CC BY
8Research article
DOI: https://doi.org/10.48554/SDEE.2023.2.2
Model of Cross-Financing for Research and Development Costs in a Federal
District
Dmitrii Rodionov1 , Egor Koshelev2* , Lo Thi Hong Van3
1 Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia, drodionov@spbstu.ru
2 Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia, ekoshelev@yandex.ru
3 University of Economics and Business, Vietnam National University, Hanoi, Vietnam, hongvan289@gmail.com
* Corresponding author: ekoshelev@yandex.ru
Abstract
The issue of an optimal amount of funding for research and development (R&D) costs within the Russian regions that have the appropriate scientific potential is investigated. For this purpose, a model is developed to optimise and plan the cross-financing of R&D costs in a federal district, which takes into consideration the specific technological and economic results of R&D in the regions. This model makes different R&D expenditures by type of work dependent on three planning directions of innovative development in the regions of the district: investment, production, and financial. All three processes are considered simultaneously. Investment planning is reflected by investment in fixed capital, production planning (by gross regional product), and financial planning (by indebtedness of legal entities on loans). Nonlinear regressions of R&D costs by type of work are optimised using a genetic algorithm, simulated annealing, and pattern search, which eventually allow calculation of the reserve or deficit of the corresponding R&D costs in each region of the federal district. The results of global optimisation reflect the conclusion that in conditions of saving federal budget funds, the federal district can partially finance all R&D costs in those regions that need it. Identifying such regions more reasonably requires analysing this situation in more detail, that is, in terms of various R&D costs by type of work. For the Privolzhsky Federal District, the findings indicate that the Samara region, the Republic of Bashkortostan, and the Perm region are the most in need of financing various types of R&D expenditures. However, the main donor for the costs of different types of R&D is the Nizhny Novgorod region. The findings of this model can allow considerable savings in the federal budget funds allocated for scientific and, consequently, innovative development of the regions.
Keywords: innovative development, region investment planning, production planning, financial planning, research and development costs
Citation: Rodionov, D., Koshelev, E., Lo, T.H.V., 2023 Model of Cross-Financing for Research and Development Costs in a Federal District. Sustainable Development and Engineering Economics 2, 2. https://doi.org/10.48554/SDEE.2023.2.2
This work is licensed under a CC BY-NC 4.0
© Rodionov, D., Koshelev, E., 2023. Published by Peter the Great St. Petersburg Polytechnic University
24
Enterprises and sustainable development of regions
Научная статья УДК 332.142.2
DOI: https://doi.org/10.48554/SDEE.2023.2.2
Модель Перекрестного Финансирования Затрат на Научно-Исследовательские Работы в Федеральном Округе
Дмитрий Родионов1 , Егор Кошелев2* , Ло Тхи Хонг Ван3
1 Санкт-Петербургский политехнический университет Петра Великого, Санкт-Петербург, Россия, drodionov@spbstu.ru
2 Нижегородский государственный университет им. Н.И. Лобачевского, Нижний Новгород, Россия, ekoshelev@yandex.ru
3 Вьетнамский национальный университет, Ханой, Вьетнам, hongvan289@gmail.com * Автор, ответственный за переписку: ekoshelev@yandex.ru
Аннотация
Исследуетсявопросоптимальногообъемафинансированиязатратнанаучно-исследовательские работы (НИР) в пределах регионов страны, имеющих соответствующий научный потенциал. Для этого р азработана модель оптимизации и планирования перекрестного финансирования затрат на НИР в федеральном округе, учитывающей конкретные технологические и экономические результаты НИР регионов округа. Данная модель ставит в зависимость различные затраты на НИР по видам работ от трех направлений планирования инновационного развития регионов округа: инвестиционного, производственного, финансового. При этом все три процесса рассматриваются одновременно. Инвестиционное планирование отражают инвестиции в основной капитал, производственное планирование - валовой региональный продукт, а финансовое планирование -задолженность юридических лиц по кредитам. Нелинейные регрессии затрат на НИР по видам работ оптимизируются с помощью генетического алгоритма, имитационного отжига и поиска по шаблону, что позволяет в итоге вычислить резерв или недостаток соответствующих затрат на НИР в каждом регионе федерального округа. Результаты глобальной оптимизации позволяют сделать вывод, что в условиях экономии федеральных бюджетных средств федеральный округ может частично сам профинансировать все затраты на НИР в тех регионах, которые в этом нуждаются. Чтобы более обоснованно определить такие регионы, необходимо анализировать эту ситуацию подробнее, т. е. в разрезе различных затрат на НИР по видам работ. Для Приволжского федерального округа (ПФО) получено, что наиболее нуждающимися в финансировании различных видов затрат на НИР оказываются Самарская область, республика Башкортостан и Пермский край. Но при этом основным донором затрат на различные виды НИР является Нижегородская область. Это позволило бы существенно сэкономить федеральные бюджетные средства, выделяемые на научное и, как следствие, инновационное развитие регионов страны.
