Scheduling a batch processing system has been extensively studied in the last decade.A batch processing system is modelled as a machine that can process up to b jobs simultaneously as a batch.Th e scheduling problem involves assigning all n jobs to batches and determining the batch sequence in such a way that certain objective function of job completion times C j is minimized.In this paper, we address the scheduling problem under the on-line setting in the sense that we construct our schedule irrevocably as time proceeds and do not know of the existence of any job that may arrive later.Our objective is to minimize the total weighted completion time σw j C j . We provide a linear time on-line algorithm for the unrestrictive model (i.e., b ≥ n) and show that the algorithm is 10/3-competitive. For the restrictive model (i.e., b < n), we first consider the (off-line) problem of finding a maximum independent vertex set in an interval graph with cost constraint (MISCP), which is NP-hard. We give a dual fully polynomial time approximation scheme for MISCP, which leads us to a (4 + ε)-competitive on-line algorithm for any ε > 0 for the original on-line scheduling problem. These two on-line algorithms are the first deterministic algorithms of constant performance guarantees. © 2001 Springer Berlin Heidelberg.
CITATION STYLE
Chen, B., Deng, X., & Zang, W. (2001). On-line scheduling a batch processing system to minimize total weighted job completion time. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2223 LNCS, pp. 380–389). https://doi.org/10.1007/3-540-45678-3_33
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