现实生活中的并行机调度问题可以由以下特征刻画：(i) 在调度时关于确切任务持续时间的有限信息，以及 (ii) 每次任务处理完成且机器变为空闲时，重新调度剩余任务的机会。鲁棒优化是处理持续时间不确定性这一第一特征的自然方法论，然而现有的关于鲁棒调度的文献并未明确考虑第二个特征——随着关于任务持续时间的更多信息变得可用而调整决策的可能性，尽管每次新信息出现时重新优化调度是标准做法。在本文中，我们开发了一种调度方法，该方法在规划期开始时就考虑了调度决策可以被调整的可能性。我们证明所提出的方法能够带来更好的即时决策和更好的完工时间保证。为此，我们开发了首个用于可调鲁棒调度的混合整数线性规划模型，以及一种可扩展的两阶段近似启发式算法，其中我们最小化最坏情况下的完工时间。利用该模型，我们通过数值研究表明，与静态方法相比，可调调度能够带来具有更好且更稳定的完工时间实现的解决方案。
英文摘要：
Real-life parallel machine scheduling problems can be characterized by: (i) limited information about the exact task duration at 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 a 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 adjustable robust scheduling, and a scalable two-stage approximation heuristic, where we minimize the worst-case makespan. Using this model, we show via a numerical study that adjustable scheduling leads to solutions with better and more stable makespan realizations compared to static approaches.
On parallel machine scheduling with variable energy consumption functions
University of Modena and Reggio Emilia（摩德纳和雷焦艾米利亚大学）；Universidad Torcuato Di Tella（托尔夸托迪泰拉大学）；Consejo Nacional de Investigaciones Científicas y Técnicas（国家科学研究委员会）
