Search For Optimal Socio-Economic Determinant Values Of Territory Development Sustainability

General description of the technique

In the framework of assessing the territories development sustainability, we establish the following requirement to achieve indicators of socio-economic development in the identified areas of sustainability: as close to the planned level of socio-economic development and as far from the negative version of the development level as possible. It is possible to assess the fulfilment of this requirement by applying the method of ordered preference through similarities with the ideal solution (TOPSIS). Many of the criteria that are proposed in the framework of this method have been reduced to the identified areas (aspects) of sustainability. The application of the method was described in detail and tested by the authors on the example of the Krasnoyarsk Territory (Ferova et al., 2019; Lobkova, 2020).

In this article, the authors conducted a study in the direction of finding the optimal values of the socio-economic determinants of the territory development sustainability on the basis of previously obtained assessment results.

The sustainability of the development of the territory socio-economic system depends on the totality of specialization industries, supporting and related industries, types of economic activity (testing was carried out by the authors on the example of the Krasnoyarsk Territory). Several aspects of sustainability assessment and a set of private indicators of assessment are highlighted:

• metallurgical production (Rme): the share of the industry in the structure of the region's added value,% (X1); share of people employed in the industry,% (X2); the ratio of the average monthly accrued wages per employee in the industry to the average wage in the region (X3); return on sales of goods, products (works, services) of industry organizations,% (X4);

• oil and natural gas (Rp) production: specific gravity of the industry in the region's added value structure,% (X5); share of people employed in the industry,% (X6); the ratio of the average monthly accrued wages per employee in the industry to the average wage in the region (X7); profitability of sold goods, products (works, services) of industry organizations,% (X8);

• electricity generation (Reg): the share of the industry in the structure of the region's added value,% (X9); share of people employed in the industry,% (X10); the ratio of the average monthly accrued wages per employee in the industry to the average wage in the region (X11); return on sales of goods, products (works, services) of industry organizations,% (X12);

• agriculture (Rag): share of the industry in the structure of the region's added value,% (X13); share of people employed in the industry,% (X14); the ratio of the average monthly accrued wages per employee in the industry to the average wage in the region (X15); return on sales of goods, products (works, services) of industry organizations,% (X16);

• trade (Rt): the share of the industry in the structure of the region's added value,% (X17); share of people employed in the industry,% (X18); the ratio of the average monthly accrued wages per employee in the industry to the average wage in the region (X19); profitability of sold goods, products (works, services) of industry organizations,% (X20);

• social aspect (Ms): life expectancy at birth, years (X21); the proportion of the population with cash incomes above the subsistence level established in the subject of the Russian Federation,% (X22); level of employment in working age,% (X23); the ratio of per capita cash income to the cost of living (X24);

• financial and investment aspect (Rfi): ratio of revenues and expenses of the consolidated budget of the region, % (X25); share of unprofitable organizations, in% of the total number of organizations (X26); arrears of wages per employee, to which there is arrears, rub. (X27); investment in fixed assets per capita, rub. (X28);

• transport sector (Rtr): departure of passengers by public railway, thousand people (X29); dispatch of goods by public rail, million tons (X30); freight turnover of automobile transport of organizations of all types of activity, mln t-km. (X31); the proportion of paved roads in the total length of public roads, % (X32).

For each aspect of sustainability, including a set of private assessment indicators, an integral level indicator was calculated using the TOPSIS method. In the study of the optimal level of development sustainability components based on the dynamic programming method, the authors used an indicator of the volume of investments in fixed assets by types of economic activity and assessment aspects for the analysed period.

Statement of the dynamic programming problem

In the framework of the task, it is required to determine the level of particular indicators for assessing sustainability and each of the eight components that maximize the composite indicator of the territory development sustainability with the available volumes of investment in the socio-economic sphere.

The territory development sustainability is considered as the state of the controlled system S . As a multi-step task process, we consider the process of investing in the fixed capital of the i -th volume of monetary units by type of economic activity. With a step-by-step solution of the problem, a maximum of the composite indicator of the territory development sustainability is searched.

To compile a recurrence equation of the problem, a number of procedures are required. The dynamic programming problem is solved by the step-by-step control method. As the i -th step of the methodology, we take the amount of investment in the totality of economic activities during the planning period. The number of steps N in this task should be taken equal to eight, which corresponds to the number of types of economic activity (aspects or components) by which the level of the territory development sustainability is estimated. At each step of the assessment, y _i volume of conventional units for the development of the territory in the areas of production, social, financial, investment and transport are considered. Decisions implemented by the volume of investment of conventional units and the type of economic activity (direction of assessment) fall at one step.

