Multi-Criterion Support for the Decision Problem Solving in the Food Packaging Process

Jacek Postrozny; Robert Bucki; Petr Suchánek

doi:10.31181/dmame8120251353

Authors

Jacek Postrozny Institute of Engineering and Technical Sciences, Cavalry Captain Witold Pilecki State University of Malopolska in Oswiecim, Oswiecim, Poland https://orcid.org/0009-0006-1431-4643
Robert Bucki Institute of Management and Information Technology in Bielsko-Biała, Poland https://orcid.org/0009-0006-1431-4643
Petr Suchánek Department of informatics and Mathematics, School of Business Administration in Karvina, Silesian University in Opava, Karvina, Czech Republic https://orcid.org/0009-0006-1431-4643

DOI:

https://doi.org/10.31181/dmame8120251353

Keywords:

Food packaging process; fuzzy evaluation; decision making; optimization criteria, Pare-to optimum

Abstract

The paper highlights the problem of the two-stage procedure for optimizing food packaging where the first stage involves selecting the optimal packaging structure and the second stage allows for the optimal selection of parameters of the packaging machine taking into account two criteria: the efficiency of the packaging process and the oxygen content in the packaging. The use of the modified Baas and Kwakernaak method in an industrial experiment allowed for the determination of the optimal packaging configuration assuming there are two types of criteria: deterministic ones focusing on the unit cost of packaging and tightness of the packaging and fuzzy ones focusing on appearance, smell and taste of the packaged product. The optimal packaging variant is variant a7 with the highest weighted average rating value equal to 0,7113. As part of parametric optimization, based on the obtained experimental results, the analyzed optimization criteria are presented in the form of regression equations and then these equations are subjected to statistical analysis. The form of the substitute criterion is formulated for the resulting single-criterion optimization problem. To deter-mine the set of Pareto optimal variants, the weight method is used, changing weight values every 0.05. Finally, the best variant is selected due to two opposing criteria using the distance function method implementing the Euclidean metric. The decision variables of the optimal variant also constitute the optimal parameters of the packaging machine due to the adopted optimization criteria. The optimal variant of the packaging process is variant 9 for which the value of the distance function di[f(x)] reaches the lowest value, i.e. 0.5533

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