Ключевые слова: инновационное развитие, регион, инвестиционное планирование, производственное планирование, финансовое планирование, затраты на научно-исследовательские работы
Цитирование: Родионов, Д., Кошелев, Е., Ло, Т.Х.В., 2023. Модель Перекрестного Финансирования Затрат на Научно-Исследовательские Работы в Федеральном Округе. Sustainable Development and Engineering Economics 2, 2. https://doi.org/10.48554/SDEE.2023.2.2
Эта работа распространяется под лицензией CC BY-NC 4.0
© Родионов, Д., Кошелев, Е., 2023. Издатель: Санкт-Петербургский политехнический университет Петра Великого
Предприятия и устойчивое развитие регионов
25
1. Introduction
Currently, the cost of research and development (R&D) is an important component of Russian state budget expenditures. The financing of R&D allows the state to solve the problems of global technological challenges, including the problems of implementing the import substitution policy. However, the issues of the optimal amount of funding for R&D expenditures within the country and its regions, which have the appropriate scientific potential, have not been completely resolved. By scientific potential, we refer to both research institutes and universities, and scientists working in these institutes. It seems impossible to solve such problems in isolation from the specific technological and economic results of regional R&D. Planning of these results, as well as the resources necessary to achieve them, is an urgent task to optimise the costs of R&D. In this regard, we distinguish three types of planning: investment, production, and financial. We consider all three processes simultaneously. This will allow us to cover a wide range of tasks to optimise R&D costs in the regions and contribute to their innovative development.
Similar optimisation issues have been studied in detail by many scientists in relation to the business development planning of companies. For example, Kruschwitz and Lorenz (2019) studied the processes of simultaneous investment and financial planning, as well as simultaneous investment and production planning. Limitovskiy (2019) supplemented their results by taking into consideration the systemic financial effects of investment programmes. By such effects, the author referred to cross-financing, cross-subsidization, cross-holding, and cross-hedging. Despite the usefulness of these studies, there is still a need to create programmes of innovative development for manufacturing companies and industrial regions. In this regard, Fabiana et al. (2016) studied how the technological innovation process occurs in small and medium technology companies located in Parana Valley Metropolitan Region and Northern Coast, Brazil. The study revealed that the development of innovations depends on the type of economic activity that the company develops and the interactions it undertakes with the internal and external environments. Vasconcellos et al. (2016) argued that the resources invested in research do not guarantee immediate practical application. With the aim of developing and presenting a methodology for evaluating a research portfolio and selecting the best research investment, the author showed that risk and return criteria should be used to manage R&D portfolios when selecting projects.
To this end, the present study explores the issue of the optimal amount of funding for R&D costs within the regions of the country that have the appropriate scientific potential.
2. Literature review
Although the abovementioned findings are of real practical interest for implementing the successful development of commercial firms, we aim to leverage them to optimise and plan national and regional R&D expenditures. Other useful results from various researchers in this field include those of Xu (2018), who found that regional investment in R&D in the area of human resources has a positive effect on the efficiency of the internal R&D of an enterprise. The scientist formulated three policy recommendations: increasing regional investment in R&D, expanding, and consolidating the enterprise as the basis of R&D status, and increasing regional investment in R&D in human resources. Chen et al. (2019) found that the production elasticity of R&D capital in China was much higher than that of R&D personnel, suggesting that R&D capital is the main driver of the research results. The elasticity of substitution between R&D capital and personnel has changed from replacement to additional since 2014. To ensure sustainable growth in research results, the contribution of R&D with positive output elasticity should be increased, or the contribution of R&D with negative output elasticity should be decreased with the necessary compromises made according to the ratio of substitution between the two R&D inputs.
Dobrzanski and Bobowski (2020) determined whether funds spent on R&D are used in the countries of the Association of Southeast Asian Nations (ASEAN). Fifteen countries were examined over the period of 2000-2016. R&D spending efficiency was measured using a non-parametric data envelopment analysis (DEA) methodology, which measures input-output efficiency. Hong Kong and the Philippines were found to be the best performing countries in R&D when analysed using the constant returns to
scale approach. However, Hong Kong, Indonesia, Singapore, and the Philippines are the most efficient ASEAN countries under the variable returns to scale approach. The study also confirmed that increasing spending on innovation leads to disproportionate effects. Dehmer et al. (2019), relying on recent developments in spending on science in countries such as China, Korea, India, and Brazil, have found that global scientific activity is undergoing major shifts. Using the evolving pattern of past R&D expenditures for forward-looking projections and in the absence of notable changes in science policy and spending priorities, the authors predicted the continuation of a major shift in R&D geography towards Asian countries and an ongoing large and, in many respects, growing gap between the scientific haves and have-nots in the world.
