Коэффициент рационального размещения

L.V. Latypova

candidate of economic science, professor of

Surgut state teacher’s training university

Formation of a methodical approach (the model) rational distribution of forest industries

Investigation of the forest industry is the basis for developing a methodical approach to the rational allocation of logging and timber processing enterprises in the region. In developing of the approach must be taken of one of the main principles: the principle of rational use of wood raw material, and also deep processing of the entire timber with its distribution by type of production and release of finished or semi-finished products. In these circumstances it is important to correctly determine the direction of expansion and inclusion in the combined company of new types of production, i.e. give directions to optimize the process of combining and becoming specialized enterprises in the combined and vertically integrated .

According V.E. Levanova[1]“Every production process has a huge number of obvious and hidden, complex web of relationships, to understand that it is impossible. Before you build a model that should be based on statistical methods, especially factor analysis, determine the size of various factors. This analysis reveals the influence of various factors on the patterns of the studied parameters. But it does not measure quantitatively the extent of this influence or determine the analytical expressions of functions that characterize the patterns of change of the indicators. For this purpose it is necessary to use the method of regression analysis, which allows, with the help of the regression coefficients, to evaluate quantitatively the degree of influence on the dependent variable of different technical and economic factors, varying from accidental changes. These random fluctuations, as a rule, not previously considered in the development of regulatory indicators. Application of correlation and factor analysis provides a normative value indicators, in which, together with the existing patterns and trends, will be reflected various and random changes in production”.

The main problem of the development of a methodological approach rational distribution of the forest industry is the problem of formalization (quantification results of the evaluation). Any quantification is expressed in numerical terms (figures, indices, etc.) otherwise the difference in the various levels of phenomena under study will not be seen. To make a comparison, we need some criteria, unified for enterprise - objects of comparative analysis.

All of the methodological approaches have a significant drawback - they do not take into account the quantitative impact of factors on the distribution of enterprises.

We have developed an algorithm for rational distribution of timber processing enterprises of the district (see Fig. 1).

Fig.1. The algorithm for rational distribution enterprises of forest industries

The algorithm identified three levels, which determine the rational distribution of the forest industry at the regional level.

The purpose of our model for the placement of the forest industry is as follows:

-  formation scheme rational distribution of forest industries based on sustainable use of raw materials.

Results of research:

-  definition of the structure of products for the rational distribution of forest industries;

-  deep processing of raw materials;

-  integrated use of wood.

We offer the basic stages of formation of rational distribution of timber processing enterprises of the district:

1. Formulation of the problem and identify the factors influencing the rational distribution of  timber processing enterprises of the district;

2. Prepare background information and solution on the PC;

3. Develop regression models.

Calculations rational distribution of the forest industry hampered by the multiplicity of industrial relations and a large number of enterprises. Forest products are widely used in other industries. The specificity of the industry in determining the rational distribution of the forest industry, requires a phased solution of the problem using a certain system models. Phasing the solution of the rational distribution of enterprises is a consistent definition of the proportions of the production of forest industry.

The first step is to use factor analysis, which enables to find the relation between the factors and determine the resulting figure. Methods of factor analysis have properties suitable for use in the composition of other statistical methods, most often in the regression analysis, cluster analysis, etc.

To determine the factors influencing the rational distribution of enterprises, we decided to use the method of regression analysis, the accuracy of the results of which largely depends on the number of observations. The more, the higher the confidence level of the identified dependencies. Of course, that all the factors of - different effects on the distribution of enterprises, selected factors for inclusion in the regression model covers the main aspects of the forest industry.

Based on our understanding of the rational distribution of enterprises and on the basis of existing models of corporate location, were the following indicators that reflect industry characteristics of the functioning of enterprises.

First, the amount actually taken harvested wood, as an indicator of industrial and business.

Secondly, the data on the annual allowable cut, reflecting the availability of raw materials.

Third, the dynamics of production volumes, reflecting the activity of enterprises.

Fourth, before the level of installed production capacity of enterprises, reflecting the maximum output.

