成时间，被拒绝作业的总拒绝成本，以及对接受作业的最大延误的惩罚。我们从近似算法的角度研究了这个新的重新调度问题，因为它概括了几个经典的 NP-hard 调度问题；我们设计了一种伪多项式时间动态规划精确算法，当总拒绝成本无界时，我们将精确算法发展为完全多项式时间近似方案。