Kiselakova et al. (2018) examined the relationship between R&D expenditures and the development of global competitiveness in Slovakia, as well as in member states of the European Union from Central and Eastern Europe (CEE EU (11)). To assess the competitiveness of the CEE EU (11) countries, the researchers used the Global Competitiveness Index processed by the World Economic Forum and found that an increase in R&D spending can contribute significantly to the level of competitiveness of CEE EU (11) countries. All the analyses confirmed the importance of focusing on increasing R&D expenditure, especially in the higher education sector, as it has a significant impact on improving the global competitiveness of the CEE EU (11) countries in the case of a number of Global Competitiveness Index sub-indices.
In this regard, the issue of national and regional R&D expenses is especially important. According to Feoktistova (2014), when planning R&D and its financing, the project approach should be used by selecting the expected results from implementing a research project as one of the key criteria and selecting the results already achieved by the research project by its would-be executor as the key criterion. Gaponenko (2018) considered situations in which it is potentially possible to reduce the actual costs of performing R&D: (1) performing R&D similar to work previously performed by the same contractor—a scientific organisation or a researcher; (2) performing R&D similar to work previously performed by other contractors—scientific organisations; (3) performing (possibly simultaneous) of similar R&D for different customers; (4) using previously obtained research results or previously assembled installations in new research, if the subjects of old and new research are not analogous to each other; and (5) including in the terms of reference of tasks that do not correspond to the goal of R&D, the results of which can be used, for example, in another R&D or a publication, a patent.
Nevertheless, in our opinion, these studies did not sufficiently elaborate on the problem of selecting reasonable quantitative benchmarks for planning the R&D expenditures of the regions. The issue of planning the redistribution of R&D expenditures among regions also remains open. On the contrary, in the work by Yashin et al. (2020), a foresight of the evolution of the innovation system in a federal district based on the use of a multipurpose genetic algorithm revealed that to increase the synergy effect of the federal district, it is planned to redirect investment resources and R&D costs to those regions where resources are scarce. This will eventually increase the average per-capita income in the regions of the federal district, which will lead to population growth. This highlights the necessity of solving the problem of optimising regional R&D expenditures and, above all, selecting the most rational methods for this purpose. Thus, Ildirar et al. (2016) provided new estimates of the impact of R&D expenditures on economic growth. They found that there are different types of R&D expenditures, each of which has a different significance for economic growth. The authors found that all R&D expenditures have a positive and significant impact on economic growth in individual OECD countries, but their importance varies. Therefore, policymakers should develop policies to stimulate R&D based on the characteristics of these countries. Accordingly, countries should allocate more resources to different types of R&D expenditures to achieve sustainable growth rates.
Salimi and Rezaei (2018) pointed out that assigning the same level of importance to different R&D indicators, which is a common approach in existing studies, may oversimplify the R&D measurement process and lead to misinterpretations of effectiveness and, consequently, incorrectly chosen R&D strat-
egies. Their findings showed that assigning different weights to different R&D indicators (as opposed to simple averages) leads to different rankings of firms and allows R&D managers to formulate more effective strategies to improve their firm's R&D effectiveness by applying knowledge of the importance of various R&D indicators. Bina et al. (2015) proposed comprehensive criteria for selecting R&D and innovation projects under conditions of uncertainty and taking into consideration the real constraints applicable to the Brazilian electricity sector using a combination of integer programming formulations and a method based on the PROMETHEE method. The authors identified the best results of the proposed application in solving the regulatory problems of the electricity sector, which emphasises the compliance of companies with R&D and innovation expenditure commitments. Thus, although selecting R&D and innovation projects is not a typical example of optimisation, under certain regional, sectoral, or organisational constraints, it may be the best solution.
Huang et al. (2020), taking into consideration the paradox of the spillover effect of R&D spared from the global supply chain, used a computational general equilibrium model with the GTAP v10 database to analyse the impact of Japanese public investment in R&D on key sectors of the global supply chain—chemical and pharmaceutical, electronic equipment, machinery, and transportation equipment— to assess its output, foreign trade, and welfare. Performance parameters initiated by public investments in R&D are calibrated from the SciREX Policymaking Intelligence Assistance System - Economic Simulator (SPIAS-e). The simulation results showed a significant increase in Japanese production and exports of chemical and pharmaceutical, electronic equipment, and transportation equipment. The study provides a comprehensive global analysis of manufacturing networks and an analysis to assess the spillover effects of R&D investments.
Sadollah et al. (2020) set the main goal of optimisation as improving overall sustainability, including environmental, social, economic, and energy resource sustainability, through the implementation of corresponding target functions. Since energy optimisation is one of the main objectives of sustainable development, it is studied from an energy perspective. Further, the concept, definitions, and elements of sustainability and optimisation were presented, and metaheuristic optimisation algorithms used in recently published papers related to sustainability and sustainable development were reviewed. Hyk (2021) determined the optimal cost structure for innovation and its impact on sales revenues, with a focus on the use of elements of economic and mathematical modelling. The scientific novelty of the work lies in the development of a model that substantiates the relationship between the studied indicators of costs for innovation, enables predicting the amount of revenue from sales, and ensures the achievement of its optimal value. The author also assessed the impact of the economy of innovation on the environment, which results in preserving the potential of natural resources to achieve sustainable economic development.
