The constrained minimum weighted sum of job completion times problem

  • Authors:

  • Asaf Levin;Gerhard J. Woeginger

  • Affiliations:

  • Department of Statistics, The Hebrew University, 91905, Jerusalem, Israel;Dept. of Math., Univ. of Twente, P.O. Box 217, 7500, Enschede, AE, The Netherlands and Dept. of Math. and Comp. Sci., TU Eindhoven, P.O. Box 513, 5600, MB, Eindhoven, The Netherlands

  • Venue:
  • Mathematical Programming: Series A and B
  • Year:
  • 2006

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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.