Тензорная сетевая модель системы логистики

Abstract

The goal is to create a network model of logistics that ensures the distribution of product flows from producers to consumers in conditions of growing volumes of information, changing economic ties. To create a model, a tensor method of calculating processes is used when changing the structure of network models of technical and economic systems, including decomposition and calculation in parts. The network is considered as a tensor, the projections of which are various connections of branches. The coordinates in the network space are closed and open paths. When changing the network structure, a new solution is obtained using a path transformation matrix. As a result, for the first time, a network model of logistics was created with branches of producers, consumers (determine the basis of open paths) and routes (determine the basis of closed paths). The resistances of the branches set the tariffs for the storage and transportation of products. The product flows of producers and consumers are set by voltage sources that create part of the distribution of flows along routes. To supplement up to full product flows, voltage sources are introduced in the branches of the routes, which give additional currents. For routes in excess of the number of open paths, the values of the complement currents should be selected. The sum of currents from all sources gives the values of product flows from suppliers to consumers, solving the logistics task. The network model is used to calculate product flows along routes without iterations, the cost of transportation, as well as to transform the solution when routes, tariffs, supply and demand change, using algorithms of the tensor method of dual networks.