Fifth, consideration of forest product exports, export orientation as a defining enterprises.

Sixth, represented the cost of one ruble of commodity output, reflecting the economic condition of enterprises.

In the seventh, brought average number of workers, reflecting the level of employment in the manufacturing process.

Eighth, consider the ratio of monthly average wages of workers to minimum wage, in order to determine the standard of living.

For selected indicators were introduced the following notation:

X1 - the actual volume of harvested timber;

X2 - annual leave wood (allowable cut);

X3 - the dynamics of production;

X4 - the level of the installed capacity of the enterprise;

X5 - export of forest products;

X6 - The cost of 1 rub. marketable products;

X7 - average number of workers;

Х8 - the ratio of average wages to minimum wage;

Cr - coefficient of rational placement.

At the preparatory stage of our statistical material was collected from 8 enterprises of Ust-Ilim region for the period 2000-2009 years. In the process of constructing the model it was decided to combine data on the companies for the quarters in the period under review, one set of 40 observations. The feasibility of this association is to increase the sample size, leading to greater statistical significance of the model.

Assessment of baseline data was performed using formulas 1, 2:

                                                     N-p-1 > 30                                                 (1)

                                                       N/p > 4                                                     (2)

Where N - number of observations,

            p - the number of factors included in the model.

Inserting initial information in the formulas 1 and 2 we obtain the following inequality:

40 - 8 - 1  = 31

31  > 30

40/8 =5

5 > 4

The foregoing suggests that the amount of information is sufficient for further analysis.

The outcomes of the linear correlation analysis[2] is a set of linear coefficients of pair correlation rxу in assessing the closeness relation studied phenomena.

For the analysis of the obtained values of the correlation coefficient, assessing the degree of closeness of the relationship between indicators of use scale, which is presented in Table 1.

Table 1

Scale of assessment of the closeness of relationships of the

analyzed indicators by the coefficients of the pair of linear correlation

As the dependence of our chosen rational distribution coefficient (Cr).

An analysis of the values we can conclude that the variables X1 and X3 - collinear (since they are together in a linear relationship, rх1, х2  > 0.7), it eliminates from the model of overlapping factors. So figure X1 from further analysis be deleted as a result of strong correlation, and rates of X2, X3, X4, X7, X8 were excluded from the model sequentially, as they showed the lowest correlation coefficient with respect to the coefficient of sound placement.

When calculating the regression model was an important factor in checking the adequacy of the model is to test the significance of each regression coefficient, whose value should not be greater than t - test Styudenta[3]. In the model submitted by factors X5, X6 (see Table. 2) according to the criterion Styudenta providing the most significant influence on the resultant variable.

Table  2

The matrix coefficients of pair correlation

X5 - export of forest products;

X6 - The cost of 1 rub. marketable products;

Cr - coefficient of rational placement.

In calculating the important point is the information obtained in the third line, where the correlation coefficients showing the degree of influence of the studied parameters on the resulting sign (coefficient of rational accommodation).

Using a scale assessing the degree of closeness of relationship, we obtained the following results:

- during the observation period there was a high degree of direct linear

relationship between the export of timber and the coefficient of rational accommodation (0,803);

- there is a strong degree of inverse linear relationship between the cost  of 1 rub. commodity production and rational distribution coefficient (-0.823).

In this case, analysis of data showed a high confinement of the relationship between Cr and X5 (0,80), as well as between the Cr and X6 (-0.82), so you should leave Cr, X5, X6.

Application of correlation analysis allowed us to identify the factors affecting the distribution of enterprises, and use them in constructing an optimization model of rational distribution of  timber processing enterprises.

As a result of regression analysis, we have received multiple regression equation of the form:

Cr = 1,00 + 0,004* Х5  - 0,019*Х6,

            Where X5 - export of forest products;

          X6 - The cost of 1 rub. marketable products;

Analysis of this equation makes it possible to draw conclusions: to increase the cost of 1 rub. commodity production unit, the coefficient rational distribution of the forest industry decreased by 0,019.

