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A best on-line algorithm for the single machine parallel-batch scheduling with restricted delivery times

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Abstract

We consider a single batch machine on-line scheduling problem with delivery times. In this paper on-line means that jobs arrive over time and the characteristics of jobs are unknown until their arrival times. Once the processing of a job is completed it is delivered to the destination. The objective is to minimize the time by which all jobs have been delivered. For each job J j , its processing time and delivery time are denoted by p j and q j , respectively. We consider two restricted models: (1) the jobs have small delivery times, i.e., for each job J j , q j ≤p j ; (2) the jobs have agreeable processing and delivery times, i.e., for any two jobs J i and J j , p i >p j implies q i ≥q j . We provide an on-line algorithm with competitive ratio \((\sqrt{5}+1)/2\) for both problems, and the results are the best possible.

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Authors and Affiliations

  1. Department of Mathematics, Zhengzhou University, Zhengzhou, Henan, 450052, People’s Republic of China

    Jinjiang Yuan, Shisheng Li, Ji Tian & Ruyan Fu

Authors
  1. Jinjiang Yuan
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  2. Shisheng Li
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  3. Ji Tian
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  4. Ruyan Fu
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Corresponding author

Correspondence to Jinjiang Yuan.

Additional information

Project supported by NSFC (10671183).

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Yuan, J., Li, S., Tian, J. et al. A best on-line algorithm for the single machine parallel-batch scheduling with restricted delivery times. J Comb Optim 17, 206–213 (2009). https://doi.org/10.1007/s10878-007-9108-y

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  • DOI: https://doi.org/10.1007/s10878-007-9108-y

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