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Unbounded parallel-batch scheduling under agreeable release and processing to minimize total weighted number of tardy jobs

  • Yuan Gao
  • Jinjiang YuanEmail author
Article
  • 25 Downloads

Abstract

We study the unbounded parallel-batch scheduling problem with the jobs having agreeable release dates and processing times to minimize the total weighted number of tardy jobs. In this problem, we consider two types of jobs: batch jobs and drop-line jobs. For batch jobs, the completion time of a job is given by the completion time of the batch containing this job. For drop-line jobs, the completion time of a job is given by the starting time of the batch containing this job plus the processing time of this job. For both of batch jobs and drop-line jobs, we show that (1) the problems are binary NP-hard, (2) the problems are solvable in pseudo-polynomial times, and when the number of weights is a constant, the problems are solvable in polynomial times, and (3) the problems have a fully polynomial-time approximation scheme.

Keywords

Parallel-batch scheduling Release dates Drop-line jobs Polynomial-time approximation scheme 

Notes

Acknowledgements

The authors would like to thank the associate editor and two anonymous referees for their constructive comments and helpful suggestions. This research was supported by NSFC (11671368, 11771406, 11571323).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsZhengzhou UniversityZhengzhouPeople’s Republic of China

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