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The Constrained Minimum Weighted Sum of Job Completion Times Problem

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Integer Programming and Combinatorial Optimization (IPCO 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3064))

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Abstract

We consider the problem of minimizing the weighted sum of job completion times on a single machine (subject to certain job weights) with an additional side constraint on the weighted sum of job completion times (with respect to different job weights). This problem is NP-hard, and we provide a polynomial time approximation scheme for this problem. Our method is based on Lagrangian relaxation mixed with carefully guessing the positions of certain jobs in the schedule.

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Author information

Authors and Affiliations

  1. Faculty of Industrial Engineering and Management, Technion, Haifa, 32000, Israel

    Asaf Levin

  2. Department of Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Gerhard J. Woeginger

  3. Department of Mathematics and Computer Science, TU Eindhoven, Eindhoven, P.O. Box 513, 5600 MB, The Netherlands

    Gerhard J. Woeginger

Authors
  1. Asaf Levin
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  2. Gerhard J. Woeginger
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Editor information

Editors and Affiliations

  1. Department of IEOR, Columbia University, 500 West 120th Street, 10027, New York, NY, USA

    Daniel Bienstock

  2. H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    George Nemhauser

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© 2004 Springer-Verlag Berlin Heidelberg

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Levin, A., Woeginger, G.J. (2004). The Constrained Minimum Weighted Sum of Job Completion Times Problem. In: Bienstock, D., Nemhauser, G. (eds) Integer Programming and Combinatorial Optimization. IPCO 2004. Lecture Notes in Computer Science, vol 3064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25960-2_23

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  • DOI: https://doi.org/10.1007/978-3-540-25960-2_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22113-5

  • Online ISBN: 978-3-540-25960-2

  • eBook Packages: Springer Book Archive

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