Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

A metric for total tardiness minimization

  • Large Scale Systems Control
  • Selected Articles from Upravlenie Bol’shimi Sistemami
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Lazarev, A.A. and Kvaratskheliya, A.G., Metrics in Scheduling Problems, Dokl. Math., 2010, vol. 81, no. 3, pp. 497–499.

    Article  MathSciNet  MATH  Google Scholar 

  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. 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.

    Article  Google Scholar 

  4. Baptiste, P., Scheduling Equal-Length Jobs on Identical Parallel Machines, Discret. Appl. Math., 2000, no. 103, pp. 21–32.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  7. Lawler, E.L., A Pseudopolynomial Algorithm for Sequencing Jobs to Minimize Total Tardiness, Ann. Discret. Math., 1977, no. 1, pp. 331–342.

    Article  MathSciNet  MATH  Google Scholar 

  8. Lawler, E.L., A Fully Polynomial Approximation Scheme for the Total Tardiness Problem, Oper. Res. Lett., 1982, no. 1, pp. 207–208.

    Article  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. A. Lazarev.

Additional information

Original Russian Text © A.A. Lazarev, P.S. Korenev, A.A. Sologub, 2015, published in Upravlenie Bol’shimi Sistemami, 2015, No. 57, pp. 123–137.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lazarev, A.A., Korenev, P.S. & Sologub, A.A. A metric for total tardiness minimization. Autom Remote Control 78, 732–740 (2017). https://doi.org/10.1134/S0005117917040142

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117917040142