In closed-loop or online scheduling the realization of uncertainty in plant operations is addressed in real-time though consistent and frequent reoptimization and rescheduling. Although some simulation studies have explored the robustness of closed-loop scheduling for specific case studies, there are no theoretical results addressing the robustness of closed-loop scheduling. In this paper, we present and justify an appropriate definition of robustness for closed-loop scheduling subject to large and infrequent disturbances such as breakdowns and delays. Assuming that a reasonable reference trajectory for the nominal system is available, we construct a novel terminal constraint and corresponding terminal cost for a general production scheduling problem. Through appropriate assumptions we establish that the proposed closed-loop scheduling algorithm is inherently robust to large, infrequent disturbances. We conclude with an example to illustrate the implications of this analysis. For this example, the proposed algorithm outperforms a typical online scheduling algorithm.

在闭环或在线调度中，通过一致且频繁的重新优化和重新调度，实时解决工厂运营中不确定性的实现。尽管一些模拟研究已经针对特定案例研究探索了闭环调度的鲁棒性，但没有解决闭环调度鲁棒性的理论结果。在本文中，我们提出并证明了闭环调度的稳健性的适当定义，该定义受到诸如故障和延迟等大且不常见的干扰的影响。假设标称系统的合理参考轨迹可用，我们为一般生产调度问题构造了一个新的终端约束和相应的终端成本。通过适当的假设，我们确定所提出的闭环调度算法对大的、不频繁的干扰具有内在的鲁棒性。我们以一个例子结束，以说明这种分析的含义。对于这个例子，所提出的算法优于典型的在线调度算法。