The Complexity of Mean Flow Time Scheduling Problems with Release Times

@article{Baptiste2007TheCO,
  title={The Complexity of Mean Flow Time Scheduling Problems with Release Times},
  author={Philippe Baptiste and Peter Brucker and Marek Chrobak and Christoph D{\"u}rr and Svetlana A. Kravchenko and Francis Sourd},
  journal={J. Scheduling},
  year={2007},
  volume={10},
  pages={139-146}
}
We study the problem of preemptive scheduling n jobs with given release times onm identical parallel machines. The objective is to minimize the average ow time. We show that when all jobs have equal processing times then the problem can be solved in polynomial time using linear programming. Our algorithm can also be applied to the open-shop problem with release times and unit processing times. For the general case (when processing times are arbitrary), we show that the problem is unary NP-hard. 
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