The inherent robustness of closed-loop scheduling

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.