In the present study, we apply metaheuristic algorithms to optimise R&D costs in the regions of the federal district. This will further allow for planning the cross-financing of R&D within a single district. Of the available metaheuristic algorithms, we use the following three, which have significant advantages: (1) a genetic (evolutionary) algorithm (GA) is a highly effective way to find multiple efficient solutions in a single simulation run (Kalyanmoy, 2001); (2) simulated annealing (SA) makes it possible to avoid "trapping" in the local extrema of the function being optimised and to continue the search for a global extremum (Lopatin, 2005). Compared to GA, adaptive simulated annealing (ASA) does not yield to genetic algorithms in most problems and wins in many (Ingber and Rosen, 1992); and (3) pattern search (PS), a direct search method, can be used to solve problems for which the target function is not differentiable or even continuous (Conn et al., 1991; Conn et al., 1997; Kolda et al., 2006).
1. Materials and methods
Using the above metaheuristic algorithms, we created a model to optimise and plan the cross-financing of R&D costs in a federal district (Fig. 1). The model includes five stages, as shown in Fig. 1.
Fig. 1. A model for optimising and planning the cross-financing of R&D costs in a federal district
Stage 1 - Collect and prepare statistical data on the dynamics of investment, GRP, and indebtedness of legal entities in the regions. At this stage, we collect and adjust for inflation data on the dynamics of investment in fixed capital (x1), gross regional product (GRP) (x2), and the debt of legal entities on loans (x3) of the regions of the federal district over a long period spanning 10 years. These data are available on the website of the Federal State Statistics Servicel. Here, parameter x1 characterises investment planning, x2 refers to production planning, and x3 captures the financial planning of the district.
Stage 2 - Collect and prepare statistical data on the dynamics of regional R&D expenditures by type of work. Here, we collect and adjust for inflation statistical information on the internal current expenditures on R&D in total (y), as well as by types of work, which are divided into fundamental research (y1), applied research (y2), and developments (y3). These data are collected for the same period of time as in the previous stage.
Stage 3 - Build non-linear regressions for the target functions of R&D costs by type of work.
We use multiple non-linear regressions of R&D costs of the form y = f (x1, x2, x3), which more realistically reflects economic processes in comparison with linear ones. These are constructed using the Statistica software.
Stage 4 - Optimise the regressions on the given intervals by GA, SA, and PS. We perform global optimisation of the regression target functions in MATLAB using the three metaheuristic algorithms: GA, SA, and PS. To refine the results of the GA and SA methods, we supplement the optimisation results of the target functions with the hybrid functions of pattern search and the interior-point method (Babynin and Zhadan, 2008). That is, the GA or SA algorithms are applied first, and then their results are used as a starting point for the subsequent optimisation of the target function. This allowed for obtaining better solutions in each specific case of optimisation of the corresponding R&D costs.
In each particular case, we search for the global maximum of R&D costs in the federal district; that is, we calculate how much funds can be allocated to R&D maximally and on what values of parameters xl, x2, and x3 this maximum depends. We then optimise the obtained regressions for each type of R&D on the segments of parameters x1, x2, and x3, which are typical for each region of the federal district under study.
Stage 5 - Calculate the reserve or deficit of the respective R&D costs in each region. At this stage, we compare the obtained optimum R&D expenditures for each region of the district with its actual maximum value for the period under study and calculate the reserve or deficit of the respective R&D expenditures in each region as a difference between the actual and optimum values. This enables planning the possibilities of cross-financing R&D within the same district in more detail, that is, by region.
3. Results
In what follows, we demonstrate how this model works using the example of the Privolzhsky Federal District (PFD), considering only those regions (regions or republics) in which pilot innovation territorial clusters from the list approved by the government of the Russian Federation are located. These are the industrial regions where PFD's main R&D is carried out.
1 Federal State Statistics Service. URL: https://www.gks.ru_
Sustain. Dev. Eng. Econ. 2023, 2, 2. https://doi.org/10.48554/SDEE.2023.2.2 29
Stage 1 - Collect and prepare statistical data on the dynamics of investment, GRP, and indebtedness of legal entities in the regions. At this stage, the necessary initial data were collected from the website of the Federal State Statistics Service2 and adjusted for inflation. They are presented in the 2020 prices in columns x1, x2, and x3 of Table 1. Since the above website contains data on domestic current expenditures on R&D only for 2010 and the period 2015-2020, we took the data on investment in fixed capital, GRP, and indebtedness of legal entities on loans for the same years.
