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Minimum Weighted Completion Time

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 184 Accesses

Years and Authors of Summarized Original Work

  • 1999; Afrati et al.

Problem Definition

The minimum weighted completion time problem involves (i) a set J of n jobs, a positive weight w j for each job j ∈ J, and a release date r j before which it cannot be scheduled; (ii) a set of m machines, each of which can process at most one job at any time; and (iii) an arbitrary set of positive values {pi, j}, where pi, j denotes the time to process job j on machine i. A schedule involves assigning jobs to machines and choosing an order in which they are processed. Let C j denote the completion time of job j for a given schedule. The weighted completion time of a schedule is defined as ∑j ∈ Jw j C j , and the goal is to compute a schedule that has the minimum weighted completion time.

In the scheduling notation introduced by Graham et al. [8], a scheduling problem is denoted by a 3-tuple α | β | γ, where α denotes the machine environment, β denotes the additional constraints on jobs, and γdenotes...

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Recommended Reading

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Acknowledgements

The Research of V.S. Anil Kumar and M.V. Marathe was supported in part by NSF Award CNS-0626964. A. Srinivasan’s research was supported in part by NSF Award CNS-0626636.

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Authors and Affiliations

  1. Virginia Bioinformatics Institute, Virginia Tech, 1880 Pratt Drive, Research Building XV, 24061, Blacksburg, VA, USA

    V. S. Anil Kumar

  2. Virginia Bioinformatics Institute, Virginia Tech, 1880 Pratt Drive, Research Building XV, 24061, Blacksburg, VA, USA

    MadhaV. Marathe

  3. IBM T.J. Watson Research Center, Hawthorne, NY, USA

    Srinivasan Parthasarathy

  4. Department of Computer Science, University of Maryland, College Park, MD, USA

    Aravind Srinivasan

Authors
  1. V. S. Anil Kumar
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  2. MadhaV. Marathe
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  3. Srinivasan Parthasarathy
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  4. Aravind Srinivasan
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Corresponding author

Correspondence to V. S. Anil Kumar .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Kumar, V.S.A., Marathe, M., Parthasarathy, S., Srinivasan, A. (2016). Minimum Weighted Completion Time. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_240

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