Abstract
The purpose of the article is to develop the method for solving two‐ and three‐index fuzzy transportation problems. The fuzzy models of transportation problems allow formalizing situation for the using of fuzzy resources which should take into account in case of the uncertainty in the determination of the volume of production and consumption. Additional information is introduced in these models about the possible values of the needs in the form of fuzzy sets. The corresponding membership functions can be viewed as a way to approximate an expert display of available non‐formalized his ideas about the real value of the parameter on the basis of which the various possible values of each particular parameter values are assigned to the membership functions. Research methods is a mathematical modeling based on transport problem, solved on a network, that consists of a finite number of nodes and arcs between them, is a linear programming problem (LPP), if the total cost of transport and restrictions on traffic volumes are defined by linear functions. Scientific novelty of the research is to solve transportation problems with intermediate points that reduce to solving two‐index and three‐index tasks are considered. The ways to find the optimal solution of fuzzy transportation problem, in which resources are given in the form of triangular fuzzy numbers. Conclusions. Method of transformation in the system of constraints for the solving the crisp and fuzzy transportation problems with intermediate points has been proposed. The proposed method is illustrated by the example of real transportation problem.
Highlights
The main essence of the transportation problem (TP), which is one of the examples in mathematical programming problems, it is optimal distributing of the «producers» similar products among a group of «consumers» with the defined limits on the «supply» and «demand».Description and study of transport‐type tasks devoted a lot of scientific publications (Voloshyn and Mashchenko, 2010)
The corresponding membership functions can be viewed as a way to approximate an expert display of available non‐formalized his ideas about the real value of the parameter on the basis of which the various possible values of each particular parameter values are assigned to the membership functions
Research methods is a mathematical modeling based on transport problem, solved on a network, that consists of a finite number of nodes and arcs between them, is a linear programming problem (LPP), if the total cost of transport and restrictions on traffic volumes are defined by linear functions
Summary
A wide class of applied problems of resource allocation belongs to the class of multi‐index problems. In this article is offered the method of solving of two‐index and three‐index traditional and fuzzy transportation problems. This method is used for case of fuzzy constraints of resources. The fuzzy models of transportation problems allow to formalize situation for the using of fuzzy resources which should take into account in case of the uncertainty in the determination of the volume of production and consumption. In these models is introduced additional information about the possible values of the needs in the form of fuzzy sets.
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