Real-life parallel machine scheduling problems can be characterized by: (i) limited information about the exact task duration at the scheduling time, and (ii) an opportunity to reschedule the remaining tasks each time a task processing is completed and a machine becomes idle. Robust optimization is the natural methodology to cope with the first characteristic of duration uncertainty, yet the existing literature on robust scheduling does not explicitly consider the second characteristic the possibility to adjust decisions as more information about the tasks duration becomes available, despite that re-optimizing the schedule every time new information emerges is standard practice. In this paper, we develop an adaptive robust optimization scheduling approach that takes into account, at the beginning of the planning horizon, the possibility that scheduling decisions can be adjusted. We demonstrate that the suggested approach can lead to better here-and-now decisions and better makespan guarantees. To that end, we develop the first mixed integer linear programming model for adaptive robust scheduling, and a two-stage approximation heuristic, where we minimize the worst-case makespan. Using this model, we show via a numerical study that adaptive scheduling leads to solutions with better and more stable makespan realizations compared to static approaches.

现实生活中的并行机调度问题具有以下特征：(i) 关于调度时任务确切持续时间的信息有限，以及 (ii) 每次任务处理完成且机器空闲时，都有机会重新调度剩余任务. 稳健优化是应对持续时间不确定性的第一个特征的自然方法，但现有关于稳健调度的文献并未明确考虑第二个特征，即随着有关任务持续时间的更多信息可用，调整决策的可能性，尽管重新优化每次出现新信息时的时间表都是标准做法。在本文中，我们开发了一种自适应鲁棒优化调度方法，该方法在规划范围开始时考虑了，可以调整调度决策的可能性。我们证明，建议的方法可以导致更好的此时此地决策和更好的完工期保证。为此，我们开发了第一个用于自适应鲁棒调度的混合整数线性规划模型，以及一个两阶段近似启发式算法，我们在其中最小化最坏情况下的完工时间。使用此模型，我们通过数值研究表明，与静态方法相比，自适应调度可带来具有更好、更稳定的完工时间实现的解决方案。我们最小化最坏情况下的完工时间。使用此模型，我们通过数值研究表明，与静态方法相比，自适应调度可带来具有更好、更稳定的完工时间实现的解决方案。我们最小化最坏情况下的完工时间。使用此模型，我们通过数值研究表明，与静态方法相比，自适应调度可带来具有更好、更稳定的完工时间实现的解决方案。