The Bernoulli splitting line: analytical and semi-analytical evaluation of the steady-state performance

Hadžić, Neven; Ložar, Viktor; Opetuk, Tihomir; Andrić, Jerolim

doi:10.1080/00207543.2021.1974115

Cited by 4 publications

(10 citation statements)

References 28 publications

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“…Here, a brief outline of the random-process-based finite-state method is presented, as it is employed later to construct a digital twin of fabrication lines. Further details regarding the development and verification of the finite-state method in different cases are available in the existing literature (e.g., [3]).…”

Section: Mathematical Modelingmentioning

confidence: 99%

“…The key performance indicators (KPIs), such as the production rate, work-in-process, and probabilities of blockage and starvation, can be evaluated upon the formulation of the system-level steady-state probability distribution (Equation ( 4)). Because a detailed formulation of the key performance indicators is available in the literature [3,7,33,37], only their final form will be outlined here for clarity reasons. Thus, the production rate (PR ξ ), as an expected number of finished products per cycle time, equals…”

Section: Key Performance Indicatorsmentioning

confidence: 99%

“…Presently, the digital twinning of the ship production process is seldom addressed in the research literature and, when it is, it remains at the level of simulations, often yielding immeasurable results. Therefore, the main goal of the present paper is to develop and present the digital twinning of fabrication lines in shipyards based on Markovian modeling and the powerful finitestate method [3]. This approach can be employed as an efficient way to perform predictive analytics and, consequently, enhance the decision-making processes at different stages of ship production planning and implementation.…”

Section: Introductionmentioning

confidence: 99%

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Towards Digital Twinning of Fabrication Lines in Shipyards

Hadžić

Ložar

Opetuk

et al. 2023

JMSE

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The digital twinning concept stands as a remarkable opportunity to integrate sophisticated mathematical models within the context of existing manufacturing systems. Such models may provide shipyard management with predictive analytics, improving the final results at the strategic, tactical, and operational levels. Therefore, the possibility of integrating the Markovian-framework-based finite-state method into the context of ship production is presented in this study, including its outline, digital thread, and factory-floor data reliance. First, the predictive analytics problem is addressed by the finite-state method in the case of the shipyard’s fabrication line, and the obtained results are validated afterward using a numerical model through discrete-event theory. The predictive analytics indicate an almost ideal balancing of the fabrication line, except for the buffers storing stiffeners before the coat-dying and marking operations. In addition, the improvability analysis of the shipyard’s fabrication lines extended the scope of the predictive analytics using bottleneck identification and affecting the key performance indicators through a digital thread, as well as by improved maintenance strategies.

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Section: Mathematical Modelingmentioning

confidence: 99%

Section: Key Performance Indicatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Towards Digital Twinning of Fabrication Lines in Shipyards

Hadžić

Ložar

Opetuk

et al. 2023

JMSE

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“…Given the transition matrix, [P], Equations ( 1) and (2) can be solved directly for each cycle n. Indeed, the available formulations of transition matrices in the case of serial, splitting, and assembly Bernoulli production lines [12,13,15] stand as the key enablers of a direct approach to the problem. However, for complexity reasons, the direct solution of Equation ( 1) or (2) quickly becomes rather cumbersome, especially in the case of large-scale, dense, and transition-rich systems.…”

Section: Analytical Solutionmentioning

confidence: 99%

“…Then, an asymptotic analysis technique (or the aggregation procedure) was introduced by Lim et al [10] and successfully applied later on in many cases, including primarily the steady-state response of serial, splitting, or assembly production lines composed of machines of Bernoulli, exponential, or non-exponential reliability [11]. Finally, an analytical solution to the problem has been developed in [12], followed by the newly introduced finite-state method, e.g., [13,14]. All three approximative methodologies, the decomposition method, the aggregation procedure, and the finite-state method, were successfully applied in the steady-state case of production systems.…”

Section: Introductionmentioning

confidence: 99%

Transient Response of Homogenous and Nonhomogenous Bernoulli Production Lines

Hadžić,

Ložar,

Opetuk

et al. 2023

Mathematics

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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.

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