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Creative Commons licence CC BY-NC (Attribution-NonCommercial)Logforum. 2017. 13(3), article 5, 301-311; DOI: https://doi.org/10.17270/J.LOG.2017.3.5


Bożena Zwolińska1, Łukasz Kubica2

1AGH University of Science and Technology, Kraków, Poland
Jagiellonian University in Kraków, Kraków, Poland


Background: In terms of Lean Six Sigma, the whole process focuses on clients and their needs. Existence of a client generates the supply of companies. Extended customization has a negative impact for a structure of the production system. Dynamics of changes and no predictability of system’s state in time t+1 lead to increase of the operational costs. It particularly affects those companies which are producing goods using MTO (make – to – order) method in short series. The goal of this article is to establish a mathematical model defining how the structure of a production system is subject to change depending on the volume of the production batch for a production system in accordance with MTO. Furthermore pilot calculations have been presented which determine the probability value, how subsequent random variables are contained within three standard deviations (±3δ) from the determined expected value (ET) for the entire production structure. Months of analysis and research on introducing selected lean toolbox components to a polish company from the small and medium enterprises sector resulted in the models presented in the article. The production structure of the discussed actual facility is complex and is of converged nature in accordance with MTO, while the final products are manufactured in short production series with a relatively wide customization options.

Materials and results: Wrought models consider theories of  Klir and Maserovicz [Mesarovic 1964] and also theory of mass operation (one of the probability areas).  In the article there are results from two models which are fundamental in defining problems in logistics engineering and production in scientific research. Important attribute of presented models is a fact that they consider relations between variables in a structure of consecutive processes and also consider relations between a size of production party and a real object.

Presented models are not only theoretical coverage but also consider real relations between objects. Real productive object specialized in producing cooling devices destined to store hematogenous objects, plasma and cryoprecipitate has been analyzed. Those devices have very strict quality requirements (consistent with ISO 13485 and CE0434 in accordance with Directive 93/42/EEC).

In the article there is a presentation of three models which indicates two different functions of production time for production party of  2 ≤ k ≤ 30 and k > 30  items.  In the following model there are a few different parameters of the production system: variable parameters of processes’ times which depend on a kind of half-finished product, dependency of time needed to produce an item, size of a production party and also dependency of operational times and implemented technology.

Conclusions: It is important to customize tools to individual attributes of a system whilst implementing changes in real objects. One change can be effective in one organization and not necessarily in the other. Wrought model is a first of the steps in building a scheme necessary to validate a real object in time t+1. On the next step those theories will be implemented in IT tool environment of R Studio or Witness System Simulation Modeling to conduct statistical analysis based on historical data.

Keywords: Convergent production system, model of the changes’ dynamics
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For citation:

MLA Zwolińska, Bożena, and Łukasz Kubica. "Forming of the dynamics of the changes in convergent production system depending on size of production party." Logforum 13.3 (2017): 5. DOI: https://doi.org/10.17270/J.LOG.2017.3.5
APA Bożena Zwolińska, Łukasz Kubica (2017). Forming of the dynamics of the changes in convergent production system depending on size of production party. Logforum 13 (3), 5. DOI: https://doi.org/10.17270/J.LOG.2017.3.5
ISO 690 ZWOLIŃSKA, Bożena, KUBICA, Łukasz. Forming of the dynamics of the changes in convergent production system depending on size of production party. Logforum, 2017, 13.3: 5. DOI: https://doi.org/10.17270/J.LOG.2017.3.5