The value of the regression coefficient is statistically significant and the equation can be used for forecasting. Significance level is:

                 P-Sb0 = 0, 0000000004;    P-Sb1 = 0, 0000006;     P-Sb2 = 0,00000008.    

From these indicators, we can conclude that they are statistically significant and reliable (PS <0,05).

The quantity b0 evaluates the aggregated effect of other (except for the factors taken into account in the model X5, X6,) factors on the result.

Assessment of the reliability of the regression equations in general and target tightness connection R2Crх5х6 gives F - Fisher criterion. Ffakt. = 83, 71 the probability of obtaining such a value F - the criterion is 0.0000006, which does not exceed the permissible level of significance 5%, this shows the value of P - the value of these same tables. Consequently, the resulting value is not by chance, it was formed under the influence of significant factors, i.e., confirmed the statistical significance of the equation and figure tightness connection R2Crх5х. Based on F - Fisher criterion proved the adequacy of the constructed equation: Ffakt. > Ftabl. (α = 0,05; k1 = 8; k2 = 31) = 2, 27. Inequality observed 83,71> 2,27.

To assess the adequacy of the regression equation using the coefficient of approximation (MARE), or the average relative size of the model error. This criterion takes the value - 0.0355, indicating a high accuracy rate of approximation.

Unadjusted coefficient of multiple determination R2Сrх5х6 = 0.8230 estimates the proportion of variation due to the result presented in the equation factors in the overall variation of results. Here the proportion is 82% and indicates a very high degree of conditionality variation of result variation factors, i.e. a very high relationship factors with the result. So we can speak of a fairly high accuracy of approximation (model describes well the dependence of the location of the export of timber and the cost of 1 rub. marketable products).

The adjusted coefficient of multiple determination R2 Crх5х6 = 0,8132  determines the closeness with light degrees of freedom of general and residual variances. It gives this assessment of the closeness of communication, which does not depend on the number of factors in the model and indicates a very high determinacy result of the Cr model factors X5, X6. The regression equation is significant and there is a strong link between the signs[4].

Based on this we can conclude that the factors are considered significant.

Choosing the Ust-Ilim region as the object of study due to the following circumstances:

- area with abundant forests;

- availability of cheap water and energy resources;

- presence in the region operated enterprises for processing of raw wood (specializing in the production of export timber);

- availability of rail and waterways to support sustainable-enterprise communication between individual enterprises;

- availability of labor.

When constructing the model we take into account the structure and size of processing facilities to ensure the maximum amount of producing the best use of resources.

The solution of this problem allows us to define a system of economic-mathematical estimates, which characterizes the influence of the problem lay down the conditions on the effectiveness (maximum production volume of finished product) derived option for the future.

Algorithm implementation model developed by the author, is acceptable for other regions of the country, and to evaluate the rational distribution of timber processing enterprises of any region.

Summing up the study, we can formulate the results:

1. The method for rational distribution of forest industries in the region based on the rational use of raw materials.

2. A relation between indicators of the level of rational distribution of enterprises and the factors of production (timber exports, the costs per ruble of commodity output) using regression analysis. This dependence allows to determine the impact of major factors on the results for each region, this effect is different.

The proposed approach to rational distribution of timber processing enterprises can be seen as one step in solving complex problems to improve the efficiency of the timber industry in market conditions.

Literature

1.     Levanov V.E. Improving the analysis and planning of logging companies. - Moscow, Forestry, 1982. - Pp. 62.

2.     Statistics: Textbook. manual / Kharchenko L.P., Dolzhenkova V.G., Ionin V.G. and others; Under red. cand. economical. Science VG Ionin. - Ed. 2-e, a break. and add. - Moscow: INFRA, 2003 .- pp. 178.

3.     Eliseev S.V., Kurysheva S.V., Kosteeva T.V. etc. Econometrics: MM: Finance and Statistics, 2005. - Pp. 534.

4.     Korobov P.N. Mathematical methods of planning and governance in the forest and timber industry. Moscow: Forest Industry, 1974, - pp. 121.