Mathematical Modelling of Postindustrial Land Use Value in the Big Cities in Ukraine

The research paper deals with theoretical and methodological approaches to rational urban land use. Basing on the international scientific research, the authors offer original interpretation of the term «postindustrial land». Taking into account a drastic rapid dynamics of urbanization in large urban agglomerations worldwide and de-industrialization as a trend of urban land-use exemplified by the city of Kyiv in Ukraine a mathematical model of setting the price of postindustrial land with aimed to prediction the efficiency of industrial land transformation was developed in this study. KeywordsLand transformation, Postindustrial land, Urban land, Economic and mathematical model. International Journal of Mathematical, Engineering and Management Sciences Vol. 5, No. 2, 260-271, 2020 https://doi.org/10.33889/IJMEMS.2020.5.2.021 261


Introduction
Problem of land-use is a complex social, economic, ecological and security problem (Kopachevsky et al., 2016;Shevchenko et al., 2017;Openko et al., 2017;Ievsiukov et al., 2018). A major task of modern urban land use is the release of great areas, used before for industrial production, which due to ineffectiveness of industries are being shifted now out of cities or transformed into highly profitable, green enterprises and territories (Mishenin and Koblyanska, 2012). Because now the major part of labor resources is employed in service sector, operation management and data processing, the employment rate of economically active population in material production is decreasing (Tsvyakh and . Therefore, management decision concerning enterprises placement is more depends of logistics, the use of adjacent land, ecoeconomic factors and value of land (Mishenin and Koblyanska, 2012). At the same time, there are some important issues which are still not well-developed. In particular, streamlining the use of big city spaces, elaborating the system of economic liability of real estate developers in urban land-use, rational decision-making system based on eco-economic ground should be developed in view of industrial land transformation (Guo et al., 2018). The current land use structure in big cities with extensive postindustrial areas should be transformed according to the tendencies of industries decentralization and balanced urban use of resources (Guo et al., 2018). That is why the development of scientifically-grounded basis for rational use of postindustrial land is a topical task. According to (Voronina, 2012), the context of urban land use deindustrialization is quite ambiguous, since it is a deep transformation of a big city space. Beyond the positive effect of the release of urban territories from negative consequences of industrial period, the process of deindustrialization may be accompanied with negative social processes, because deindustrialization may be caused by an economic and social crisis, enterprises shutting down and the production decreasing. Researchers found (Guo and Xiong, 2014;Silva et al., 2014) that the decreasing of the industrial sector in the big city is connected with economy restructuring and growing a share of service sectors. This, in turn, is made possible by effective industrial development, with productivity level allowing to meet people`s material needs at a high level and, in doing so, releasing ever more resources for service industries development. Deindustrialization may be viewed in this case as a so-called by-product of industrial society evolution, based on knowledge and geo-information technologies. On the base of analysis of theoretical and methodological justification of transformation, deindustrialization, re-development of industrial facilities in a big city proposed in publications of Loures, Burley, Panagopoulos (Loures and Panagopoulos, 2007;Loures, 2008;Loures et al., 2008;Loures and Panagopoulos, 2010;Loures andBurley, 2012), Brandt et al. (2000), Berger (2006), Shevchenko et al. (2017) and others, the term of post-industrial lands was proposed. As the particularly interesting example of rational use of urban lands of non-functional industrial facilities, the Buttersea power station may be examined. This station was constructed in the 1930s on the South Bank of the River Thames in the area of Nine Elms. Reconstruction of the station and adjacent area is going to become the greatest construction in the history of modern London. The construction is scheduled to be completed in 2026. According to the plans of Battersea Power Station Development Company (BPSDC), which was set up by the investors for overseeing the project, renovation will affect not only the former power station, but also the adjacent territory of 16 ha. The industrial monument of the first half of ХХ century will be transformed into leisure and cultural and business center of the city district (Five most promising areas of Europe under construction, 2015).
