SOLUTION OF THE PARTIALLY REVERSAL MODELLING TASK OF THE MINIMUM COST FLOW FINDING IN FUZZY CONDITIONS

Abstract

This article is devoted to the development of an algorithm for solving the problem of modeling
a partially reversal flow of minimum cost in a fuzzy transportation network. The minimum cost
flow problem is a central problem in transportation planning and evacuation modelling. The relevance
of these tasks is due to necessity to find optimal transportation routes in terms of cost andtransfer the maximum flow along them. This article is devoted to solving this problem in fuzzy
conditions, since the apparatus of the theory of fuzzy sets allows you to set network parameters,
such as the capacity of road sections, the cost of transportation in a fuzzy form. This method of
assignment is convenient in situations where there is a lack of data on the modeled object, linguistic
nature of data, measurement errors, etc. In the problems of evacuation modelling, which occur
spontaneously, there is also a lack of accurate information about the capacity and cost of transportation.
The contraflow concept, which was used in the paper, allows increasing the total flow
by reversing traffic. The lane reversal technique is a modern technique for increasing the transmitted
traffic by increasing the network output capacity. The use of traffic reversal allows releasing
congested sections of the road and redistributing traffic towards unloaded roads, eliminating congestion
and "traffic jams" on the roads. A method of operating with fuzzy numbers is proposed,
which does not lead to "blurring" of the boundaries of the resulting number and allows operating
with fuzzy boundaries at the last iterations, while at the rest of the previous iterations, calculations
are performed only with the centers of fuzzy numbers. A numerical example is considered that
illustrates the operation of the proposed algorithm.