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Transient Response of Homogenous and Nonhomogenous Bernoulli Production Lines

Author

Listed:
  • Neven Hadžić

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

  • Viktor Ložar

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

  • Tihomir Opetuk

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

  • Robert Keser

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

Abstract

The transient response of production systems is of significant importance especially if present advancements in Digital Twinning technology are taken into account. While the steady-state response enables long-term strategic decision making, the transient response enables more detailed simulation concerning aspects like production losses and preventive maintenance. This is especially relevant if nonhomogenous aspects of production systems are taken into account. An analytical and approximative solution to the problem of the transient response of homogenous and nonhomogenous Bernoulli production systems is developed in this paper based on the eigendecomposition of transition matrices, the eigenvalue problem, and the finite-state method. In particular, sub-resonant and resonant nonhomogeneous production lines are introduced for the first time. Also, the most significant key performance indicators are developed as functions of the time elapsed from the first cycle. Finally, the relationship between the number of eigenvalues and the accuracy of the results is inspected by employing a sensitivity analysis. The presented theoretical framework was employed in the case of a wood processing facility to present the potential application of the theory in the case of long- and short-term management of production systems.

Suggested Citation

  • Neven Hadžić & Viktor Ložar & Tihomir Opetuk & Robert Keser, 2023. "Transient Response of Homogenous and Nonhomogenous Bernoulli Production Lines," Mathematics, MDPI, vol. 11(24), pages 1-24, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4945-:d:1299601
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    References listed on IDEAS

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    4. Liang Zhang & Chuanfeng Wang & Jorge Arinez & Stephan Biller, 2013. "Transient analysis of Bernoulli serial lines: performance evaluation and system-theoretic properties," IISE Transactions, Taylor & Francis Journals, vol. 45(5), pages 528-543.
    5. Semyon M. Meerkov & Liang Zhang, 2011. "Unbalanced production systems with floats: analysis and lean design," International Journal of Manufacturing Technology and Management, Inderscience Enterprises Ltd, vol. 23(1/2), pages 4-15.
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