DOI: https://doi.org/10.62204/2336-498X-2023-4-2
SIMULATION OF THE SYSTEM OF SOCIALLY ORIENTED
PERSONNEL MANAGEMENT OF HIGHLY ADAPTIVE ENTERPRISES
Dmytro Dyachkov,
Doctor of Economic Sciences, Professor,
Director of the Educational and Scientific Institute of
Economics, Management, Law and Information Technologies,
Poltava State Agrarian University, Ukraine,
dmytro.dyachkov@pdau.edu.ua; ORCID: 0000-0002-2637-0099
Viktoriia Skrypnyk,
Ph.D. in Economics, Associate Professor,
Luhansk Taras Shevchenko National University, Poltava, Ukraine,
viktoriaskrypnyk777@gmail.com; ORCID: 0000-0003-1813-1749
Serhii Yanechko,
Ph.D. student,
Kyiv National University of Technologies and Design, Ukraine,
syanechko@gmail.com; ORCID: 0009-0002-2115-3287
Annotation. With the help of game theory, the size of the optimal monetary incentive was investigated depending on the type of additional payments on the example of specific highly adaptive enterprises in the context of socially oriented personnel management. The strategy for the development of enterprises at different levels of management, which under any external conditions will provide an opportunity to obtain even a minimal, but guaranteed profit, has been determined.
Keywords: modeling, system, socially oriented management, personnel management, adaptive management, enterprises.
Formulation of the problem. The financial and economic development of macro-, meso- and micro-systems, in particular at the level of a highly adaptive enterprise, is a complex, multifactorial process, so every business entity faces the question of assessing development prospects, taking into account all factors affecting the final result. One of the important links in the strategic development of a highly adaptive enterprise of any level is personnel management in the management system. Therefore, an important aspect of managing any economic system is the availability of tools for assessing the main indicators of system development and achieved results, the possibility of comparing them with other entities, as well as the possibility of constant control over the dynamics and directions of change of key development indicators. In this connection, there is a need to choose the most effective methods for research, analysis and forecasting of each of the structural elements of a highly adaptive enterprise at different levels of management. The use of effective evaluation tools will contribute to the strengthening of the motivational mechanism, as one of the key factors of socially oriented personnel management, and as a consequence to the increase of labor productivity, product quality and ensuring the competitiveness of the economic entity in general. Therefore, it is important to effectively manage the motivational mechanism of personnel as the basis for increasing efficiency, which should not be considered as a narrow complex of economic and organizational components, united only with the formation of personal earnings, but more broadly and more fully as a system that is a component of the organizational, economic and social mechanism of enterprise functioning.
Analysis of recent research and publications. Lozhachevska O. et al. (2021) in the management system of logistics and marketing behavior of innovative clusters of territorial communities in the conditions of digitalization of society and the online market emphasize the systematization of concepts of socially oriented management [4]. Bazeliuk V. et al. (2021) investigate the system of forming and diagnosing the levels of innovative and entrepreneurial competence of future managers of education in the conditions of the knowledge economy [1]. Zoria O. et al. (2022) analyze the theoretical and methodological foundations of investment support for innovation-oriented development of agricultural production at highly adaptive enterprises [10]. Hutorov A. O. et al. (2019) model the cycle of the reproductive process in the agricultural sector of the economy of Ukraine from the standpoint of socially oriented management [3]. Oseredchuk O. et al. (2022) update new approaches to monitoring the quality of higher education in the process of distance learning, in particular the provision of social competencies [7]. Voznyuk A. et al. (2021) focus on interdisciplinary educational technology based on the social concept [9]. Bilan Y. et al. (2017) study the design of the social component of effective land resource management [2]. Mykhailichenko M. et al. (2021) systematize competitive personnel management strategies in the business processes of agricultural enterprises focused on digitization [5].
In the complex of personnel management in the system of socially oriented management, there is not only the management of the motivational mechanism of personnel, but also the study, research, analysis of other aspects of personnel management at the financial, economic, and production levels. In particular, justification at the economic-mathematical level using research methods and models and modeling of management processes. One such method is game theory. The study of the elements of game theory and the wide application of this theory in solving problems of enterprise management allows to significantly reduce the level of uncertainty when making management decisions in order to ensure targeted actions to increase the efficiency of the business entity. Game theory methods allow finding the best guaranteed outcome from the worst possible options. This makes it possible to choose a strategy for the development of a highly adaptive enterprise at different levels of management, which, under any external conditions, will provide an opportunity to obtain, albeit minimal, but guaranteed profit [6; 8].