Table 1. Initial data on the Privolzhsky Federal District in 2020 prices (million rubles)
Year Investments in fixed capital Gross regional product Indebtedness of legal entities on loans Internal current costs of R&D by type of work
Total Fundamental research Applied research Developments
xi x3 y y1 y2 y3
1. Nizhny Novgorod Region
2010 354041 1203299 335116 49755.1 2257.5 7763.1 39734.3
2015 286275 1345281 438699 69259.4 2328.5 6359.8 60571.1
2016 268126 1341478 392014 76640.5 2197.6 7618.6 66824.4
2017 276481 1422534 356981 72458.5 2283.8 7463.4 62711.2
2018 280429 1478448 361167 71571 2399.5 9863.7 59307.8
2019 309749 1462590 385278 80671.8 4970.6 9972.7 65728.4
2020 383102 1474561 361554 68750.3 5220.1 8560.3 54969.9
2. Republic of Mordovia
2010 75165 194177 80800 884 156.1 267.3 460.6
2015 64242 219641 114539 996.8 147.6 293.9 555.3
2016 60822 233116 97935 896.2 141.2 173.2 581.9
2017 65984 242754 112000 885.7 126.5 212.9 546.4
2018 56551 245720 98970 1049.4 168.1 470 411.4
2019 54751 240875 102512 1009.9 125.3 438 446.6
2020 48969 238909 88007 1081.5 107.1 433.5 540.9
3. Ulyanovsk Region
2010 88464 328536 75419 9242.4 175.8 1451.9 7614.6
2015 96771 370808 96010 9672 228 5190 4254.2
2016 81562 375920 99058 9114.9 262.8 4511.5 4340.6
2017 94796 375951 71717 12565.8 230.2 2038.7 10296.8
2018 89649 376064 84054 12206.9 302.8 1267.4 10636.7
2019 75555 339226 78955 9659.3 218.5 1791.1 7649.6
2020 61181 312577 85313 10288.1 265.6 2607.6 7414.9
4. Samara Region
2010 284644 1282274 390241 22679.8 665.6 1249.4 20764.6
2015 368865 1540461 423126 19921.2 681.9 1616.6 17622.8
2016 296748 1468075 449779 13454.2 641.7 1220.8 11591.5
2017 292574 1520781 453792 15631.9 844.7 1282.3 13504.9
2018 286479 1633018 398565 14861.2 649 1197.6 13014.5
2019 301737 1632825 319233 19929.2 614.4 1020.9 18294
2020 202462 1648019 298558 15492.5 761 713.0 14018.6
5. Perm Territory
2010 257417 1148574 276981 12308.4 2383.9 1325.1 8599.4
2015 275493 1295517 312592 14528.9 982.9 1873.9 11671.9
2016 276655 1266576 221842 14107 1027.2 1568.8 11511
2017 276337 1343064 215175 15007.6 843.4 1745.3 12418.8
2018 263369 1425398 243162 13788.9 1032.6 1428.7 11327.6
2019 305392 1456557 274316 15591 1090.2 1716.1 12784.6
2 Federal State Statistics Service. URL: https://www.gks.ru
2020 290460 1467320 306550 15636.3 1148.2 1797.1 12691
6. Udmurt Republic
2010 94280 506122 121689 821.4 451.2 85.2 285
2015 99676 630842 114739 1297.2 380.9 163.9 752.4
2016 100692 614648 119263 1263 337.2 155.7 770.1
2017 94358 622590 89959 1986 237.5 458.6 1289.9
2018 104844 682300 89920 2481.4 657.3 233.1 1591.1
2019 105451 668360 110349 2332.8 731.4 126.8 1474.5
2020 107187 675545 85536 1846.9 811.5 123.1 912.2
7. Republic of Tatarstan
2010 606333 1846263 540376 11366.2 1526.8 1864.5 7974.9
2015 751565 2274027 660546 13926.5 2495.5 1772.2 9658.8
2016 735575 2234011 710836 13841.8 2196.6 1856.1 9789.2
2017 718755 2412123 699269 17574.2 2626.4 2249.4 12698.4
2018 680801 2669465 594273 18420.6 2422.4 2444.6 13553.6
2019 672302 2522721 496504 16617.8 2611.1 2232 11774.7
2020 655319 2549636 414215 16878.6 2896.6 2557.3 11424.7
8. Republic of Bashkortostan
2010 283173 1772189 213167 7236.3 1806 1958.3 3472
2015 386986 1603409 371940 9869.2 1420.5 996 7452.7
2016 410388 1546257 334792 9960.4 1193.1 2229.1 6538.3
2017 314046 1589666 328141 9739.9 1161.9 2568.5 6009.5
2018 289657 1809428 327419 11196.7 1408.7 2582.6 7205.5
2019 337919 1746876 328865 10490.5 1361 2644.6 6484.9
2020 326850 1754979 323670 10527.2 1417.7 2483.4 6626.1
We forecast the missing data on investment in fixed capital and GRP in 2020 prices, using the period from 2009-2018 and the Wolfram Alpha search service3. The results of the forecast are shown in Table 1 in italics.
