Predictive–reactive scheduling on a single resource with uncertain future jobs

We consider a scheduling problem where the firm must compete with other firms to win future jobs. Uncertainty arises as a result of incomplete information about whether the firm will win future jobs at the time the firm must create a predictive (planned) schedule. In the predictive schedule, the firm must determine the amount of planned idle time for uncertain jobs and their positions in the schedule. When the planned idle time does not match the actual requirements, certain schedule disruptions occur. The firm seeks to minimize the sum of expected tardiness cost, schedule disruption cost, and wasted idle time cost. For the special case of a single uncertain job, we provide a simple algorithm for the optimal planned idle time and the best reactive method for schedule disruptions. For the case of multiple uncertain jobs, a heuristic dynamic programming approach is presented.