Application of economic-mathematical models for optimization of arable lands from manifestation of degradation processes

Abstract

The system of management in market conditions depends on the efficient use of resources. Excessive use of arable land leads to economic and environmental losses. As a part of agricultural land in Ukraine there is a significant amount of arable land with the manifestation of degradation processes. The search for an optimal solution is possible with the help of mathematical methods and models in land management. The mathematical model is one of the important methods of scientific knowledge and is therefore used in all branches of science. Since land organization is considered as an interconnection with the organization of production, such land management project design problems are always experimental and require constant research.

The object of optimization of arable land, which has in its composition degraded and depleted land is the forest-steppe Right Bank province of Kiev region. In order for the investigated economic process to meet the current realities in the calculation, we use statistical data. The main purpose of the calculation is to establish optimal rotation parameters for the research object. According to the forecasted calculation for the Forest-steppe Right Bank province of Kiev region, the economic effect will be expressed in the increase of the crop. Increasing the crop will cover the lack of output on an area that will not be sown, but removed from cultivation for stopping and minimizing.

Keywords: economic-mathematical model optimization, degradation processes.

Relevance of the problem. Agriculture is the most vital sector in every country. For Ukraine, it has a special historical significance in the development of society. However, the ruin of agricultural land in Ukraine is excessive and does not correspond to rational use. Excessive use of arable land leads to economic and environmental losses. In the arable land there is a significant number of degraded, exhausted by intensive use of scarce soils. It is necessary to pay attention to the rational use of agricultural land to ensure the economic efficiency of modern agroformations. The search for an optimal solution is possible with the help of mathematical methods and models in land management.
The aim of the study is to optimize arable land with the manifestation of degradation processes through the methods of mathematical modeling on the example of the Forest-Steppe Provincial Province of the Kiev region.
Analysis of recent research and publications. Economic and mathematical models are used to verify the effectiveness of the decisions taken and the choice of the most optimal design solution in land management. A number of scientists are engaged in the search for optimal placement of crop rotation, lands, organization of rational use and processing of geodetic measurements using econometric and mathematical solutions in land management: Martin AG, Butenko Ye.V., Chumachenko O.M., Zhuk O.P., Krivovedy E.V. and other scholars [3,4].
The mathematical model is one of the important methods of scientific knowledge and is therefore used in all branches of science. Since land organization is considered as an interconnection with the organization of production, such land management project design problems always have an experimental character. Therefore, the search for a solution and the application of economic and mathematical methods in land management require constant research using various mathematical models and approaches for optimizing the use of land resources.
Presenting main material. Optimum use is to choose the best possible production option, while providing at least the cost, the minimum time spent on the cultivator and the maximum profit. Finding the optimal solution is through the use of various methodological approaches. To summarize the available techniques and find the optimal value between the profit, the time spent and the cost of the tasks set, we translate into a mathematical language, forming a mathematical model. In land management, the main condition is the ordering of the land, therefore the mathematical model will have the nature of optimization of ecological and economic dependencies, where in the final calculation should be satisfied the ratio of agricultural land to all available land in the region and obtaining in the future a greater amount of cultivated products.
In order for the investigated economic process to correspond to modern realities, at the initial stage in the calculation we use statistical data. The compliance of the calculated and statistical data is checked by the correlation dependence of the two values. The formation of a model of an economic-mathematical problem is solved by the definition of variables. Variable quantities are introduced into the matrix model, classifying them as the main and auxiliary. To solve the problem of optimization of agricultural lands, in particular arable land to the main variables, we will relate: the quality of soils, yields by statistical data, arable land, the balance of nutrients and the impact of degradation processes. The interdependence between two or more criteria (coefficients) of a system of linear equations or linear transformations is recorded through a mathematical object-matrix [3]. Further solution by methods of linear programming through the matrix system requires the setting of clear tasks for their solution.
To more accurately calculate the data, we introduce into our mathematical calculation the auxiliary variables. In this economic-mathematical model without them it is impossible to accurately calculate in the future. To the auxiliary variables we will include the increase in yield, the difference between the accounting and cultivated area of arable land. To control the data acquisition process, we use the experimental method of preparing indicators. With this method, there is an opportunity in the research process to reduce the number of variables that can not be covered by observations. At the same time, we establish a different level of influence of factors, which makes it possible to use only the most influential data and leave them for calculation. The object of optimization of arable land, which has in its composition degraded and depleted land is the forest-steppe Right Bank province of Kiev region. At the first stage of the calculation, we find the number of degraded and depleted arable land by experimenting the variables in the matrix model.

The second stage of the calculation is the establishment of optimal rotation parameters for the research object. According to the agroecological assessment of Ukrainian soils, the plow is considered to be favorable at the level of 25%, conditionally favorable - at the level of 25 - 60% and unfavorable - at the level of 60 - 80%. According to other calculations of domestic scientists, the optimal ecological parameters of the level of cultivation of the territory should be 40 - 45%, and the maximum permissible - 60% [4]. It should also be borne in mind that the territory of Ukraine is located in different natural and agricultural zones, which, in turn, affects the size of the optimal plow, that is, the level of plowing will increase from the regions of Polissya to Steppe. Using these studies, we can assume that the optimal level of cultivation for the forest-steppe zone should be at the level of 40 - 50% [1]. According to the preliminary calculation, determining the coefficients of the impact of degradation processes and depleted arable land, we can calculate quantitatively in the area and calculate the optimization of arable land for the research object.

After optimizing the arable land and removing degraded and unproductive land, we can calculate the maximum effect in the absence of negative factors. According to the forecasted calculation for the Forest-steppe Right Banking Province of Kyiv region, the economic effect will be expressed in increasing the yield to 19%. The increase in crop will cover the shortage of output on an area that will not be sown, but brought out to cultivate to stop and minimize the effects of degradation processes.

Conclusions Our calculations by means of the economic-mathematical model of the matrix problem show that optimization of arable areas is one way to increase the economic efficiency of using arable land in the form of increasing the number of crops. At the expense of optimization of arable land, the ecological stability of land use improves. In particular, optimization of cultivation and stimulation of landowners to the introduction of sustainable land use and rational nature management, which will positively affect the environmental stabilization of the natural environment.
The introduction and observance of the proposed norms of the optimal ratio of arable land should be considered as a necessary measure in preventing excessive development and farming of agricultural lands.