Stage 2 - Collect and prepare statistical data on the dynamics of regional R&D expenditures by type of work. At this stage, we collected and adjusted for inflation statistical information on the internal current costs of R&D in total, as well as by type of work: fundamental research, applied research, and developments. These data were collected for the same period as in the previous stage. They are presented in the 2020 prices in columns y, y1, y2, and y3 of Table 1.
Stage 3 - Build non-linear regressions for the target functions of R&D costs by type of work.
According to the data in Table 1, the following most accurate non-linear regressions were obtained in Statistica:
- regression for all R&D costs (Fig. 2)
y = 82426.01 + 0.06x2 -8303.97ln x3, R2 = 0.948, adjusted R2 = 0.938 ;
- regression for fundamental research (Fig. 3)
y = 1782 - 57170107 -738Z0171, R2 = 0.484 , adjusted R2 = 0.444 ;
- regression for applied research (Fig. 4)
y2 =-58921.7 + 3523.1lnx1 + 1925.2lnx3, R2 = 0.244, adjusted R2 = 0.185 ;
- regression for developments
y3 =-315317.4-0,02542966x2 -0.6432493x3 -950912100 + 981.9057^ + 9314139000 ,R2 = 0.447 , adjusted R2 = 0.392 . 1 3
3 Wolfram Alpha search service. URL: www.wolframalpha.com_
Sustain. Dev. Eng. Econ. 2023, 2, 2. https://doi.org/10.48554/SDEE.2023.2.2 31
y = 82426.01 + 0.06 x- 8303.97 Inx,
x 10 2 3
Fig. 2. Regression plot for all R&D costs y1 = 1782 - 57170107 / x^ -73870171 / *3
1400
Loans (x^}
Investments )
Fig. 3. Regression plot for fundamental research
y2 = - 58921.7 + 3523.1 + 1925.2 Inx^
- 14000
Fig. 4. Regression plot for applied research
Stage 4 - Optimize the regressions on the given intervals by GA, SA, and PS. The global optimisation of the target regression functions was performed using MATLAB. GA, SA, and PS were used for this purpose. To refine the results of the GA and SA methods, the optimisation results were supplemented with hybrid functions of the pattern search and interior-point method (fmincon). All target functions were investigated on the segments of actual values of parameters x1, x2, and x3 for the period under study, according to the data in Table 1, marked in bold type.
As an example, for all the costs of R&D in PFD, the optimisation results are given in Table 2. As shown in the table, the most reliable result is obtained by PS. Adding this algorithm or the interior-point method (fmincon) as a hybrid function for GA or SA also allowed achieving a high-quality solution to the optimisation problem.
Table 2. Results of the global optimisation of the regression for all R&D costs for PFD (million rubles)
Algorithm Investments in fixed capital Gross regional product Indebtedness of legal entities on loans Total expenses on R&D Maximum actual value
xi X2 x3 y y
GA - 2 655 302 84 056 147 583.4 80 671.8
GA + fmincon - 2 669 465 71 717 149 751.5
GA + PS - 2 669 465 71 717 149 751.5
SA - 1 474 311 381 367 64 166.1
SA + fmincon - 2 669 465 71 717 149 751.5
SA + PS - 2 669 465 71 717 149 751.5
PS - 2 669 465 71 717 149 751.5
Table 2 also shows that the maximum actual value of all R&D costs is significantly lower than the maximum possible total costs of R&D with the respective values of GRP and indebtedness of legal entities on loans. This indicates that there are real possibilities for financing R&D in a larger volume. This issue, however, requires a more detailed solution. Thus, we conducted the same global optimisation of
all types of R&D costs for each PFD region separately, applying the same metaheuristic algorithms. The previous target regression functions were investigated for each region on its segments of actual values of parameters x1, x2, and x3 for the period under study, according to the data in Table 1. The results of global optimisation are shown in Tables 3-6.
