Preemptive Multi-Machine Scheduling of Equal-Length Jobs to Minimize the Average Flow Time
<|reference_start|>Preemptive Multi-Machine Scheduling of Equal-Length Jobs to Minimize the Average Flow Time: We study the problem of preemptive scheduling of n equal-length jobs with given release times on m identical parallel machines. The objective is to minimize the average flow time. Recently, Brucker and Kravchenko proved that the optimal schedule can be computed in polynomial time by solving a linear program with O(n^3) variables and constraints, followed by some substantial post-processing (where n is the number of jobs.) In this note we describe a simple linear program with only O(mn) variables and constraints. Our linear program produces directly the optimal schedule and does not require any post-processing.<|reference_end|>
@article{baptiste2004preemptive,
    title={Preemptive Multi-Machine Scheduling of Equal-Length Jobs to Minimize the
  Average Flow Time},
    author={Philippe Baptiste, Marek Chrobak, Christoph Durr, Francis Sourd},
    journal={arXiv preprint arXiv:cs/0412094},
    year={2004},
    number={This paper is now part of the report cs.DS/0605078.},
    archivePrefix={arXiv},
    eprint={cs/0412094},
    primaryClass={cs.DS}
}