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Optimality proof of the Kise–Ibaraki–Mine algorithm

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Abstract

Kise, Ibaraki and Mine (Operations Research 26:121–126, 1978) give an O(n 2) time algorithm to find an optimal schedule for the single-machine number of late jobs problem with agreeable job release dates and due dates. Li, Chen and Tang (Operations Research 58:508–509, 2010) point out that their proof of optimality for their algorithm is incorrect by giving a counter-example. In this paper we give a correct proof of optimality for their algorithm.

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References

  • Baptiste, P. (1999). An O(n 4) algorithm for preemptive scheduling of a single machine to minimize the number of late jobs. Operations Research Letters, 24, 175–180.

    Article  Google Scholar 

  • Baptiste, P., Peridy, L., & Pinson, E. (2003). A branch and bound to minimize the number of late jobs on a single machine with release time constraints. European Journal of Operational Research, 144, 1–11.

    Article  Google Scholar 

  • Dauzere-Peres, A., & Sevaux, M. (2004). An exact method to minimize the number of tardy jobs in single machine scheduling. Journal of Scheduling, 7, 405–420.

    Article  Google Scholar 

  • Kise, H., Ibaraki, T., & Mine, H. (1978). A solvable case of the one-machine scheduling problem with ready and due times. Operations Research, 26, 121–126.

    Article  Google Scholar 

  • Lawler, E. L. (1990). A dynamic programming algorithm for preemptive scheduling of a single machine to minimize the number of late jobs. Annals of Operations Research, 26, 125–133.

    Article  Google Scholar 

  • Lawler, E. L. (1994). Knapsack-like scheduling problems, the Moore–Hodgson algorithm and the “tower of sets” property. Mathematical and Computer Modelling, 20, 91–106.

    Article  Google Scholar 

  • Lenstra, J. K., Rinnooy Kan, A. H. G., & Brucker, P. (1977). Complexity of machine scheduling problems. Annals of Discrete Mathematics, 1, 343–362.

    Article  Google Scholar 

  • Li, S., Chen, Z.-L., & Tang, G. (2010). A note on the optimality proof of the Kise–Ibaraki–Mine algorithm. Operations Research, 58, 508–509.

    Article  Google Scholar 

  • Moore, J. M. (1968). An n job, one machine sequencing algorithm for minimizing the number of late jobs. Management Science, 15, 102–109.

    Article  Google Scholar 

  • Pinedo, M. (2002). Scheduling theory, algorithms, and systems (2nd ed.). Upper Saddle River: Prentice Hall.

    Google Scholar 

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Correspondence to Zhi-Long Chen.

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Li, S., Chen, ZL. & Tang, G. Optimality proof of the Kise–Ibaraki–Mine algorithm. J Sched 15, 289–294 (2012). https://doi.org/10.1007/s10951-010-0210-0

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  • DOI: https://doi.org/10.1007/s10951-010-0210-0

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