Table 3. Results of the global optimisation of the regression for all R&D costs by the regions of PFD
(million rubles)
Region Investments in fixed capital Gross regional product Indebtedness of legal entities on loans Total eXpenses on R&D MaXimum actual value Reserve (+) or deficit (-) of eXpenses
xi X2 X3 y y Ay
1. Nizhny Novgorod - 1 478 448 335 116 65 487.9 80 671.8 15 183.9
2. Mordovia - 245 720 80 800 3 336.6 1 049.4 - 2 287.2
3. Ulyanovsk - 376 064 71 717 12 147.5 12 565.8 418.3
4. Samara - 1 648 019 298 558 76 621.3 22 679.8 - 53 941.5
5. Perm - 1 467 320 215 175 68 499 15 636.3 - 52 862.7
6. Udmurtia - 682 300 85 536 29 058.4 2 481.4 - 26 577
7. Tatarstan - 2 669 465 414 215 135 189.2 18 420.6 -116 768.6
8. Bashkortostan - 1 809 428 213 167 89 103.4 11 196.7 - 77 906.7
Table 4. Results of the global optimisation of the regression for fundamental research by the regions of PFD (million rubles)
Region Investments in fixed capital Gross regional product Indebtedness of legal entities on loans Fundamental research MaXimum actual value Reserve (+) or deficit (-) of eXpenses
xi X2 X3 y1 y1 Ay,
1. Nizhny Novgorod 383 102 - 438 699 1 464.4 5 220.1 3 755.7
2. Mordovia 75 165 - 114 539 376.5 168.1 - 208.4
3. Ulyanovsk 96 771 - 99 058 445.5 302.8 - 142.7
4. Samara 368 865 - 453 792 1 464.2 844.7 - 619.5
5. Perm 305 392 - 312 592 1 358.5 2 383.9 1 025.4
6. Udmurtia 107 187 - 121 689 641.6 811.5 169.9
7. Tatarstan 751 565 - 710 836 1 602 2 896.6 1 294.6
8. Bashkortostan 410 388 - 371 940 1 444.1 1 806 361.9
Table 5. Results of the global optimisation of the regression for applied research by the regions of PFD (million rubles)
Region Investments in fixed capital Gross regional product Indebtedness of legal entities on loans Applied research MaXimum actual value Reserve (+) or deficit (-) of eXpenses
x1 X2 X3 y2 y2 Ay,
1. Nizhny Novgorod 383,102 - 438,699 11,382.8 9,972.7 -1,410.1
2. Mordovia 75,165 - 114,539 3,059.7 470 -2,589.7
3. Ulyanovsk 96,771 - 99,058 3,670.3 5,190 1,519.7
4. Samara 368,865 - 453,792 11,314.5 1,616.6 -9,697.9
5. Perm 305,392 - 312,592 9,931.7 1,873.9 -8,057.8
6. Udmurtia 107,187 - 121,689 4,426.6 458.6 -3,968
7. Tatarstan 751,565 - 710,836 14,686.1 2,557.3 -12,128.8
8. Bashkortostan 410,388 - 371,940 11,307.4 2,644.6 -8,662.8
Table 6. Results of the global optimisation of the regression for developments by the regions of PFD
(million rubles)
Region Investments in fixed capital Gross regional product Indebtedness of legal entities on loans Developments Maximum actual value Reserve (+) or deficit (-) of expenses
x1 X2 X3 y3 y3 Ay3
1. Nizhny Novgorod 383,102 1,203,299 438,699 40,998.4 66,824.4 25,826
2. Mordovia 75,165 194,177 80,800 9,503.2 581.9 -8,921.3
3. Ulyanovsk 96,771 312,577 71,717 13,603.7 10,636.7 -2,967
4. Samara 368,865 1,282,274 453,792 39,572.4 18,294 -21,278.4
5. Perm 305,392 1,148,574 312,592 30,065.7 12,784.6 -17,281.1
6. Udmurtia 107,187 506,122 121,689 3,732.2 1,591.1 -2,141.1
7. Tatarstan 751,565 1,846,263 526,041 27,961.4 13,553.6 -14,407.8
8. Bashkortostan 410,388 1,546,257 371,940 27,670.3 7,452.7 -20,217.6
Stage 5 - Calculate the reserve or deficit of the respective R&D costs in each region. The last columns of Tables 3-6 present the results of calculating the reserve or deficit of the respective R&D costs in each region as the difference between the actual and the optimal values. This allowed for planning the possibilities of R&D cross-financing within one district. For example, in Table 3, in the Nizhny Novgorod and Ulyanovsk regions, the actual maximum total R&D costs exceed the optimal costs. This leads to the tentative conclusion that in the conditions of saving federal budget funds, PFD can partially finance all R&D costs in those regions that need it. According to the data in the last column of Table 3 regarding the lack of total R&D costs, we can include the Republic of Mordovia, the Samara region, the Perm region, the Udmurt Republic, and the Republics of Tatarstan and Bashkortostan in such regions. Moreover, according to Table 3, the region in need is the Republic of Tatarstan.
To better identify these regions, the outcome was analysed in more detail—in terms of the various costs of R&D by type of work. The results in Tables 4-6, for example, show that the Republic of Tatarstan, on the contrary, had some reserve in the expenditures on fundamental research, which could be redirected to other regions of PFD. Further, for Tatarstan, the shortage of expenditures on applied research (Table 5) and developments (Table 6) in total was significantly lower than the shortage of all R&D expenditures, as reflected in Table 3. By contrast, according to Tables 4-6, the Samara region, the Republic of Bashkortostan, and the Perm region were the most in need of financing various types of R&D costs. However, the main donor of the reserve of costs for various types of R&D remained the Nizhny Novgorod region, if we again consider the internal cross-financing of R&D costs within the limits of PFD. This would allow significant savings in the federal budget funds allocated for scientific and, consequently, innovative development in the country's regions.
