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An O(n 2) algorithm for scheduling equal-length preemptive jobs on a single machine to minimize total tardiness

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Abstract

In this paper, we study the problem of scheduling n equal-length preemptive jobs on a single machine to minimize total tardiness, subject to release dates. The complexity status of this problem has remained open to date. We provide an O(n 2) time algorithm to solve the problem.

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References

  • Baker, K. R., E. L. Lawler, J. K. Lenstra and A. H. G. Rinnooy Kan, “Preemptive Scheduling of a Single Machine to Minimize Maximum Cost Subject to Release Dates and Precedence Constraints,” Operations Research, 31, 381–386 (1983).

    Google Scholar 

  • Baptiste, P., “Scheduling Equal-Length Jobs on Identical Parallel Machines,” Discrete Applied Mathematics, 103, 21–32 (2000).

    Article  Google Scholar 

  • Brucker, P. and S. Knust, “Complexity Results for Scheduling Problems,” URL: http://waw.mathematik.uni-osnabrueck.de/research/OR/class.

  • Chen, B., C. Potts and G. Woeginger, “A Review of Machine Scheduling: Complexity, algorithms and approximability,” Handbook of Combinatorial Optimization, Kluwer Academic Publishers, Boston, 1998, pp. 21–169.

    Google Scholar 

  • Cheng, T. C. E. and V. S. Gordon, “Optimal Assignment of Due-dates for Preemptive Single-machine Scheduling,” Mathematical & Computer Modeling, 20(2), 33–40 (1994).

    Article  Google Scholar 

  • Chu, C., “A Branch-And-Bound Algorithm to Minimize Total Tardiness with Different Release Dates,” Naval Research Logistics, 39, 265–283 (1992).

    Google Scholar 

  • Emmons, H., “One-machine Sequencing to Minimize Certain Functions of Job Tardiness,” Operations Research, 17, 701–715 (1969).

    Article  Google Scholar 

  • Gordon, V. S. and V. S. Tanaev, “On minimax problems of scheduling theory for a single machine (in Russian),” Vetsi Akadeii Navuk BSSR. Ser. fizika-matematychnykh navuk, 1983, pp. 3–9.

  • Graham, R. L., E. L. Lawler, J. K. Lenstra and A. H. G. Rinnooy Kan, “Optimization and approximation in Deterministic Sequencing and Scheduling: A Survey,” Annals of Operations Research, 5, 287–326 (1979).

    Google Scholar 

  • Labetoulle, J., E. L. Lawler, J. K. Lenstra and A. H. G. Rinnooy Kan, “Preemptive Scheduling of Uniform Machines Subject to Release Dates,” Progress in Combinatorial Optimization, Academic Press, New York, 1984, pp. 245–261.

    Google Scholar 

  • Pinedo, M., Scheduling: Theory, Algorithms, and Aystems. Prentice Hall, New Jersey, 1995.

    Google Scholar 

  • Szwarc, W, F. Della Croce and A. Grosso, “Solution of the single machine total tardiness problem,” Journal of Scheduling, 2, 55–71 (1999).

    Article  Google Scholar 

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Authors and Affiliations

  1. John M. Olin School of Business, Washington University, St. Louis, Missouri, 63130

    Zhongjun Tian

  2. Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Zhongjun Tian, C. T. Ng & T. C. E. Cheng

Authors
  1. Zhongjun Tian
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  2. C. T. Ng
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  3. T. C. E. Cheng
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Tian, Z., Ng, C.T. & Cheng, T.C.E. An O(n 2) algorithm for scheduling equal-length preemptive jobs on a single machine to minimize total tardiness. J Sched 9, 343–364 (2006). https://doi.org/10.1007/s10951-006-7039-6

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  • DOI: https://doi.org/10.1007/s10951-006-7039-6

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