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

• Autorzy: Stańczyk J.

Warianty tytułu

EN

Max-plus algebra application for production systems modelling and performance evaluation

• Języki publikacji: PL

Abstrakty

EN

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.

Słowa kluczowe

PL

dyskretny system zdarzeń; max-plus algebra; analiza efektywności

EN

discrete event systems; max-plus algebra; performance evaluation

• Wydawca: Polskie Towarzystwo Zarządzania Produkcją
• Czasopismo: Zarządzanie Przedsiębiorstwem
• Rocznik: 2017
• Tom: Vol. 20, nr 3
• Strony: 46--53
• Opis fizyczny: Bibliogr. 17 poz., rys.

Twórcy

autor

Stańczyk J.

• Katedra Genetyki, Uniwersytet Przyrodniczy we Wrocławiu, ul. Kożuchowska 7, 51-631 Wrocław, Polska

Bibliografia

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• [15] Stańczyk J., Max-Plus Algebra Toolbox for Matlab. Ver. 1.7, 2016, dostępny w Internecie: http://gen.up.wroc.pl/stanczyk/mpa/.
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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).