neal young / Aslam99Improved
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Two common objectives for evaluating a schedule are the
makespan, or schedule length, and the average
completion time. This short note gives improved bounds on
the existence of schedules that simultaneously optimize both
criteria. In particular, for any ρ > 0, there exists a
schedule of makespan at most 1+ρ times the minimum, with
average completion time at most 1/(1-e-ρ) times
the minimum. The proof uses an infinite-dimensional linear
program to generalize and strengthen a previous analysis by
Cliff Stein and Joel Wein
[1997].
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