4. Discussion
The present results correlate with the conclusions obtained by Yashin et al. (2020). Namely, for the Samara region, the model revealed the greatest deficit in current R&D expenditures compared to the optimal plan, which amounted to 10,673 million rubles. The region can be partially compensated for at the expense of R&D reserves of the Nizhny Novgorod and Ulyanovsk regions, the Udmurt Republic, and the Republics of Tatarstan and Bashkortostan. In total, such a reserve amounts to 8,412 million rubles, which should be allocated to the Samara region. The synergy effect of such an reallocation would be 86,153.7 million rubles. The reserve of 8,412 million rubles can also be partially allocated to R&D in the Republic of Mordovia and the Perm region, and the remainder should be transferred to the Samara region. However, the synergy effect of the entire PFD in this case will be the same as in the case if the entire reserve is allocated to R&D in the Samara region.
Comparing the obtained results with the experience of other researchers, it can be noted that in planning R&D and its financing, Feoktistova (2014) highlighted the use of the project approach, the choice of the expected results of a research project as one of the key criteria, and the choice of the results
already achieved by a research project by its potential performer as the key criterion. Gaponenko (2018) also considered situations in which it is potentially possible to reduce the actual costs of performing R&D: (1) performing R&D similar to work previously performed by the same contractor—a scientific organisation or a researcher; (2) performing R&D similar to work previously performed by other contractors—scientific organisations; (3) performing (possibly simultaneous) similar R&D for different customers; (4) using previously obtained research results or previously assembled installations in new research terms if the subjects of old and new research are not analogous to each other; and (5) including in the terms of reference tasks that do not correspond to the goal of R&D, the results of which can be used, for example, in another R&D or a publication, a patent.
We propose justified quantitative guidelines for planning the costs of R&D in an industrial region based on global optimisation of the indicated costs. The described approach can contribute to better decision making by state structures and their experts with regard to planning the innovative development of industrial regions of the country.
5. Conclusion
The following points highlight the most important findings of the study:
1. Currently, the issues of the optimal financing of R&D expenditures within the country and its regions, which have the appropriate scientific potential, have not yet been completely solved. It seems impossible to solve such problems in isolation from the specific technological and economic results of regional R&D. Planning of these results, as well as the resources required for their achievement, is an urgent task to optimise R&D expenditures. In this regard, we distinguished three types of planning: investment, production, and financial. We considered all three processes simultaneously. This allows for covering a wide range of tasks to optimise R&D costs in the regions and contribute to their innovative development.
2. The results of global optimisation allow us to draw the conclusion that in the conditions of saving the federal budget funds, the federal district authorities can partially finance all R&D costs in those regions that need it. To identify such regions more reasonably, it is necessary to analyse this situation in more detail—in terms of various R&D costs by type of work.
3. For PFD, the Samara region, the Republic of Bashkortostan, and the Perm region are the most in need of financing various types of R&D expenditures. However, the main donor of the reserve of expenditures on various types of R&D is the Nizhny Novgorod region. This is the essence of the internal cross-financing of R&D costs within PFD. It would allow significant savings in the federal budget funds allocated for scientific and, consequently, innovative development of the country's regions.
Acknowledgements
The research was carried out with the financial support of the Russian Foundation for Basic Research within the framework of scientific project No. 19-010-00932 "Creating a model for the evolution of the innovation system of industrial regions in modern conditions of socio-economic development".
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The article was submitted 11.03.2023, approved after reviewing 25.05.2023, accepted for publication 31.05.2023.
Статья поступила в редакцию 11.03.2023, одобрена после рецензирования 25.05.2023, принята к публикации 31.05.2023.
About authors:
1. Dmitrii Rodionov, Doctor of Economics, professor, Head of the Graduate School of Industrial Economics, Peter the Great St. Petersburg Polytechnic University, Saint Petersburg, Russia. drodionov@spbstu.ru, https://orcid.org/0000-0002-1254-0464
2. Egor Koshelev, candidate of economic science, Associate Professor of the Department of Management and Public Administration, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russian Federation. ekoshelev@yandex.ru, https://orcid.org/0000-0001-5290-7913
3. Lo Thi Hong Van, University of Economics and Business, Vietnam National University, Hanoi, Vietnam, hongvan289@gmail.com
Информация об авторах:
1. Дмитрий Григорьевич Родионов, доктор экономических наук, профессор, директор Высшей инженерно-экономической школы, Санкт-Петербургский политехнический университет Петра Великого, Санкт-Петербург, Российская Федерация. drodionov@spbstu.ru, https://orcid.org/0000-0002-1254-0464
2. Егор Викторович Кошелев, кандидат экономических наук, доцент кафедры менеджмента и государственного управления, Нижегородский государственный университет им. Н.И. Лобачевского, Нижний Новгород, Российская Федерация. ekoshelev@yandex.ru, https://orcid.org/0000-0001-5290-7913
3. Ло Тхи Хонг Ван, Университет экономики и бизнеса Вьетнамского национального университета, Ханой, Вьетнам, hongvan289@gmail.com
