Fuzzy model of nonlinear multi-index transportation problem

Authors

  • Лев Григорович Раскін National Technical University "KPI" St. Frunze 21, Kharkov, Ukraine, 61002, Ukraine https://orcid.org/0000-0002-9015-4016
  • Оксана Володимирівна Сіра National Technical University "KPI" St. Frunze 21, Kharkov, Ukraine, 61002, Ukraine https://orcid.org/0000-0002-4869-2371
  • Ольга Ігорівна Дунаєвська National Technical University "KPI" St. Frunze 21, Kharkov, Ukraine, 61002, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2012.5676

Keywords:

Fuzzy model, nonlinear multi-index problem, decomposition algorithm, membership function

Abstract

 

Traditional problems of transport logistics are formulated in terms of linear programming. In this case, the assumption is that the cost of product transportation at any route is proportional to its volume. In practice, this assumption often is not fulfilled. The objective of the problem then becomes nonlinear. The problem becomes more complicated if it is necessary to take into account that the cost of transportation depends not only on "supplier-consumer", but also on the type of cargo, type of vehicles used, etc. The problems that arise in this case become multi-index ones. The article includes a theorem, on which the technology for solving such problems is based. We suggested a method for solving nonlinear fuzzy transportation problems, which is based on a multi-stage decomposition procedure, at each stage of which the problems of smaller dimension are solved. The peculiarities of the procedure are illustrated on two-index problem when the suggested method becomes a two-step procedure. Thus, the blurring of parameters of the objective of the problem is taken into account at the first stage of the decomposition procedure

Author Biographies

Лев Григорович Раскін, National Technical University "KPI" St. Frunze 21, Kharkov, Ukraine, 61002

Ph.D., Professor, head of department

Department of computer-based monitoring and logistics

Оксана Володимирівна Сіра, National Technical University "KPI" St. Frunze 21, Kharkov, Ukraine, 61002

Ph.D., Associate Professor

Department of computer-based monitoring and logistics

Ольга Ігорівна Дунаєвська, National Technical University "KPI" St. Frunze 21, Kharkov, Ukraine, 61002

Assistant professor

Department of computer mathematics and mathematical modelling

References

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Published

2012-12-14

How to Cite

Раскін, Л. Г., Сіра, О. В., & Дунаєвська, О. І. (2012). Fuzzy model of nonlinear multi-index transportation problem. Eastern-European Journal of Enterprise Technologies, 6(4(60), 15–17. https://doi.org/10.15587/1729-4061.2012.5676

Issue

Section

Mathematics and Cybernetics - applied aspects