Developing of the algorithm of maximum flow of minimum cost finding in a fuzzy dynamic network

Abstract

Developing of the algorithm of maximum flow of minimum cost finding in a fuzzy dynamic network

A.V. Bozhenyuk, E.M. Gerasimenko

Incoming article date: 30.03.2013

The article considers the problem of maximum flow of minimum cost finding in fuzzy dynamic transportation network. The relevance of the problem is in its wide practical application on the rail, air, sea and other roads in finding of routes of minimum cost. The feature of the problem statement is that fuzzy nature of the network parameters, such as arc capacities and costs is taken into account. It allows us to make decisions more sensitive to environmental changes. The dependence of network parameters from flow departure is also considered, that allows to introduce the notion "dynamic" network as opposed to "stationary-dynamic", examined in the literature. The algorithm for solving the described problem in fuzzy conditions is proposed. To illustrate the algorithm a numerical example is presented.

Keywords: dynamic network, maximum flow of minimum cost, fuzzy numbers, arc capacity, transit time