Setting the purpose and objectives of the study – to investigate the simulation of the system of socially oriented personnel management of highly adaptive enterprises.
The main research material. With the help of game theory, we will determine and analyze the size of the optimal monetary incentive depending on the type of additional payments based on the example of specific highly adaptive enterprises. Three enterprises of the Poltava region were selected – SE EF “Stepne”, PAC “Zlagoda”, PE “named after Kalashnikov”, which are approximately the same in terms of size, specialization, production direction, number of management and production personnel. During the study, we take into account the seasonality of production, the complexity and tension in some production areas, and the forms of remuneration, compensation, benefits and staff incentives.
Thus, a staff survey was conducted in the studied enterprises and a list of benefits aimed at the social protection of employees was formed. Each hryvnia benefit = 1 point – the maximum number of points is 10,000 per year (Table 1).
Table 1
Proposed volumes and types of social benefits for the studied enterprises, 2024
| Types of benefits | Cost, UAH | Points (1 UAH = 1 point) |
Dependence on labor productivity growth, % – UAH |
| Tickets for concerts, cinema, theater, excursions | up to 2,000 | up to 2,000 | 5% increase – 5,000 UAH |
| Payment of a subscription to a swimming pool, fitness room, etc | up to 2,000 | up to 2,000 | |
| Education (seminars, trainings) | up to 4,000 | up to 4,000 | |
| Mobile payment | up to 1,000 | up to 1,000 |
6-10% increase – 7,500 UAH |
| Payment for own vacation (sanatorium, resort) | up to 10,000 | up to 10,000 | |
| Payment for rest (rehabilitation) of the child | up to 10,000 | up to 10,000 | |
| Compensation for the payment of communal services | up to 10,000 | up to 10,000 |
11-15% increase – 10,000 UAH |
| The possibility of receiving onetime assistance | up to 10,000 | up to 10,000 |
Source: developed by the authors
The type of benefits provided by the company can be drawn up by the employee himself at the beginning of the year of using them. In monetary terms, the employee cannot take away the granted benefit, that is, only receive the benefit paid by the company. Surcharges are a variable part of the tariff system and social incentives and depend on production conditions.
Therefore, the optimal amount of monetary incentives for various types of benefits of the investigated enterprises, as previously mentioned, will be calculated using game theory.
The amounts of additional payments for different types of benefits of the three investigated enterprises are presented in the table. 2.
Since each of the three types of benefits has a different amount of additional payments, we will bring the production model to a mathematical form and denote by x1, x2 and x3 the probabilities of receiving the incentive with the smallest, average and largest size, respectively.
Table 2 Amounts of additional payments for different types of benefits of the researched enterprises, 2024
| Activity | Type of stimulation | ||
| The smallest amount of additional payment | The average amount of the surcharge | The maximum amount of the surcharge | |
| SE EF “Stepne” Poltava district | |||
| Tickets for concerts, cinema, theater, excursions | 3,000 | 4,000 | 5,000 |
| Payment of a subscription to a swimming pool, fitness room, etc | 3,000 | 4,000 | 5,000 |
| Education (seminars, trainings) | 3,000 | 4,000 | 5,000 |
| Mobile payment | 5,000 | 6,000 | 7,500 |
| Payment for own vacation (sanatorium, resort) | 5,000 | 6,000 | 7,500 |
| Payment for rest (rehabilitation) of the child | 5,000 | 6,000 | 7,500 |
| Compensation for the payment of communal services | 8,000 | 9,000 | 10,000 |
| The possibility of receiving one-time assistance | 8,000 | 9,000 | 10,000 |
| PAC “Zlagoda” of Poltava district | |||
| Tickets for concerts, cinema, theater, excursions | 4,200 | 5,000 | 7,000 |
| Payment of a subscription to a swimming pool, fitness room, etc | 3,000 | 4,500 | 5,500 |
| Education (seminars, trainings) | 3,600 | 4,200 | 5,100 |
| Mobile payment | 4,800 | 5,000 | 7,000 |
| Payment for own vacation (sanatorium, resort) | 6,000 | 7,000 | 7,800 |
| Payment for rest (rehabilitation) of the child | 4,700 | 5,900 | 7,100 |
| Compensation for the payment of communal services | 7,300 | 7,900 | 8,400 |
| The possibility of receiving one-time assistance | 8,500 | 9,000 | 9,500 |
| PE “named after Kalashnikov” of the Poltava district | |||
| Tickets for concerts, cinema, theater, excursions | 3,500 | 3,900 | 4,000 |
| Payment of a subscription to a swimming pool, fitness room, etc | 3,500 | 3,800 | 4,000 |
| Education (seminars, trainings) | 3,800 | 4,000 | 4,400 |
| Mobile payment | 3,600 | 3,800 | 4,000 |
| Payment for own vacation (sanatorium, resort) | 5,000 | 5,500 | 6,200 |
| Payment for rest (rehabilitation) of the child | 5,000 | 5,400 | 6,000 |
| Compensation for the payment of communal services | 6,000 | 6,500 | 7,100 |
| The possibility of receiving one-time assistance | 8,000 | 8,400 | 9,000 |
Source: developed by the authors
Then x1 + x2 + x3 = 1.
