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Published in:
2004 | OriginalPaper | Chapter
The Constrained Minimum Weighted Sum of Job Completion Times Problem
Authors : Asaf Levin, Gerhard J. Woeginger
Published in: Integer Programming and Combinatorial Optimization
Publisher: Springer Berlin Heidelberg
Included in: Professional Book Archive
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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.