In our research, we use term "postindustrial lands" to denote destroyed by human activities landscapes, empty and non-functional industrial facilities on deserted (not used for purposes intended) industrial territories, damaging adjacent settlements, having negative effect on mental  , 1950-2050 * 1950 1975 2007 2025 2050 1950-1975 1975-2007 2007-2025 2025-2050 Urban population ( UN, 2008) Transformational effect of urbanization became first visible in the developed regions of the world, with the rate exceeding 80 % in Australia, New Zealand and North America. In the developed world Europe is the least urbanized, with 72% of population living in urban areas. Among developing countries particularly high urbanization rate (78%) has been reached in Latin America and the Caribbean, where it is higher than the same rate for Europe as a whole (UN, 2008). Urbanization rate is expected to rise in the decade to come in all key regions of the world, with the process in Africa and Asia proceeding faster, than in other key regions, even if the anticipated pace of urbanization drops compared to that, observed in the past decades (see Table  2). However, till the middle of the century urbanization rate in developing countries of Africa, Asia, Oceania is expected to be lower than that of developed countries, Latin America and the Caribbean. In general, the world`s population is likely to be 70% urban by 2050. The greatest number of urban dwellers is forecast to live in Asia (54 %) and Africa (19 %) (UN, 2008). Table 2. Dynamics of urbanization, 1950Dynamics of urbanization, -2050Dynamics of urbanization, * 1950Dynamics of urbanization, 1975Dynamics of urbanization, 2007Dynamics of urbanization, 2025Dynamics of urbanization, 2050Dynamics of urbanization, 1950Dynamics of urbanization, -1975Dynamics of urbanization, 1975Dynamics of urbanization, -2007Dynamics of urbanization, 2007Dynamics of urbanization, -2025  As it was pointed by Percyk (Voronina, 2012), the "urban giants" of 21 st centurycountries with population more than 100 mlnwill include in 2025: China (832 mln), India (630 mln), the US (281 mln.), Brazil (205 mln), Indonesia (167 mln.), Nigeria (147 mln), Pakistan (142 mln), Russia (119 mln), Mexico (117 mln), and Japan (103 mln). At the same time, this data is slightly different than that set presented in the report of the UN Social and Economic Council (Table 3). In Ukraine the process of urbanization as a complex economic phenomenon has resulted to expansion of the urban areas and, consequently, to growth of proportion of urban dwellers, basically due to reduction of the number of rural population. Urban population in Ukraine is about 69,12 % (29,673 mln people), while rural population stands at 30,88 % (13,256 mln people). Expansion of the Dynamics of urban population in Ukraine was studied on the example of Kyiv capital city. Results of the study of processes of deindustrialization in the context of urban land use were tested on the model city of Kyiv, as one of the most densely populated industrial centers of Ukraine (Tsvyakh and . According to the Kyiv City Development Strategy -2025, the following key projected figures of demographic change of the city were accepted as a basis for Kyiv master plan calculations: resident population -3,15 mln people, actual -3,68 mln people, daytimeup to 4,0 mln people (The general plan of the city of Kyiv for the period till 2020, 2001). It was found that historically local industrial areas, enterprises, storages, factories are located within valuable for urban development sites such as coastal areas, health protection zones or near the residential buildings. According to data of the Main Department of the State Statistics Service of Ukraine in Kyiv, at the moment of January 01, 2016 the total area of Kyiv covered 83,6 k ha, including 4,6 k ha agricultural lands; 35,1 k ha of woods and other forested areas; 6,7 k ha of residential areas; and 3,3 k ha of industrial lands. Analysis of dynamics of land use in Kyiv during 1995-2016 demonstrates a tendency of expanding of the building sites: from 34,0 k ha in 1995 to 37,0 k ha in 2016. At the same time, total area of industrial lands decreased during this period from 5,9 to 3,3 k ha. In our opinion, the long-term economic development of Kyiv should be based on rational urban land-use, including deindustrialization, modernization and restructuring of productive capacities, reduction its resource consumption, and improving its competitiveness.