The state of the managed system S (the territory development sustainability is considered) before each i -th step of the task is characterized by the variable y _i - the total investment of conventional units aimed at the development of types of economic activity (in the areas of assessment) that determine the territory development sustainability. The control variable u _i is also introduced, which is the amount of conventional units invested that are obtained at the i -th step of solving the problem for the i -th type of economic activity (direction of assessment) by the accumulated result (taking into account the previous evaluation steps).

The following limitations are formulated in the problem:

• the minimum value of the investment of conventional units at the i-th step of the task should correspond to the amount of necessary investment resources to ensure the i-th type of economic activity;

• the maximum value of the volume of investment of conventional units used at the i-th step of the task should correspond to the total amount of investment in fixed assets acceptable for the fulfilment at the i-th step of the limit values of the i-th type of economic activity;

• the total value of the volume of conventional units investment used to solve the problem at the i-th step should not exceed the allowable value of the volume of investment of conventional units for all types of economic activity in the territory;

• particular indicators of sustainability assessment with the lowest level of significance in the group within the framework of the criterion (direction) should not be lower than the maximum value for the evaluation period; other private indicators of sustainability should not be lower than the minimum value for the evaluation period.

As the “gain parameter”, the main economic effect of solving the problem is taken, which is the total value of the expected private indicators for assessing the territory development sustainability from the P _i -th type of economic activity (direction of assessment). The problem is solved as a maximum search. The private economic effect of P _i at the i -th step of the problem depends on the u _i -th volume of investment in the P _i -th type of economic activity (direction), i.e. P _i = P _i ( u _i ). The total economic effect for all N steps will be equal to (1):

$$P_i={\sum }_{i=\mathrm{1}}^N{P}_i\left(u_{\mathrm{1}}\right),\left(1\right)$$

where P _i is the value of the main economic effect of the task obtained from the managerial impact - “step control” u _i for all N steps of the multi-step process;

P _i (u _i )- the value of the private economic effect P _i obtained from the managerial impact - “step management” u _i at the task step i = 1 according to the i -th type of economic activity (direction).

The summary (total) level of the territory development sustainability R _ds at the i -th step is determined as follows (2):

$$R_{ds}=R_{me}\left(u1\right)+R_p\left(u2\right)+R_{eg}\left(u3\right)+R_{ag}\left(u4\right)+R_t\left(u5\right)+R_s\left(u6\right)+R_{fi}\left(u7\right)+R_{tr}\left(u8\right),\left(2\right)$$

where P _ds is the value of the composite indicator of the territory development sustainability, including a set of directions or aspects of the assessment (types of economic activity) for all N steps of a multi-step process.

The function of the multi-step process x _i = f _i (y _i-1 ; u _i ), which determines the law of change of the controlled system S , for this problem is determined by the formula (3):

$$y_i=(y_i-1+u_i),\left(3\right)$$

This equality has the following meaning: x _i the volume of investment of conventional units at the i -th step of the task for the i -th type of activity is determined by the cumulative total after the current step with number i and is equal to the total amount of investment of conventional units of a particular i -th type of economic activity (direction) by the previous step ( y _i-1 ) plus the amount of investment of conventional units u _i aimed at the p _i -th type of economic activity (direction of sustainability) at the current step of the task.

Therefore, under the action of “step control” u _i at the i -th step of the problem, the controlled system S goes into a new state (4):

$$s_{i-\mathrm{1}}=s_i-u_i,\left(\mathrm{4}\right)$$

At the next stage of the technique, a recurrence equation is introduced. We denote by fi ( S ) the maximum level of the composite indicator of the territory development sustainability of P _ds for the i last control steps. Then the main recurrent equation of the dynamic control problem expressing the conditional “optimal gain” of the P _ds problem will have the following form (5):

$$f_i\left(S\right)=max[P_{dsi}+f_i-1(S_i-1\left)\right]=max[P_{dsi}+f_i-1(S_i–u_i\left)\right]\left(5\right)$$

Based on the above approach to determining the optimal level of values of particular indicators and components of the territory development sustainability, the authors performed calculations by the dynamic programming method on the example of the Krasnoyarsk territory.