We investigate the recoverable robust single machine scheduling problem under interval uncertainty. In this setting, jobs have first-stage processing times p and second-stage processing times q and we aim to find a first-stage and second-stage schedule with a minimum combined sum of completion times, such that at least Delta jobs share the same position in both schedules. We provide positive complexity results for some important special cases of this problem, as well as derive a 2-approximation algorithm to the full problem. Computational experiments examine the performance of an exact mixed-integer programming formulation and the approximation algorithm, and demonstrate the strength of a proposed polynomial time greedy heuristic.

中文翻译：

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具有区间不确定性的可恢复鲁棒单机调度

我们研究了区间不确定下的可恢复鲁棒单机调度问题。在此设置中，作业具有第一阶段处理时间 p 和第二阶段处理时间 q，我们的目标是找到具有最小完成时间组合总和的第一阶段和第二阶段时间表，以便至少 Delta 作业共享两个时间表中的相同位置。我们为此问题的一些重要特殊情况提供了正复杂度结果，并推导出了完整问题的 2-近似算法。计算实验检查了精确混合整数规划公式和近似算法的性能，并证明了所提出的多项式时间贪婪启发式算法的强度。