PL EN


2018 | 28 | 3 | 77-97
Article title

Max-plus algebra as a tool to modelling and performance analysis of manufacturing systems

Content
Title variants
Languages of publication
EN
Abstracts
EN
This contribution discusses the usefulness of (max, +) algebra as a mathematical framework for a class of manufacturing systems. This class can be described as dynamic and asynchronous, where the state transitions are initiated by events that occur at di screte instants of time. An event corresponds to the start or the end of an activity. Such systems are known as discrete event systems (DES). An overview of the concepts of modelling and analysis using the (max, +) algebra approach to DES has been given. Also, examples of manufacturing systems have been provided to illustrate the potential of this approach. The type of production process used, such as serial line, assembly line, etc., influences the modelling of different basic manufacturing systems. We have also presented the impact of the capacity of interoperable buffers. Based on an analytical model, effectiveness and performance indexes have been evaluated.
Year
Volume
28
Issue
3
Pages
77-97
Physical description
Contributors
  • Wroclaw University of Environmental and Life Science, Department of Genetics, ul. Kożuchowska 7, 51-631 Wroclaw, Poland, jaroslaw.stanczyk@upwr.edu.pl
References
  • BACCELLI F., COHEN G., OLSDER G.J., QUADRAT J-P., Synchronisation and Linearity, an Algebra for Discrete Event Systems, Wiley, Chichester 1992.
  • CASSANDRAS C.G., LAFORTUNE S., Introduction to Discrete Event Systems, Springer, Heidelberg 2007.
  • CUNINGHAME-GREEN R., Minimax Algebra. Lecture Notes in Economics and Mathematical Systems, 1979, 166.
  • Dorot Control Valves, Adopted from Dorot materials, 2001, http://www.dorot.com/
  • GROSS D., SHORTIE J.F., THOMPSON J.M., HARRIS C.M., Fundamentals of Queueing Theory, Wiley, Hoboken 2008.
  • HEIDERGOTT B., OLSDER G.J., VAN DER WOUDE J., Max Plus at Work. Modelling and Analysis of Synchronized Systems, Princeton University Press, Princeton 2006.
  • KASHKOUSH M., ELMARAGHY H., Consensus tree method for generating master assembly sequence, Prod. Eng., 2014, 8, 233–242.
  • KOMEDA J., LAHAYE S., BOIMOND J.-L., VAN DEN BOOM T., Max-plus algebra and discrete event systems, IFAC Papers Online, 2017, 50 (1), 1784–1790.
  • LIMNIOS N., OPROŞAN G., Semi-Markov Processes and Reliability, Springer Science, Business Media, New York 2013.
  • MAIA C.A., HARDOUIN L., SANTOS-MENDES R., COTTENCEAU B., Optimal closed-loop control of timed event graphs in dioids, IEEE Trans. on Automatic Control, 2003, 12, 2284–2287.
  • MUTSAERS M., ÖZKAN L., BACKX T., Scheduling of energy flows for parallel batch processing using max-plus systems, Proc. 8 IFAC Symposium on Advanced Control of Chemical Processes, Singapore, 2012.
  • NAMBIAR A.N., IMAEV A., JUDD R.P., CARLO H.J., Production planning models using max-plus algebra, [In:] V. Modrak, R.S. Pandian (Eds.), Operations management research and cellular manufacturing systems, IGI Global, Hershey 2012, 227–257.
  • PETRI C.A., Kommunikation mit Automaten, PhD Thesis, University of Bonn, 1962.
  • RAMADGE P.J., WONHAM W.M., The control of discrete event systems, Proc. of the IEEE, 1989, 77, 81–98.
  • SELEIM A., EL MARAGHY H., Max-plus modeling of manufacturing flow lines, Proc. 47 CIRP Conference Manufacturing Systems (CMS2014), 2014, 17, 302–307.
  • SEYBOLD L., WITCZAK M., MAJDZIK P., STETTER R., Towards robust predictive fault-tolerant control for a battery assembly system, Int. J. Appl. Math. Comp. Sci., 2015, 25 (4), 849–862.
  • STAŃCZYK J., Max-Plus Algebra Toolbox for Matlab ver. 1.7, 2016, http://gen.up.wroc.pl/stanczyk/mpa/
  • STAŃCZYK J., MAYER E., RAISCH J., Modelling and performance evaluation of DES, Proc. International Conference Informatics in Control, Automation and Robotics, Setubal, Portugal, 2004, 3, 270–275.
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.desklight-4b308aad-9118-4269-bd7b-34530ff02222
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.