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Automation and Remote Control

, Volume 78, Issue 4, pp 732–740 | Cite as

A metric for total tardiness minimization

  • A. A. LazarevEmail author
  • P. S. Korenev
  • A. A. Sologub
Large Scale Systems Control Selected Articles from Upravlenie Bol’shimi Sistemami
  • 28 Downloads

Abstract

In this paper we consider the NP-hard 1|r j T j scheduling problem, suggesting a polynomial algorithm to find its approximate solution with the guaranteed absolute error. The algorithm employs a metric introduced in the parameter space. In addition, we study the possible application of such an approach to other scheduling problems.

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References

  1. 1.
    Lazarev, A.A. and Kvaratskheliya, A.G., Metrics in Scheduling Problems, Dokl. Math., 2010, vol. 81, no. 3, pp. 497–499.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Lazarev, A.A. and Gafarov, E.R., Teoriya raspisanii. Minimizatsiya summarnogo zapazdyvaniya dlya odnogo pribora (Scheduling Theory. Total Tardiness Minimization for a Single Machine), Moscow: Vychisl. Tsentr Ross. Akad. Nauk, 2006.Google Scholar
  3. 3.
    Lazarev, A.A., Sadykov, R.R., and Sevastyanov, S.V., A Scheme of Approximation Solution of Problem 1|r j|Lmax, J. Appl. Industr. Math., 2007, vol. 1, no. 4, pp. 468–480.CrossRefGoogle Scholar
  4. 4.
    Baptiste, P., Scheduling Equal-Length Jobs on Identical Parallel Machines, Discret. Appl. Math., 2000, no. 103, pp. 21–32.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Du, J. and Leung, J.Y.-T., Minimizing Total Tardiness on One Machine Is NP-Hard, Math. Oper. Res., 1990, no. 15(3), pp. 483–495.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Graham, R.L., Lawler, E.L., Lenstra, J.K., et al., Optimization and Approximation in Deterministic Sequencing and Scheduling: A Survey, Ann. Discret. Math., 1979, no. 5, pp. 287–326.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Lawler, E.L., A Pseudopolynomial Algorithm for Sequencing Jobs to Minimize Total Tardiness, Ann. Discret. Math., 1977, no. 1, pp. 331–342.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Lawler, E.L., A Fully Polynomial Approximation Scheme for the Total Tardiness Problem, Oper. Res. Lett., 1982, no. 1, pp. 207–208.CrossRefzbMATHGoogle Scholar
  9. 9.
    Lazarev, A.A. and Werner, F., Algorithms for Special Cases of the Single Machine Total Tardiness Problem and an Application to the Even-Odd Partition Problem, Math. Comp. Model., 2009, no. 49, pp. 2078–2089.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  • A. A. Lazarev
    • 1
    • 2
    • 3
    • 4
    Email author
  • P. S. Korenev
    • 1
    • 2
  • A. A. Sologub
    • 1
    • 2
  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia
  2. 2.Lomonosov State UniversityMoscowRussia
  3. 3.Moscow Institute of Physics and TechnologyMoscowRussia
  4. 4.Higher School of Economics (National Research University)MoscowRussia

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