Optimal stochastic sequencing with earliness and/or tardiness costs

We consider a single- or multi-server facility where tasks belonging to N priority classes arrive for processing. Each task has a due date associated with its service completion. An earliness or tardiness penalty (depending on the task´s priority) is incurred if the task is completed at a time other than its due date. We characterize properties of dynamic nonidling nonpreemptive as well as dynamic nonidling preemptive scheduling strategies that minimize an infinite horizon expected discounted cost due to the earliness and tardiness penalties, and provide examples that illustrate these properties