On-Line Scheduling a Batch Processing System to Minimize Total Weighted Job Completion Time

  • Bo Chen
  • Xiaotie Deng
  • Wenan Zang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2223)


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 ∑w 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 + ∈)-competitive on-line algorithm for any ∈ > 0 for the original on-line scheduling problem. These two on-line algorithms are the first deterministic algorithms of constant performance guarantees.


Schedule Problem Completion Time Interval Graph Restrictive Model Total Completion Time 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Bo Chen
    • 1
  • Xiaotie Deng
    • 2
  • Wenan Zang
    • 3
  1. 1.Department of Computer ScienceCity University of Hong KongHong KongP.R. China
  2. 2.Department of MathematicsUniversity of Hong KongHong KongP.R. China
  3. 3.Warwick Business SchoolUniversity of Warwick CoventryUK

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