Mathematical model of the formation of the portfolio of the innovation structure of the technopark

. The use of approaches and methods of mathematical analysis to the selection and justification of sources of financing for an innovative project is an important and urgent task. The approach presented in the paper is based on a system of equations that allow determining the optimal capital structure necessary to finance an innovative project. This system of equations, using methods of mathematical analysis, provides the best effect of financial leverage. The use of this methodology in the activities of commercial organizations is a modern practical tool necessary for the effective functioning of the decision support system.


Introduction
At the present stage of development of the Russian Federation, scientific and technological development is becoming a determining factor in ensuring national security, competitiveness and economic independence of the state.The leading role in which is played by defense industry enterprises that have the necessary innovative potential and key competencies to solve the tasks set by the government to increase the share of high-tech civilian products.[1][2][3] The development of the production of high-tech civilian products corresponding to the priority areas of technological development will ensure the solution of the system tasks of the defense industry (diversification, import substitution, modernization and efficiency improvement of existing production facilities, etc.).[4] Their further innovative development involves the introduction of additional financial resources and increasing the financial stability of defense industry enterprises in the context of the planned reduction in budget financing of military expenditures.[5,6] All this will contribute to the development of the economy of the regions where defense industry enterprises are located by creating new jobs, increasing the share of high-tech innovative products in the region, gross regional product and tax revenues to the budgets of the constituent entities of the Russian Federation.[7,8] Earlier studies [9,10] revealed that defense industry cooperatives were created in accordance with defense production technologies, and the development of innovative civilian products determines a new cooperative relationship.With the emergence of such a connection, there is a need to link this production into one complex, or network.The unification of this kind of cooperative connection is necessary as part of some organizational form.In our opinion, technoparks are the most suitable form of such an organization.[11,12] 2 Relevance of the study In order to understand and justify the applicability of such an organizational structure, it becomes necessary to consider the role and state of innovation infrastructure in the regions of Russia and abroad, as well as the state and activities of existing technology parks.The criteria for the effectiveness of technoparks [13,14] as an innovative project for the production of high-tech civilian products on the objects of innovative infrastructure are highlighted.
However, the functioning of technoparks is carried out without taking into account the need to build cooperative ties with defense industry enterprises.In this regard, it is necessary to reconsider not only the mechanisms of operation of such technoparks, but also conceptual approaches to the formation of management of their activities.
Taking into account the peculiarities of the production of high-tech civilian products, in this paper we propose the following additional principles: 1.The principle of the network approach to the formation of the innovation structure of the regions; 2. The principle of forming a portfolio of orders for the production and diversification of civilian products by defense enterprises; 3. The principle of repayment of the state support funds involved.The implementation of the above principles requires the solution of such tasks as: • Building a network; • Formation of a portfolio of projects operating within the network; • Selection of criteria for the formation of this portfolio; To date, there is no scientifically based system for evaluating the criteria for the effectiveness of technoparks, which would be multidimensional in nature.There are single systems of criteria, often without proper justification.
When developing an efficiency assessment system, it is more expedient to proceed from the integrity of such a system that would take into account all aspects in the functioning of the technopark, since they are ultimately somehow related to its economic efficiency.
When optimizing the technopark's project portfolio, we propose, given that financial support is provided by the budget of various levels of government, criteria for budget efficiency.[15,16] The budgetary efficiency of the implementation of the portfolio of projects, taking into account the state incentives provided, is characterized by tax deductions to the budget of the subject of the Russian Federation and the federal budget when obtaining financial results of the implementation of innovative projects, interest deductions, as well as income from the sale of shares.

The methodology of the study
The methodological basis of the study was the materials published in the scientific literature and periodicals [17][18][19][20], as well as the results obtained in previous studies [21,22].
The information on the study was compiled by regulatory and legislative acts of the Russian Federation, the Ministry of Economic Development of the Russian Federation, as well as other information on the topic published in the open press and the Internet, scientific articles and other materials, Internet information resources.[23,24]

The results of the study and their discussion
In this paper, a mathematical model has been developed for the formation of a portfolio of innovative structures of technoparks based on financial programming methods, where there is an alleged innovative project proposed for consideration.[25,26] In the proposed innovation network of projects, for each of the n projects, the budget efficiency g1(x)(i = l, n) is known, depending on the amount X determined for it.The data are presented in Table 1.It is necessary to distribute funds among the participants of Project C so that the volume of support for fn(C) is most effective.For convenience, we will divide the data into steps.As the n-th step, we will take the investment of n project participants.C -the stock of unencumbered funds.Parameters of "step control" x1, x2, ..., xn -funds allocated by participants.The profit at step n is determined by the increase in the funds of gn(x) of the n-th participant of the project, depending on the funds invested in it x (step control).
To determine the need for state support, we will use the recurrent ratio expressed by the formula fn(C) = max[gn(x)+fn-1(C-X)] (1) where fn-1(C-X) is the maximum value of the increase in support at the previous step (n-1), when distributing the sum with (n-1) С (n-1)= Cn-xn between (n-1) participants, 0≤x≤C.Next, consider the distribution of funds for each project.The distribution of funds for one project is shown in table 2. The distribution of funds for the two projects is shown in table 3. The distribution of funds for the three projects is shown in table 4. The distribution of funds for the four projects is shown in table 5.In Table 5, f4(C) = 128 is the maximum increase in output.Such an increase can be obtained if X4(C)= 80 million conventional units are invested in the fourth project (optimal control at the fourth step).The new state of the system C (cash reserve of funds not yet invested) C` = 200 -80 = 120.The value C = 120 corresponds to the optimal value X3(C) = 0 (Table 4) -the funds invested in the third project.The next state of the system C` = 120 -0 = 120.The value C = 120 corresponds to the optimal value X2(C) = 0 (Table 3).The state of the system in this case takes the value C` = 120 -0 = 120.
Thus, the maximum increase in output of four projects with the distribution of 200 million conventional units between them is 128 and will be obtained if 120 million conventional units are invested in the first project, 0 in the second, 0 in the third, 40 million conventional units in the fourth, X = (60, 0, 0, 40).

Conclusions
The results obtained vary depending on the amount of state support.If public investment is not effective, the implementation of the project becomes very unlikely.Based on the assessment of the actual and optimal capital structure of these participants, we determine in what form to provide support.
Based on the above calculations, it can be concluded that the maximum efficiency of state support was achieved in the fourth project, with a volume of support of 80 million conventional units.the maximum efficiency of the project was 128 million conventional units.

Table 1 .
The amount of budget receipts in the form of

Table 2 .
Distribution of funds for the first project

Table 3 .
Distribution of funds for two projects

Table 4 .
Distribution of funds for three projects

Table 5 .
Distribution of funds for four projects