|Lev Mazelis||Laboratory Department of Mathematics and Modelling, Vladivostok State University of Economics and Service, st. Gogol 41, Vladivostok 690014, Russia|
|Kirill Lavrenyuk||Human Resources Directorate, RT-Techpriemka, Electric lane 1/12, Moscow 123557, Russia|
|Andrey Krasko||Laboratory Department of Mathematics and Modelling, Vladivostok State University of Economics and Service, st. Gogol 41, Vladivostok 690014, Russia|
This study was performed as part of an essential task of accumulating and developing regional human capital in the digital economy. In this age of uncertainties, risks, and scarcity of resources, regional leadership faces the task of the optimal allocation of available financial resources among strategic projects that directly or indirectly affect the development of regional human capital. The aim of this study was to develop and test the economic and mathematical method of forming the optimal portfolio of strategic projects to maximize progress towards achieving the target values of key indicators of regional development through the development of human capital using a fuzzy approach. A fuzzy model is proposed, and its objective function is an integrated index that takes into account the degrees of achievement of strategic indicators of the social and economic development of a region. The information base of the study is composed of statistical data from official information resources. The model is a fuzzy mathematical programming problem in which the uncertainty and lack of information are modeled using a fuzzy approach. The variables used for the optimization are the Boolean variables of the inclusion of a project in a particular investment area at a certain point in time in a project portfolio. The transition from a fuzzy optimization problem to a crisp one is performed by setting confidence levels for the objective function and constraints. The choice of a certain confidence level allows, to some extent, one to take into account the uncertainty, which in turn affects the structure of the investment allocation. For the Primorsky Region, an example of the formation of an optimal portfolio of projects is considered by each year of a given planning period, which allows for maximum progress towards achieving the targets of development for the region.
Economic and mathematical model; Fuzzy logic; Project portfolio optimization; Regional human capital; Social and economic development
Currently, regions operate in the context of the on-going digital transformation of the economy and social environment. The penetration of cutting-edge technologies into the environment of human functioning produces new innovative businesses and products and results in the automation and digitalization of business processes (Berawi, 2019). However, the integration of technological innovations into everyday life also demands new requirements for the quality and pace of the development of human capital (Santoso et al., 2019). The modification of human capital is associated with the rapid emergence of new digital competencies and their continual development. In turn, public authorities can contribute to the development of human capital through the implementation of projects that are aimed at creating favorable conditions for organizing educational processes that, for example, meet the requirements of employers, deliver quality medical care (Berawi, 2020), etc. This leads to the need to address the issue of the optimal allocation of resources that are available in a region among such projects to obtain a maximum effect.
Currently, there is ongoing research on the problems of the development of human capital at various levels. The research data can be logically structured into three groups.
Group I includes studies that focus on the quantitative assessment of human capital. One of the most popular tools for assessing human capital is the human development index (UNDP, 2019). Gurban (2015) presents the value of human capital by subjects of the Russian Federation as the average of the following components: demography, education, employment, science, and social culture. Lim et al. (2018) made a systematic analysis of human capital for 195 countries and regions for the period 1990–2016. There are many studies devoted to the subject of the quantitative assessment of human capital in different geographical areas, for example, in the U.S. (Christian, 2014) and China (Li et al., 2016).
Group II includes studies that focus on assessing the impact of the investment process on human capital. For example, Pelinescu (2014) considers the impact of investments aimed at ensuring the birth rate, creating a training system for highly qualified specialists and the social welfare of the population, and developing a region’s human capital. Percoco (2016) analyses the impact of changes in the secondary and higher education systems in a country on the change in the human capital development index. In addition, Soubjaki (2017) analyses the relationship between negative contributors to the health status of the population and human capital. Fraumeni et al. (2019) proposes a new complex measure of human capital investment.
Group III includes studies that focus on the assessment of the impact of human capital on the development of a specific social and economic system. For example, McDonald (2019) describes the positive impact of investment in human capital of the U.S. defense sector on the economic growth of the states and the country as a whole. Olopade et al. (2019) analyses the impact of human capital development on poverty reduction in terms of long-term economic growth. Teixeira and Queirós (2016) note that in 1960–2011, the investment in human capital and the dynamics of production specialization were critical economic growth factors for developed countries. Zallé (2019) indicates clear feedback between the rate of exploitation of natural resources and the level of development of human capital.
The analysis of referenced works allows us to discuss the lack of tools that would allow the reasonable formation of an optimal set of regional strategic projects that directly or indirectly affect the development of regional human capital to maximize progress towards achieving the targets of the development of a region. When forming an optimal project portfolio, the current parameters and specifics of the region, the planning period, and available resource constraints should be taken into account. Special focus should be directed toward the consideration of environmental uncertainties and incomplete information. Aras et al. (2008) consider the use of fuzzy logic for modeling social and economic processes. The fuzzy set approach is viewed as a promising direction, which allows the modeling of uncertainties of verbal expert estimates of model parameters and potential risks by representing parameters and functional dependencies in the form of fuzzy numbers (Carlsson et al., 2007). Fuzzy problems require special solution methods. However, the lack of examples of implementations of the proposed methods and approaches in real cases of the formation of time-variant project portfolios presents considerable difficulties in their further use in optimization models. Fuzzy optimization models with fuzzy objective functions and constraints allow the results to vary when setting various exogenously established confidence levels (Anshin, 2015).
Thus, the aim of this study was to develop an economic and mathematical method of forming the optimal portfolio of strategic projects to achieve the target values of key indicators of regional development through the development of its human capital in a fuzzy setting.
The fuzzy economic and mathematical model has been developed, which allows the formation of an optimal portfolio of regional strategic projects that directly or indirectly affect the development of regional human capital. The objective function of the model is an integrated index that characterizes the degrees of achievement of the targets of social and economic development of the region for a given planning period. The variables used for optimization are the Boolean variables of the inclusion of a project in a particular investment area at a certain point in time.
In comparison with previous studies, a distinctive feature of this model is the consideration of two levels of uncertainty in the formation of an optimal portfolio of regional strategic projects. The first level is associated with the reliability of estimates of numerical coefficients of dependencies (Equation 2) and (Equation 3). The second level is associated with the need to set a number of parameters for dependencies (Equation 5) and (Equation 6) and restrictions (Equation 10) through (Equation 12), which are determined by the experts. To model these uncertainties, a fuzzy-multiple approach is used, and the developed model is a fuzzy mathematical programming problem.
This study proposes a method to identify a solution for the fuzzy problem of forming an optimal portfolio of regional strategic projects. The idea of the approach is to reduce the fuzzy optimization model to a crisp one by converting fuzzy inequalities for the objective function and restrictions into crisp ones at given confidence levels.
The formation of the optimal portfolio of strategic projects for the Primorsky Region considers the computation aspects of the proposed model. The resulting structure of the regional budget investments by investment areas is formed on the basis of a pool of strategic projects. A comparative analysis of the investment structure resulting from the use of the model and reflected in the draft regional budget was performed. The analysis showed a higher efficiency of financial resources expressed in a greater degree of achieving the integrated index and the targets of social and economic development for the regional project portfolio formed on the basis of the proposed model.
The study was sponsored by the Russian Foundation for Basic Research (RFBR) as part of research project No. 18-010-01010.
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