The contribution of x1, x2 and x3 to the amount of additional payments is described by the inequalities for the studied agricultural enterprises in the table. 3.
where V is the optimal size of the surcharge.
V = Zmax.
We carry out mathematical operations and transfer V to the left side of the inequalities, and we have the following problem of linear programming of the amounts of surcharges for different types of benefits of the three researched agricultural enterprises of the Poltava region, 2024 (Table 4).
Table 3 Mathematical formulation of the amounts of additional payments for different types of benefits of the researched enterprises, 2024
| Inequalities | ||
| SE EF “Stepne” Poltava district | PAC “Zlagoda” of Poltava district | PE “named after Kalashnyk” of Poltava district |
| 3,000х1+4,000х2+5,000х3≥V | 4,200х1+5,000х2+7,000х3≥V | 3,500х1+3,900х2+4,000х3≥V |
| 3,000х1+4,000х2+5,000х3≥V | 3,000х1+4,500х2+5,500х3≥V | 3,500х1+3,800х2+4,000х3≥V |
| 3,000х1+4,000х2+5,000х3≥V | 3,600х1+4,200х2+5,500х3≥V | 3,800х1+4,000х2+4,400х3≥V |
| 5,000х1+6,000х2+7,500х3≥V | 4,800х1+5,000х2+7,000х3≥V | 3,600х1+3,800х2+4,000х3≥V |
| 5,000х1+6,000х2+7,500х3≥V | 6,000х1+7,000х2+7,800х3≥V | 5,000х1+5,500х2+6,200х3≥V |
| 5,000х1+6,000х2+7,500х3≥V | 4,700х1+5,900х2+7,100х3≥V | 5,000х1+5,400х2+6,000х3≥V |
| 8,000х1+9,000х2+10,000х3≥V | 7,300х1+7,900х2+8,400х3≥V | 6,000х1+6,500х2+7,100х3≥V |
| 8,000х1+9,000х2+10,000х3≥V | 8,500х1+9,000х2+9,500х3≥V | 8,000х1+8,400х2+9,000х3≥V |
Source: developed by the authors
Table 4 Linear programming models and the objective function of the amounts of surcharges for different types of benefits of the researched enterprises, 2024
| Linear programming models and objective function | ||
| SE EF “Stepne” Poltava district | PAC “Zlagoda” of Poltava district | PE “named after Kalashnyk” of Poltava district |
| 3,000х1+4,000х2+5,000х3-V ≥ 0 | 4,200х1+5,000х2+7,000х3 -V ≥0 | 3,500х1+3,900х2+4,000х3 -V ≥0 |
| 3,000х1+4,000х2+5,000х3-V ≥ 0 | 3,000х1+4,500х2+5,500х3 -V ≥0 | 3,500х1+3,800х2+4,000х3-V ≥0 |
| 3,000х1+4,000х2+5,000х3-V ≥ 0 | 3,600х1+4,200х2+5,500х3 -V ≥0 | 3,800х1+4,000х2+4,400х3 -V ≥0 |
| 5,000х1+6,000х2+7,500х3-V ≥ 0 | 4,800х1+5,000х2+7,000х3 -V ≥0 | 3,600х1+3,800х2+4,000х3 -V ≥0 |
| 5,000х1+6,000х2+7,500х3-V ≥ 0 | 6,000х1+7,000х2+7,800х3 -V ≥0 | 5,000х1+5,500х2+6,200х3 -V ≥0 |
| 5,000х1+6,000х2+7,500х3-V ≥ 0 | 4,700х1+5,900х2+7,100х3 -V ≥0 | 5,000х1+5,400х2+6,000х3 -V ≥0 |
| 8,000х1+9,000х2+10,000х3-V ≥ 0 | 7,300х1+7,900х2+8,400х3 -V ≥0 | 6,000х1+6,500х2+7,100х3 -V ≥0 |
| 8,000х1+9,000х2+10,000х3-V ≥ 0 | 8,500х1+9,000х2+9,500х3 -V ≥0 | 8,000х1+8,400х2+9,000х3 -V ≥0 |
| х1+х2+х3+0V =1 | х1+х2+х3+0V =1 | х1+х2+х3+0V =1 |
| 0х1+0х2+0х3+1V = Zmax | 0х1+0х2+0х3+1V = Zmax | 0х1+0х2+0х3+1V = Zmax |
Source: developed by the authors
Next, we solve the problem in the Microsoft Excel environment using the Solver tool, executed by the Data→Solver command As a result, we get the following result:
x1 = 0; x2 = 0; x3 = 1; V = 5,000 SE EF “Stepne” of Poltava district. x1 = 0; x2 = 0; x3 = 1; V =5,100 PAC “Zlagoda” of Poltava district
x1 = 0; x2 = 0; x3 = 1; V = 4,900 PE “named after Kalashnyk” of Poltava district
That is, the optimal amount of additional payments in the investigated agricultural enterprises is:
SE EF “Stepne” Poltava district 5,000 UAH.
PAC “Zlagoda” Poltava district 5,100 UAH.
