Minimizing the number of imprecisely scheduled tasks in real-time system

We consider the problem of preemptively scheduling a set of imprecise computation tasks on a single processor, with the 0/1 constraint. In the imprecise computation model each task consists of two parts, mandatory and optional, with its mandatory part required to be completed while its optional part can be left uncompleted. If a task has its optional part unfinished then it incurs an error equal to the processing time of its unfinished portion. In the 0/1 constraint environment, each optional subtask is either fully scheduled or entirely discarded