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A revised proof of the optimality for the Kise–Ibaraki–Mine algorithm

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Abstract

For the problem of scheduling n-jobs on one-machine with agreeable job release dates and due dates to minimize the number of late jobs, Kise, Ibaraki and Mine (Oper. Res. 26:121–126, 1978) gave an O(n 2)-time algorithm and proved its optimality by four lemmas. Li et al. (Oper. Res. 58:508–509, 2010) gave a counter-example to show that one lemma is invalid in some case and therefore the optimality is also invalid. In this paper, we revise the lemma and prove that the algorithm is still valid.

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References

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Authors and Affiliations

  1. Department of Mathematics, Zhengzhou University, Zhengzhou, 450001, Henan, China

    Baoqiang Fan

  2. Department of Mathematics and Information, Ludong University, Yantai, 264025, Shandong, China

    Baoqiang Fan

  3. Department of Basic Course, Henan Polytechnic Institute, Nanyang, 473009, Henan, China

    Yeping Sun

  4. Department of Mathematics, Changzhou Institute of Technology, Changzhou, 213002, Jiangsu, China

    Rongjun Chen

  5. Institute of Management Engineering, Shanghai Second Polytechnic University, Shanghai, 201209, China

    Guochun Tang

Authors
  1. Baoqiang Fan
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  2. Yeping Sun
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  3. Rongjun Chen
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  4. Guochun Tang
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Correspondence to Baoqiang Fan.

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Fan, B., Sun, Y., Chen, R. et al. A revised proof of the optimality for the Kise–Ibaraki–Mine algorithm. Optim Lett 6, 1951–1955 (2012). https://doi.org/10.1007/s11590-011-0373-4

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  • DOI: https://doi.org/10.1007/s11590-011-0373-4

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