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The constrained minimum weighted sum of job completion times problem

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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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Authors and Affiliations

  1. Department of Statistics, The Hebrew University, Jerusalem, 91905, 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, P.O. Box 513, 5600, MB, Eindhoven, The Netherlands

    Gerhard J. Woeginger

Authors
  1. Asaf Levin
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  2. Gerhard J. Woeginger
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Correspondence to Asaf Levin.

Additional information

An earlier version of this paper appeared in the Proceedings of the 10th International IPCO Conference.

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Levin, A., Woeginger, G. The constrained minimum weighted sum of job completion times problem. Math. Program. 108, 115–126 (2006). https://doi.org/10.1007/s10107-005-0691-3

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  • DOI: https://doi.org/10.1007/s10107-005-0691-3

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