Lower Bounds for Smith’s Rule in Stochastic Machine Scheduling

  • Caroline Jagtenberg
  • Uwe Schwiegelshohn
  • Marc Uetz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6534)

Abstract

We consider the problem to minimize the weighted sum of completion times in nonpreemptive parallel machine scheduling. In a landmark paper from 1986, Kawaguchi and Kyan [5] showed that scheduling the jobs according to the WSPT rule –also known as Smith’s rule– has a performance guarantee of \(\frac{1}{2}(1+\sqrt{2})\approx 1.207\). They also gave an instance to show that this bound is tight. We consider the stochastic variant of this problem in which the processing times are exponentially distributed random variables. We show, somehow counterintuitively, that the performance guarantee of the WSEPT rule, the stochastic analogue of WSPT, is not better than 1.243. This constitutes the first lower bound for WSEPT in this setting, and in particular, it sheds new light on the fundamental differences between deterministic and stochastic scheduling problems.

Keywords

stochastic scheduling WSEPT exponential distribution 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Caroline Jagtenberg
    • 1
  • Uwe Schwiegelshohn
    • 2
  • Marc Uetz
    • 3
  1. 1.Dept. of MathematicsUtrecht UniversityUtrechtThe Netherlands
  2. 2.Robotics Research InstituteTU DortmundDortmundGermany
  3. 3.Dept. of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands

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