In general, in big developing cities there is an acute lack of lands of residential and civil use, especially in downtown. In this context, the question of territory choice for real estate construction became a topical: most convenient and optimal on technical indicators and townplanning conditions areas turn out to be occupied with industrial facilities, many of which eventually become unprofitable, environmentally hazardous or non-functional. This situation is caused by the following factors: historically formed urban infrastructure, lack of systematic approach to the process of zoning and overall city planning, as well as its rapid and eventually chaotic development, when radically different zones, e.g. industrial and residential zones become mixed. Development of mathematical model for setting the price of postindustrial lands in a big city requires determination of factors directly affecting to market land value. In our opinion, among the key factors, affecting the market value of postindustrial land (Y), the following are distinguished:  inflation rate in Ukraine (Х1), %;  inflation rate in Ukraine (progressive total) (Х2), %;  average US dollar rate for the respective assessment period (Х3), UAH;  existence of a subway station nearby (Х4), m;  distance from downtown (Х5), m;  existence of water bodies (Х6), m;  distance from recreation areas -parks, squares, woodlands etc.) (Х7), m;  existence of residential areas nearby (Х8), m;  existence of railway nearby (Х9), m;  distance to city center (city center -site of the main post office) (Х10), km;  total area of land (Х11), ha;  proportion of the land, belonging to industrial zones as per the master plan (Х12), %;  dynamics of the average monthly wage of those, employed in industries (Х13), UAH;  average income of the population of Kyiv (Х14), mln UAH;  fixed investments in the city (Х15), mln UAH.
Adhering to the scheme of the least-squares method, we have to find min F (b, c), which is formulated as the following optimization problem: (1) Which in fuzzy numbers becomes: In the determination of regression coefficients b, c we have two equations, expressed in the derivatives: Since derivatives of the function (3) equal: To do the sum we get a system of equations: Consequently, having done the system of equations, (5) we get the following values of coefficients: that is an analogue of formulas for calculating coefficients of two-dimensional regression for exact numbers.

Results of the Modeling
The findings allow extending methods of regressive analysis of fuzzy numbers from a relatively narrow range of triangular fuzzy numbers to the whole range of fuzzy arbitrary numbers (Table  4).
To create the mathematical model, stepwise multiple regression was used, which is applicable when the resultant figure (Y) depends on multiple factors (X), in our caseon X1, Х2, Х3, Х4, Х10, Х13, Х14, Х15 (7) Using the least-square method, we can found the unknown parameters а of the searched mathematical model by means of Microsoft Excel software, namely, built-in LINEST function. To obtain a form of linear dependence (eq. 8) it is necessary to turn the stepwise regression into a linear form by taken the logarithms of the regression equation and make a replacement of variables.  Having regard to the scale of interpretation of the correlation coefficient, eight factors (Х1, Х2, Х3, Х4, Х10, Х13, Х14, Х15) were singled out, which to a certain extent affect the market value of postindustrial land (Y), from among Х1, Х2, Х3, Х10, Х13, Х14 -having a mean effect; factors Х4, Х15 -a low effect, а Х5, Х6, Х7, Х8, Х9, Х11, Х12, do not affect the land value at all (Table 5).
According to our parameters, the general regression equation will be following: If we calculate (based on the least squares method) y′ and x′, we can determine the regressors a′0, а1, а2, а3, а4, а10, а13, а14, а15. Hence, the mathematical model of stepwise multiple regression, allowing to evaluate postindustrial land in Kyiv, will be presented as follows: where х1, х2, х3, х4, х10, х13, х14, х15factors х, affecting the resultant figure (postindustrial land value). Thus, we develop the mathematical model, allowing to predict postindustrial land value in Kyiv based on the known factors х1, х2, х3, х4, х10, х13, х14, х15 and, consequently, to model the efficiency of land deindustrialization.
Based on the economic and mathematical model, expert monetary evaluation of the researched land was made (N =160) and depicted graphically (Figure 1), showing that curve Y (estimated) somehow describes curve Y (result).

Conclusions
The proposed economic and mathematical model of stepwise multiple regression allowing to predict a postindustrial land value, can be used for analysis of typical big cities. It should also be noted that this model enables to simulate rational land use and determine key directions of transforming postindustrial urban lands into a highly profitable territorial resource. It was found that the prime costs, related to the application of the mathematical model of expert monetary evaluation of postindustrial lands in a big city, cover the maintenance and upkeep the costs of data matrix of an expert monetary evaluation of typical lands. The determined dependency will allow automating the process of expert evaluation of similar lands in a big city based on the model developed. Economic efficiency of its application may be manifested in lower transaction costs related to staffing of immovable property valuators. In addition, positive effects of application of the economic and mathematical model in the field of management were determined, in particular objective and impartial decision-making as to the market postindustrial land value. For this reason, regardless the long-term process of creating, populating and updating an info-base of expert monetary evaluation of postindustrial land, which underlies the development of the model, it is emphasized, that its further application will reduce the subjective impact of valuators to the land evaluation.