We consider the problem of preemptively scheduling a set of n jobs on m (identical, uniformly related, or unrelated) parallel machines. The scheduler may reject a subset of the jobs and thereby incur job-dependent penalties for each rejected job, and he must construct a schedule for the remaining jobs so as to optimize the preemptive makespan on the m machines plus the sum of the penalties of the jobs rejected. We provide a complete classification of these scheduling problems with respect to complexity and approximability. Our main results are on the variant with an arbitrary number of unrelated machines. This variant is APX-hard, and we design a 1.58-approximation algorithm for it. All other considered variants are weakly NP-hard, and we provide fully polynomial time approximation schemes for them.
CITATION STYLE
Hoogeveen, H., Skutella, M., & Woeginger, G. J. (2000). Preemptive scheduling with rejection (Extended abstract). Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 1879, 268–277. https://doi.org/10.1007/3-540-45253-2_25
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