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Accuracy of Semi-Analytical and Numerical Approaches in the Evaluation of Serial Bernoulli Production Lines

Author

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  • Viktor Ložar

    (Department of Naval Architecture and Ocean Engineering, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000 Zagreb, Croatia)

  • Neven Hadžić

    (Department of Naval Architecture and Ocean Engineering, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000 Zagreb, Croatia)

  • Tihomir Opetuk

    (Department of Naval Architecture and Ocean Engineering, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000 Zagreb, Croatia)

  • Vedran Slapničar

    (Department of Naval Architecture and Ocean Engineering, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000 Zagreb, Croatia)

Abstract

The manufacturing industry has a great impact on the economic growth of countries. It is, therefore, crucial to master the skills of the production system by mathematical tools that enable the evaluation of the production systems’ performance measures. Four mathematical approaches toward the modeling of steady-state behavior of serial Bernoulli production lines were considered in this study, namely, the analytical approach, the finite state method, the aggregation procedure, and numerical modeling. The accuracy of the performance measures determined using the semi-analytical methods and the numerical approach was validated using numerous theoretical examples and the results obtained using the analytical model. All of the considered methods demonstrated relevant reliability, regardless of the different theoretical backgrounds.

Suggested Citation

  • Viktor Ložar & Neven Hadžić & Tihomir Opetuk & Vedran Slapničar, 2021. "Accuracy of Semi-Analytical and Numerical Approaches in the Evaluation of Serial Bernoulli Production Lines," Mathematics, MDPI, vol. 9(13), pages 1-25, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1461-:d:579808
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    References listed on IDEAS

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    1. Robert A. Jarrow & David Lando & Stuart M. Turnbull, 2008. "A Markov Model for the Term Structure of Credit Risk Spreads," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 18, pages 411-453, World Scientific Publishing Co. Pte. Ltd..
    2. Zhiyang Jia & Liang Zhang & Jorge Arinez & Guoxian Xiao, 2016. "Performance analysis for serial production lines with Bernoulli Machines and Real-time WIP-based Machine switch-on/off control," International Journal of Production Research, Taylor & Francis Journals, vol. 54(21), pages 6285-6301, November.
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