Nonpreemptive scheduling on the parallel task system

We study a newly proposed scheduling model, called the Parallel Task System, in which a task may be executed an one or more processors. Our main interest is in examining the complexity of scheduling Parallel Task Systems on rn greater than or equal to 2 identical processors so as to minimize the mean Pow time. The nonpreemptive scheduling discipline is considered in this paper. The Parallel Task System is similar to Me Multiprocessor Task System proposed and studied by Blazewicz et al; [5]. The difference between the two systems is that a task must be executed simultaneously by a pre-specified number of processors in the Multiprocessor Task System, whereas in the Parallel Task System, it can be executed by any number not exceeding m. Based on the Parallel Task: System, me investigate the complexity of minimizing the mean pow time for the nonpreemptive scheduling discipline. We show that the problem is ordinary NP-hard even for any fixed m greater than or equal to two, and it is strongly NP-hard for arbitrary m.