PE “named after Kalashnikov” of Poltava district 4,900 UAH.
So, summing up, it should be noted that the use of economic-mathematical modeling, in particular optimization problems and problems of game theory, in the conditions of specific enterprises allows modeling the management of the motivational mechanism of personnel, which can stimulate socially and in production activity as a whole.
Connecting the conducted research, modeling and forecasting of the elements of personnel management, we will continue with a more detailed analysis of the factors influencing the personnel management on the results of the enterprise.
So, using the financial statements of the investigated agricultural enterprises, the study, research, analysis, modeling and forecasting of the main factor characteristics of personnel management and the effective indicator of production activity were carried out using multiple production regression.
It is known that dependencies of this type can be described by a multiple linear production function of the type:
Ŷ= a0 + a1X1 + a2X2 + …+aₙXₙ. (1)
The main task of multiple production regression is the study of the influence of the main factors on the result of the economic entity.
So, we determine the main factors and factors of influence of three agricultural enterprises of the SE EF “Stepne” of the Poltava District, PAC “Zlagoda” of the Poltava District and PE “named after Kalashnikov” of Poltava district:
- the level of staff stability, % – the ratio of the number of employees with more than one year of experience in the organization (for a certain period) to the average registered number of employees for the corresponding period.
- personnel turnover ratio, % – the ratio of the number or number of employees dismissed for absenteeism and other violations of labor discipline, due to their health and at their own will to the average number of employees.
- amount of monetary incentive, UAH.
The result indicator in the study is the labor productivity of the 1st average annual employee, thousand UAH. Research, data processing, analysis, modeling of the proposed factors of three economic entities are carried out on the basis of multiple linear regression over the past seven years in several stages: presentation of the dynamics of the main factors and performance indicators, formulation of a mathematical model, analytical characteristics of the obtained results and forecasting for the next period.
At the first stage of the research, we will conduct an analysis of factors and indicators on the basis of which we will conduct calculations. The dynamics of influencing factors on the performance indicator and the indicator for the last seven years are presented in the table. 5.
For further calculation and bringing the production models to a mathematical form, we denote the factors and the indicator as variables:
X0 is a fictitious factor (must be used when calculating the regression);
X1 – staff stability level, %;
X2 – personnel turnover ratio, %;
X3 – amount of monetary incentive, UAH
Y– labor productivity of the 1st average annual employee, thousand UAH.
Further calculations are carried out using Microsoft Excel spreadsheets, built-
in statistical and mathematical functions, arrays, namely CORREL; MDETERM, MINVERSE, CHIINV, TRANSPOSE, MMULT, FINV and LINEST.
