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International Workshop on Randomization and Approximation Techniques in Computer Science

International Workshop on Approximation Algorithms for Combinatorial Optimization

RANDOM 1999, APPROX 1999: Randomization, Approximation, and Combinatorial Optimization. Algorithms and Techniques pp 144–155Cite as

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

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Part of the book series: Lecture Notes in Computer Science ((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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Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Sekr. MA 6-1, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Rolf H. Möhring & Marc Uetz

  2. MIT, Sloan School of Management and Operations Research Center, E53-361, 30 Wadsworth St, Cambridge, MA, 02139, USA

    Andreas S. Schulz

Authors
  1. Rolf H. Möhring
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  2. Andreas S. Schulz
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  3. Marc Uetz
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Editor information

Editors and Affiliations

  1. Department of Industrial Engineering and Operations Research and Walter A. Haas School of Business, University of California, Berkeley

    Dorit S. Hochbaum

  2. Institute for Computer Science, University of Kiel, Olshausenstrasse 40, 24118, Kiel, Germany

    Klaus Jansen

  3. Centre Universitaire d’Informatique, Battelle Bâtiment A, Route de Drize 7, 1227, Carouge, Geneva, Switzerland

    José D. P. Rolim

  4. Computer Science Division, University of California, 94720, Berkeley, CA

    Alistair Sinclair

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© 1999 Springer-Verlag Berlin Heidelberg

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Möhring, R.H., Schulz, A.S., Uetz, M. (1999). Stochastic Machine Scheduling: Performance Guarantees for LP-Based Priority Policies. In: Hochbaum, D.S., Jansen, K., Rolim, J.D.P., Sinclair, A. (eds) Randomization, Approximation, and Combinatorial Optimization. Algorithms and Techniques. RANDOM APPROX 1999 1999. Lecture Notes in Computer Science, vol 1671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48413-4_16

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  • DOI: https://doi.org/10.1007/978-3-540-48413-4_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66329-4

  • Online ISBN: 978-3-540-48413-4

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