Abstract
We consider here the problem of scheduling tasks each of which is logically decomposed into a mandatory subtask and an optional subtask. The mandatory subtask must be executed to completion in order to produce an acceptable result. The optional subtask begins after the mandatory subtask is completed and refines the result in order to reduce the error in the result. If the available processor time is insufficient, the optional subtask can be left incompleted. The error in the result of a task is equal to the processing time of the unexecuted portion of the optional subtask. We describe a preemptive algorithm for scheduling n dependent tasks with rational ready times, deadlines, and processing times on uniprocessor systems.