Skip to main content

Production Line Optimization with Model Based Methods

  • Chapter
  • First Online:
Math for the Digital Factory

Part of the book series: Mathematics in Industry ((TECMI,volume 27))

Abstract

In this paper we deal with different models of production lines of factories and consider the makespan optimization problem based on these models. We consider state-of-the-art and novel mathematical optimizers including exact and heuristic methods. We apply these optimizers to both standard academic and industrial data sets. We see that in a large rate of the considered cases the novel exact optimizers converged to the optimum fast which is surprising being the problems NP-hard and the problem sizes big. This shows the importance of exploiting the structure present in the industrial data using standardized industrial data sets for testing mathematical algorithms devoted to solve industrial problems and that some provided exact mathematical optimizers are fast and perform accurately on the considered industrial problems.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Baker, K.R.: Introduction to Sequencing and Scheduling. Wiley, New York (1974)

    Google Scholar 

  2. Hajba, T., Horváth, Z.: New effective MILP models for PFSPs arising from real applications. Cent. J. Oper. Res. 21, 729–744 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Hajba, T., Horváth, Z.: MILP models for the optimization of real production lines. Cent. J. Oper. Res. 23, 899–912 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  4. Johnson, S.M., Optimal two -and three stage production schedules with setup times included. Nav. Res. Logist. Q. 1(1), 61–68 (1954)

    Article  MATH  Google Scholar 

  5. Jósvai, J.: Production process modeling and planning with simulation method, mounting process optimisation. In: The International Conference on Modeling and Applied Simulation. Universidad de La Laguna, 23–25 September 2009, pp. 240–245 (2009)

    Google Scholar 

  6. Kan, A.H.G.R.: Machine Scheduling Problems: Classifications, Complexity and Computation. Nijhoff, The Hague (1976)

    Book  Google Scholar 

  7. Lageweg, B.J., Lenstra, J.K., Kan, A.H.G.R.: A general bounding scheme for the permutation flow-shop problem. Oper. Res. 26, 53–67 (1978)

    Article  MATH  Google Scholar 

  8. Liao, C.L., You, C.T.: An improved formulation for the job-shop scheduling problem. J. Oper. Res. Soc. 43, 1047–1054 (1992)

    Article  MATH  Google Scholar 

  9. Manne, A.S.: On the job-shop scheduling problem. Oper. Res. 8, 219–223 (1960)

    Article  MathSciNet  Google Scholar 

  10. Nawaz, M., Enscore, E.E., Ham, I.: A heuristic algorithm for the m-machine n-job flow-shop sequencing problem. Omega 11, 91–95 (1983)

    Article  Google Scholar 

  11. Nowicki, E., Smutnicki, C.: A fast tabu search algorithm for the permutation flow-shop problem. Eur. J. Oper. Res. 91, 160–175 (1996)

    Article  MATH  Google Scholar 

  12. Pan, C.H.: A study of integer programming formulations for scheduling problems. Int. J. Sys. Sci. 28, 33–41 (1997)

    Article  MATH  Google Scholar 

  13. Rajendran, C., Ziegler, H.: Ant-colony algorithms for permutation flowshop scheduling to minimize total makespan/total flowtime of jobs. Eur. J. Oper. Res. 155, 426–438 (2004)

    Article  MATH  Google Scholar 

  14. Stafford, E.F.: On the development of a mixed-integer linear programming model for the flowshop sequencing problem. J. Oper. Res. Soc. 39, 1163–1174 (1988)

    Article  MATH  Google Scholar 

  15. Stafford, E.F., Tseng, F.T.: On the Strikar-Gosh MILP model for the N × M SDST flowshop problem. Int. J. Prod. Res. 28, 1817–1830 (1990)

    Article  Google Scholar 

  16. Stafford, E.F., Tseng, F.T.: Two models for a family of flowshop sequencing problems. Eur. J. Opr. Res. 142, 282–293 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  17. Stafford, E.F., Tseng, F.T.: New MILP models for the permutation flowshop problem. J. Oper. Res. Soc. 59, 1373–1386 (2008)

    Article  MATH  Google Scholar 

  18. Stafford, E.F., Tseng, F.T., Gupta, N.D.: An empirical anlysis of integer programming formulations for the permutation flowshop. Omega 32, 285–293 (2004)

    Article  Google Scholar 

  19. Stafford, E.F., Tseng, F.T., Gupta, N.D.: Comparative evaluation of the MILP Flowshop models. J. Opr. Res. Soc. 56, 88–101 (2005)

    Article  MATH  Google Scholar 

  20. Taillard, E.: Benchmarks for basic scheduling problems. Eur. J. Oper. Res. 64, 278–285 (1993)

    Article  MATH  Google Scholar 

  21. VDI: Digital Factory Fundamentals. VDI 4499 Guideline, Düsseldorf (2008)

    Google Scholar 

  22. Wagner, H.M.: An integer linear-programming model for machine scheduling. Nav. Res. Log. Q. 6, 131–140 (1959)

    Article  MathSciNet  Google Scholar 

  23. Wilson, J.M.: Alternative formulations of a flow-shop scheduling problem. J. Oper. Res. Soc. 40, 395–399 (1989)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Z. Horváth .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Hajba, T., Horváth, Z., Kiss-Tóth, C., Jósvai, J. (2017). Production Line Optimization with Model Based Methods. In: Ghezzi, L., Hömberg, D., Landry, C. (eds) Math for the Digital Factory. Mathematics in Industry(), vol 27. Springer, Cham. https://doi.org/10.1007/978-3-319-63957-4_8

Download citation

Publish with us

Policies and ethics