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Journal of Scheduling

, Volume 16, Issue 4, pp 429–435 | Cite as

An improved FPTAS for maximizing the weighted number of just-in-time jobs in a two-machine flow shop problem

  • Amir ElaloufEmail author
  • Eugene Levner
  • Huajun Tang
Article

Abstract

Recently, Shabtay and Bensoussan (2012) developed an original exact pseudo-polynomial algorithm and an efficient \(\upvarepsilon \)-approximation algorithm (FPTAS) for maximizing the weighted number of just-in-time jobs in a two-machine flow shop problem. The complexity of the FPTAS is \(O\)((\(n^{4}/\upvarepsilon \))log(\(n\)/\(\upvarepsilon \))), where \(n\) is the number of jobs. In this note we suggest another pseudo-polynomial algorithm that can be converted to a new FPTAS which improves Shabtay–Bensoussan’s complexity result and runs in \(O(n^{3}/\upvarepsilon )\) time.

Keywords

Just-in-time scheduling Flow shop  Complexity Pseudo-polynomial algorithm FPTAS 

Notes

Acknowledgments

The authors wish to thank Refael Hassin and the anonymous reviewer for helpful suggestions that improved the paper.

References

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Bar Ilan UniversityRamat GanIsrael
  2. 2.Ashkelon Academic CollegeAshkelonIsrael
  3. 3.Macau University of Science and TechnologyMacauChina

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