Skip to main content
SpringerLink
Log in

Flow shop scheduling jobs with position-dependent processing times

  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

The paper is devoted to some flow shop scheduling problems, where job processing times are defined by functions dependent on their positions in the schedule. An example is constructed to show that the classical Johnson's rule is not the optimal solution for two different models of the two-machine flow shop scheduling to minimize makespan. In order to solve the makespan minimization problem in the two-machine flow shop scheduling, we suggest Johnson's rule as a heuristic algorithm, for which the worst-case bound is calculated. We find polynomial time solutions to some special cases of the considered problems for the following optimization criteria: the weighted sum of completion times and maximum lateness. Some furthermore extensions of the problems are also shown.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Bachman and A. Janiak,Scheduling jobs with position-dependent processing times, Journal of the Operational Research Society55 (2004), 257–264.

    Article  MATH  Google Scholar 

  2. A. B. Badiru,Computational survey of univariate and multivariate learning curve models, IEEE Transactions on Engineering Management39 (1992), 176–188.

    Article  Google Scholar 

  3. D. Biskup,Single-machine scheduling with learning considerations, European Journal of Operational Research115 (1999), 173–178.

    Article  MATH  Google Scholar 

  4. J. R. Dejong,The effects of increasing skill on cycle time and its consequences for time standards, Ergonomics1 (1957), 51–60.

    Article  Google Scholar 

  5. R. L. Graham, E. L. Lawler, J. K. Lenstra and A. H. G. Rinnooy Kan,Optimization and approximation in deterministic sequencing and scheduling: a survey, Annals of Discrete Mathematics5 (1979), 287–326.

    Article  MATH  MathSciNet  Google Scholar 

  6. S. M. Johnson,Optimal two and three stage production schedules with setup times included, Naval Research Logistics Quarterly1 (1954), 61–68.

    Article  Google Scholar 

  7. G. Mosheiov,Scheduling problems with a learning effect, European Journal of Operational Research132 (2001), 687–693.

    Article  MATH  MathSciNet  Google Scholar 

  8. G. Mosheiov,Parallel machine scheduling with a learning effect, Journal of the Operational Research Society52 (2001), 1165–1169.

    Article  MATH  Google Scholar 

  9. G. Mosheiov and J. B. Sidney,Scheduling with general job-dependent learning curves, European Journal of Operational Research147 (2003), 665–670.

    Article  MATH  MathSciNet  Google Scholar 

  10. C. C. Pegels,On start-up or learning curves: an expanded view, AIIE Transactions1 (1969), 316–322.

    Google Scholar 

  11. M. Pinedo,Scheduling: Theory, Algorithms and Systems, Prentice hall, Englewood cliffs, New jersey, 1995.

    Google Scholar 

  12. J.-B. Wang and Z.-Q. Xia,Flow shop scheduling with a learning effect, Journal of the Operational Research Society (to appear).

  13. J.-B. Wang and Z.-Q. Xia,No-wait or no-idle permutation flowshop scheduling with dominating machines, J. Appl. Math. & Computing (to appear).

  14. T. P. Wright,Factors affecting the cost of airplanes, Journal of the Aeronautical Sciences3 (1936), 122–128.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Science, Shenyang Institute of Aeronautical Engineering, 110034, Shenyang, P. R. China

    Ji-Bo Wang

Authors
  1. Ji-Bo Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ji-Bo Wang.

Additional information

Ji-Bo Wang is an assistant professor at the Department of Science at Shenyang Institute of Aeronautical Engineering. He is a Ph. D student at Dalian University of Technology. Mr. Wang's research interests are the scheduling problems and operations research methods and applications.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, JB. Flow shop scheduling jobs with position-dependent processing times. JAMC 18, 383–391 (2005). https://doi.org/10.1007/BF02936581

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02936581

AMS Mathematics Subject Classification

Key words and phrases

Search

Navigation