Table 5 Dynamics of the main factors of personnel management and labor productivity of the 1st average annual employee of the researched enterprises, 2016-2022
| Years |
Staff stability level, % |
Staff turnover rate, % | Amount of monetary incentive, UAH. |
Labor productivity of the 1st average annual employee, thousand UAH. |
| SE EF “Stepne” Poltava district | ||||
| 2016 | 55.64 | 36.70 | 1,000 | 149.36 |
| 2017 | 69.57 | 29.10 | 1,040 | 254.53 |
| 2018 | 66.09 | 48.30 | 1,200 | 327.60 |
| 2019 | 49.15 | 51.30 | 1,300 | 319.43 |
| 2020 | 51.97 | 43.50 | 2,500 | 344.57 |
| 2021 | 52.59 | 52.52 | 3,000 | 354.67 |
| 2022 | 56.14 | 56.10 | 3,200 | 353.78 |
| PAC “Zlagoda” of Poltava district | ||||
| 2016 | 58.21 | 35.80 | 950 | 182.24 |
| 2017 | 68.00 | 33.20 | 1,080 | 234.17 |
| 2018 | 67.86 | 38.30 | 1,200 | 262.13 |
| 2019 | 51.28 | 41.20 | 1,350 | 314.40 |
| 2020 | 53.91 | 42.00 | 1,500 | 352.54 |
| 2021 | 50.62 | 42.80 | 2,500 | 367.63 |
| 2022 | 53.39 | 45.31 | 2,800 | 364.88 |
| PE “named after Kalashnyk” of Poltava district | ||||
| 2016 | 61.15 | 34.80 | 1,100 | 223.21 |
| 2017 | 63.64 | 33.90 | 1,300 | 252.05 |
| 2018 | 62.03 | 33.00 | 2,400 | 267.03 |
| 2019 | 62.50 | 42.10 | 2,500 | 295.00 |
| 2020 | 63.00 | 39.40 | 3,500 | 320.04 |
| 2021 | 60.71 | 41.86 | 3,500 | 332.67 |
| 2022 | 60.66 | 43.60 | 4,000 | 352.41 |
Source: developed by the authors
Next, when studying multiple linear models, we check multicollinearity using the algorithm of the Farrar-Glober method. The term “multicollinearity” means that in a multiple regression model, two or more independent variables (factors) are linearly related to each other, or, in other words, have a high degree of correlation. This phenomenon is considered negative in the economic analysis of multiple production regression.
If the calculated value of Xi2calculated is greater than its critical tabular value, then the general multicollinearity of the matrix of factors exists, and if it is the opposite, then it does not exist.
In our study, the general multicollinearity of the matrix of factors:
SE EF “Stepne” of Poltava district does not exist (Xi^2 (3.99)< Xi^2kp (7.81);
PAC “Zlagoda” of Poltava district exists (Xi^2 (8.85)>Xi^2kp(7.81);
PE “named after Kalashnikov” of the Poltava district does not exist (Xi^2(4.86)<Xi^2kp (7.81);
Fisher’s F-test with a reliability of P = 0.95 examines the multicollinearity of each factor with a set of other factors. For this, the critical and calculated values of the F-criterion for each factor are determined. In our case, there is multicollinearity of each factor with a number of other factors.
Next, we compare the calculated values of the t-statistic with its critical value to determine the presence of multicollinearity of a pair of factors.
If the modulus of the estimated value is greater than the critical value, then with a probability of error of 5% it can be concluded that there is multicollinearity of this pair of factors.
In this case, multicollinearity of each factor with a set of other factors does not exist, because the critical value of the t-statistic is greater than its calculated value.
As previously mentioned, the phenomenon of multicollinearity is a negative phenomenon in econometric analysis, and to eliminate it, the method of excluding one of the factors from consideration is used by calculating paired correlation coefficients, but in our case, the task is to analyze in detail which factors affect the performance indicator. Therefore, from this point of view, we will not exclude any of the studied factors from further econometric analysis.
Next, we calculate pairwise correlation coefficients. Paired correlation coefficients indicate the influence of individual factors on the Y indicator, i.e. the labor productivity of the 1st average annual employee of the studied enterprises. As for pairwise correlation coefficients, it is known that the obtained dependencies are evaluated according to the level of indicators of closeness of connection. If their absolute value is less than 0.3, the connection is weak; when it is in the range of 0.3-0.7 – average, if 0.7 – tight and when the absolute value is equal to 1 – then this indicates a practical-functional connection.
Characterizing the paired correlation coefficients, it should be noted that the correlation coefficients are different and each of the factors has an impact on the performance indicator. Also, in models of multiple production functions, partial correlation coefficients are defined, which, like paired ones, characterize the relationship between variables. But unlike even partial coefficients, partial coefficients characterize the closeness of the relationship, provided that other independent variables remain constant (Table 6).
