Multiclass job scheduling on a single machine: Updating optimal control strategies when due-dates change in real-time

The problem of scheduling jobs, belonging to different classes, on a single machine, can be dealt with under a control-theoretic framework, with the aim of determining optimal (closed-loop) control strategies, instead of optimal (open-loop) scheduling decisions. In the model considered by the authors, optimal control strategies can be determined through a constructive procedure, based on the application of dynamic programming. However, in the case that one or more due-dates change in real-time, the strategies (determined off-line and used in real-time to find, at each decision instant, the optimal actions to be adopted) may become invalid. In this paper, sufficient conditions about the validity of the optimal control strategies are provided, in connection with some specific cases of change of due-dates; moreover, the algorithm to be used to determine the new strategies, when these conditions are violated, is also provided in the paper.