- BUILDING MATERIALS AND PRODUCTS
- Ranking Model of Factors Affecting the Production of Building Materials
- UDC 691:330.111.4

**Evgeny V. TARARUSHKIN**, e-mail: evgeny.tararushkin@yandex.ru

Russian University of Transport (MIIT), ul. Obraztsova, 9, building 9, Moscow 127994, Russian Federation

**Abstract**. A mathematical model of the ranking of factors influencing the production of building materials is proposed. The aim of the ranking factors is to identify the degree of significance of factors that makes it possible to pay more attention to the most significant factors and, possibly, to eliminate the least significant factors, both in the organization of production of materials and during the production process. This will help to improve the quality of products. A technique for constructing a directed graph and its corresponding stochastic matrix (the Markov matrix) for factors determined by the designer or an expert on the basis of the initial data for the production of building materials is considered. Two types of directed graphs are proposed for consideration: with equiprobable weights of outgoing edges from one vertex and with different weights of outgoing edges from one vertex. The power method and the PageRank algorithm used to solve the ranking problem of graph vertices are described. The power method is used for indecomposable Markov matrices, the PageRank algorithm is applied to both decomposable and indecomposable matrices. Examples of ranking factors for a model with equiprobable weights of graph edges and with assigned weights of graph edges are given.

**Key words**: ranking, factors of production, building materials, oriented graph, power method. - REFERENCES

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