Stochastic Machine Scheduling: Performance Guarantees for LP-Based Priority Policies

  • Rolf H. Möhring
  • Andreas S. Schulz
  • Marc Uetz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1671)

Abstract

We consider the problem to minimize the total weighted completion time of a set of jobs with individual release dates which have to be scheduled on identical parallel machines. The durations of jobs are realized on-line according to given probability distributions, and the aim is to find a scheduling policy that minimizes the objective in expectation. We present a polyhedral relaxation of the corresponding performance space, and then derive the first constant-factor performance guarantees for priority policies which are guided by optimum LP solutions, thus generalizing previous results from deterministic scheduling. In the absence of release dates, our LP-based analysis also yields an additive performance guarantee for the WSEPT rule which implies both a worst-case performance ratio and a result on its asymptotic optimality.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Rolf H. Möhring
    • 1
  • Andreas S. Schulz
    • 2
  • Marc Uetz
    • 1
  1. 1.Fachbereich Mathematik, Sekr. MA 6-1Technische Universität BerlinBerlinGermany
  2. 2.MIT, Sloan School of Management and Operations Research CenterCambridgeUSA

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