Skip to main content

Max-Plus Algebraic Modelling of Cyclical Multi-assortment Manufacturing System

  • Chapter
  • First Online:
Modelling and Performance Analysis of Cyclic Systems

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 241))

  • 277 Accesses

Abstract

In this chapter, multi-assortment production systems are considered, which can be described as Discrete Event Systems (DES). Due to the implementation of a certain number of products, they are characterized by repetitive, cyclical (rhythmic) behavior. Analyzing multi-assortment, cyclic production, there are a number of phenomena that have a direct impact on the behavior of systems, such as ending the production of one product or launching, in an already existing production system, the production of an additional, new product. And it is the modeling of such phenomena that is presented in this chapter.

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 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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. Baccelli, F., Cohen, G., Olsder, G.J., Quadrat, J.P.: Synchronisation Linearity. Wiley, New York (1992)

    Google Scholar 

  2. Butkovič, P.: Max-linear Systems: Theory and Algorithms. Springer, Berlin (2010)

    Google Scholar 

  3. Cassandras, C.G., Lafortune, S.: Introduction to Discrete Event Systems, 2nd edn. Springer, Berlin (2007)

    MATH  Google Scholar 

  4. Cuninghame-Green, R.: Minimax Algebra. Lecture Notes in Economics and Mathematical Systems, vol. 166. Springer, Berlin (1979)

    Book  Google Scholar 

  5. Darabi, H., Jafari, M., Manapure, S.: Finite automata decomposition for flexible manufacturing systems control and scheduling. IEEE Trans. Syst. Man Cybern. 33(2), 168–175 (2003)

    Article  Google Scholar 

  6. David-Henriet, X., Hardouin, L., Raisch, J.: Max-Plus-Linear Systems for Modeling and Control of Manufacturing Problems. In: Ghezzi, L., Hömberg, D., Landry, C. (eds.) Math for the Digital Factory, pp. 37–60. Springer (2017)

    Google Scholar 

  7. Gaubert, S.: Max-Plus: Methods and Applications of (max, +) Linear Algebra. Technical Report RR-3088, INRIA. https://hal.inria.fr/inria-00073603 (1997). Accessed 29 March 2019

  8. Girault, C., Valk, R.: Petri Nets for Systems Engineering. Springer, Berlin (2003)

    Chapter  Google Scholar 

  9. Heidergott, B., Olsder, G.J., van der Woude, J.: Max Plus at Work: Modeling and Analysis of Synchronized Systems. Princeton University Press, Princeton (2005)

    Google Scholar 

  10. Indriyani, D., Subiono, S.: Scheduling of the crystal sugar production system in sugar factory using max-plus algebra. Int. J. Comput. Appl. Math. 2(3), 33–37 (2016)

    Article  Google Scholar 

  11. Komenda, J., Lahaye, S., Boimond, J.L., van den Boom, T.J.: Max-plus algebra in the history of discrete event systems. Ann. Rev. Control 45, 240–249 (2018)

    Article  MathSciNet  Google Scholar 

  12. León, F.P., Kiencke, U.: Ereignisdiskrete Systeme. Oldenbourg Verlag (2013)

    Google Scholar 

  13. Nambiar, A.N., Imaev, A., Judd, R.P., Carlo, H.J.: Production Planning Models using Max-Plus Algebra. In: Modrák, V., Pandian, R.S. (eds.) Operations Management Research and Cellular Manufacturing Systems, pp. 227–257. IGI Global (2012)

    Google Scholar 

  14. Papadopoulos, C.T., Li, J., O’Kelly, M.E.: A classification and review of timed markov models of manufacturing systems. Comput. Ind. Eng. 128(1), 219–244 (2019)

    Article  Google Scholar 

  15. Seleim, A., El Maraghy, H.: Max-plus modeling of manufacturing flow lines. In: Proceedings of \(47\)th CIRP Conference on Manufacturing Systems (CMS2014), vol. 17, pp. 302–307 (2014). https://doi.org/10.1016/j.procir.2014.01.133

    Article  Google Scholar 

  16. Stańczyk, J.: Max-Plus Algebra Toolbox for Matlab, ver. 1.7. http://gen.up.wroc.pl/stanczyk/mpa/ (2016). Accessed 29 March 2019

  17. Stańczyk, J.: Max-plus algebra as a tool for the modelling and performance analysis of manufacturing systems. Oper. Res. Decis. 28(3), 77–97 (2018). https://doi.org/10.5277/ord180307

    Article  Google Scholar 

  18. Yu, A.J.: Queueing Theory Applications in Manufacturing Systems. In: Bhat, U.N. (ed.) An Introduction to Queueing Theory, pp. 239–253. Springer (2015)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jarosław Stańczyk .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Stańczyk, J. (2020). Max-Plus Algebraic Modelling of Cyclical Multi-assortment Manufacturing System. In: Bożejko, W., Bocewicz, G. (eds) Modelling and Performance Analysis of Cyclic Systems. Studies in Systems, Decision and Control, vol 241. Springer, Cham. https://doi.org/10.1007/978-3-030-27652-2_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-27652-2_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-27651-5

  • Online ISBN: 978-3-030-27652-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics