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Zastosowanie max-plus algebry w modelowaniu i analizie efektywności systemów produkcyjnych

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Warianty tytułu
Max-plus algebra application for production systems modelling and performance evaluation
Języki publikacji
In response to increased competition, manufacturing systems are becoming more complex in order to provide the flexibility and responsiveness required by the market. The increased complexity requires decision support tools that can provide insight into the effect of system changes on performance in an efficient and timely manner. This contribution discusses the usefulness of (max, +) algebra as a mathematical framework for a class of production systems. The class can be described as a dynamic and asynchronous where the state transitions are initiated by events that occur at discrete instants of time. An event corresponds to the start or the end of an activity. A common property of such examples is that the start of an activity depends on termination of several other activities. Such systems are known as discrete event systems (DES). In the paper an overview of the modeling and analysis concepts of the (max, +) algebra approach for DES is given. Also, an application examples from manufacturing systems are provided to illustrate the potential of this approach. Considered systems have been represented as (max, +) algebraic state space models. How to model different basic manufacturing systems depends on production type, like serial line, assembly line, etc. as well as impact of capacity of interoperable buffers have been presented. Based on an analytical model, effectiveness evaluation or performance indexes have been calculated for different configurations of the same production system. So, finally the best solution, for given criteria, has been obtained. All exemplary calculations have been made using the Max-Plus Algebra Toolbox for Matlab, the software package developed by author and available on his homepage.
Opis fizyczny
Bibliogr. 17 poz., rys.
  • Katedra Genetyki, Uniwersytet Przyrodniczy we Wrocławiu, ul. Kożuchowska 7, 51-631 Wrocław, Polska
  • [1] Baccelli F., Cohen G., Olsder G.J., Quadrat J-P., Synchronisation and Linearity, an Algebra for Discrete Event Systems. Wiley, 1992.
  • [2] Cassandras C.G., Lafortune S., Introduction to Discrete Event Systems, Springer, 2007.
  • [3] Cuninghame-Green R., Minimax Algebra. “Lecture Notes in Economics and Mathematical Systems” 166/1979.
  • [4] Dorot Control Valves, Materiały firmy Dorot. 2001, dostępny w Internecie
  • [5] Gross D., Shortie J.F., Thompson J.M., Harris C.M., Fundamentals of Queueing Theory. Wiley&Son, New Jersey, Hoboken 2008.
  • [6] Heidergott B., Olsder G.J., van der Woude J., Max Plus at Work: Modeling and Analysis of Synchronized Systems. Princeton University Press, 2005.
  • [7] Kashkoush M., El Maraghy H., Consensus tree method for generating master assembly sequence. “Production Engineering” 8/2014, pp. 233-242.
  • [8] Limnios N., Opro¸san G., Semi-Markov Processes and Reliability. Springer, 2013.
  • [9] Maia C.A., Hardouin, L., Santos-Mendes R., Cottenceau B., Optimal Closed-Loop Control of Timed Event Graphs in Dioids. “IEEE Transactions on Automatic Control” 12/2003, pp. 2284-2287.
  • [10] Mutsaers M., Özkan L., Backx T., Scheduling of energy flows for parallel batch processing using max-plus systems. Mat. 8 IFAC Symposium on Advanced Control of Chemical Processes, Singapore 2012.
  • [11] Nambiar A.N., Imaev A., Judd R.P., Carlo H.J., Production Planning Models using Max-Plus Algebra. “Operations Management Research and Cellular Manufacturing Systems” 2012, pp. 227-257.
  • [12] Petri C.A., Kommunikation mit Automaten. PhD Thesis. University of Bonn, Bonn 1962.
  • [13] Ramadge P.J., Wonham W.M., The Control of Discrete Event Systems. “Proceedings of the IEEE” 77/1989, pp. 81-98.
  • [14] Seleim A., El Maraghy H., Max-Plus Modeling of Manufacturing Flow Lines. Mat. 47 CIRP Conference on Manufacturing Systems (CMS2014), 17/2014, pp. 302-307.
  • [15] Stańczyk J., Max-Plus Algebra Toolbox for Matlab. Ver. 1.7, 2016, dostępny w Internecie:
  • [16] Stańczyk J., Mayer E., Raisch J., Modelling and Performance Evaluation of DES. Mat. Int. Conf. Informatics in Control, Automation and Robotics, ICINCO’04, 3/2004. pp. 270-275.
  • [17] Van den Boom T., De Schutter B., Properties of MPC for Max-Plus-Linear Systems. “European Journal of Control” 5/2002, pp. 453-462.
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
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