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.

翻译：在这种背景下,工作有第一阶段处理时间 p 和第二阶段处理时间 q,我们的目标是找到第一阶段和第二阶段处理时间 q,我们的目标是找到一个第一阶段和第二阶段处理时间,最低加在一起的完成时间,使至少德尔塔工作在两个时间表中的位置相同。我们为这一问题的一些重要特殊案例提供了积极的复杂结果,并为整个问题得出了一种2级兼容算法。计算实验检查了精确的混合整数编程和近似算法的性能,并展示了拟议中的多盘时间贪婪的超值的强度。