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. © Springer-Verlag Berlin Heidelberg 2004.
CITATION STYLE
Levin, A., & Woeginger, G. J. (2004). The constrained minimum weighted sum of job completion times problem. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3064, 298–307. https://doi.org/10.1007/978-3-540-25960-2_23
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