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DOI: 10.4230/LIPIcs.STACS.2014.639
URN: urn:nbn:de:0030-drops-44946
URL: http://drops.dagstuhl.de/opus/volltexte/2014/4494/
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Skutella, Martin ; Sviridenko, Maxim ; Uetz, Marc

Stochastic Scheduling on Unrelated Machines

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Abstract

Two important characteristics encountered in many real-world scheduling problems are heterogeneous processors and a certain degree of uncertainty about the sizes of jobs. In this paper we address both, and study for the first time a scheduling problem that combines the classical unrelated machine scheduling model with stochastic processing times of jobs. Here, the processing time of job j on machine i is governed by random variable P_{ij} , and its realization becomes known only upon job completion. With w_j being the given weight of job j, we study the objective to minimize the expected total weighted completion time E[Sum w_j.C_j] , where C_j is the completion time of job j. By means of a novel time-indexed linear programming relaxation, we compute in polynomial time a scheduling policy with performance guarantee (3+D)/2+e. Here, e>0 is arbitrarily small, and D is an upper bound on the squared coefficient of variation of the processing times. When jobs also have individual release dates r_{ij}, our bound is (2+D)+e. We also show that the dependence of the performance guarantees on D is tight. Via D=0, currently best known bounds for deterministic scheduling on unrelated machines are contained as special case.

BibTeX - Entry

@InProceedings{skutella_et_al:LIPIcs:2014:4494,
  author =	{Martin Skutella and Maxim Sviridenko and Marc Uetz},
  title =	{{Stochastic Scheduling on Unrelated Machines}},
  booktitle =	{31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
  pages =	{639--650},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-65-1},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{25},
  editor =	{Ernst W. Mayr and Natacha Portier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4494},
  URN =		{urn:nbn:de:0030-drops-44946},
  doi =		{10.4230/LIPIcs.STACS.2014.639},
  annote =	{Keywords: Stochastic Scheduling, Unrelated Machines, Approximation Algorithm}
}

Keywords: Stochastic Scheduling, Unrelated Machines, Approximation Algorithm
Seminar: 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)
Issue Date: 2014
Date of publication: 19.02.2014


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