Next, we calculate the transposed matrix, the product of matrices, the coefficients of the equation of multiple production functions to determine the theoretical and forecast values of the performance indicator of the studied enterprises – the labor productivity of the 1st average annual employee.
As a result of calculations, multiple production linear regressions have the form:
- the multiple production function of the influence of the main factors of personnel management on the productivity of the 1st average annual employee of the SE EF “Stepne” State Enterprise, Poltava District, 2016-2022.
Yr = -151.26+3.01Х1+4.81Х2+0.03Х3
- multiple production function of the influence of the main factors of personnel management on the productivity of the 1st average annual employee of PAC “Zlagoda” of Poltava district, 2016-2022.
Yr = -283.17+0.44Х1+13.13Х2+0.02Х3
- multiple production function of the influence of the main factors of personnel management on the labor productivity of the 1st average annual employee of PE “named after Kalashnikov” of the Poltava district, 2016-2022.
Yr =-101.77+3.20Х1+2.85Х2+0.03Х3
Table 6
The results of the study of paired and partial correlation coefficients of the influence of the main factors of personnel management on the labor productivity
of the 1st average annual employee of the studied enterprises, 2016-2022
| Factors |
Effective indicator: Labor productivity of the 1st average annual employee, thousand UAH, Y |
|||
|
Partial correlation coefficients, r12, r13, r23 |
Characteristics of partial correlation coefficients |
Pairwise correlation coefficients, rYX1, rYX2, rYX3 |
Characteristics of paired correlation coefficients | |
| SE EF “Stepne” of Poltava district | ||||
| Staff stability level, %, X1 | 0.38 | The relationship is medium, provided that other independent variables are constant | 0.77 | The connection is close, the direct influence of the factor on the performance indicator |
|
Personnel turnover rate, % X2 |
0.14 | The relationship is weak, provided that other independent variables are constant | 0.72 | The connection is close, the direct influence of the factor on the performance indicator |
|
Amount of monetary incentive, UAH, Х3
|
-0.55 | The relationship is mean inverse, provided that other independent variables are constant | 0.69 |
The connection is average, the direct influence of the factor on the performance indicator |
| PAC “Zlagoda” of Poltava district | ||||
| Staff stability level, %, X1 | 0.64 | The relationship is medium, provided that other independent variables are constant | 0.67 |
The connection is average, the direct influence of the factor on the performance indicator |
|
Personnel turnover rate, % X2 |
-0.15 |
The relationship is weakly inverse, provided that other independent variables are constant |
0.90 | The connection is close, the direct influence of the factor on the performance indicator |
|
Amount of monetary incentive, UAH, Х3
|
-0.73 |
The relationship is close, inverse, provided that other independent variables are constant |
0.81 | The connection is close, the direct influence of the factor on the performance indicator |
| PE “named after Kalashnikov” of the Poltava district | ||||
| Staff stability level, %, X1 | 0.21 | The relationship is weakly direct, provided that other independent variables are constant | 0.84 | The connection is close, the direct influence of the factor on the performance indicator |
|
Personnel turnover rate, % X2 |
0.10 |
The relationship is weak, direct, almost absent, provided that other independent variables are constant |
0.86 | The connection is close, the direct influence of the factor on the performance indicator |
|
Amount of monetary incentive, UAH, Х3
|
-0.74 |
The relationship is close, inverse, provided that other independent variables are constant |
0.97 | The connection is close, the direct influence of the factor on the performance indicator |
Source: developed by the authors
The parameters of the equations were calculated by the method of least squares. Each coefficient of the equation indicates the degree of influence of the corresponding factor on the performance indicator at a fixed position of the rest of the factors, that is, how the performance indicator changes with a change in a separate factor by one unit. The free term of the multiple regression equation has no economic meaning.
We determine the general coefficient of determination, which indicates the closeness of the relationship between the studied factors and the indicator and the variation of the indicator.
- SE EF “Stepne” Poltava district,
Yr = -151.26+3.01Х1+4.81Х2+0.03Х3. The overall coefficient of determination R2=0.67. The general coefficient of determination indicates the average relationship between the investigated factors and the indicator, the variation of the labor productivity of the 1st average annual employee is determined by 66.54% of the investigated factors entered into the correlation model. Factors have an indirect effect on the investigated indicator.
- PAC “Zlagoda” of Poltava district,
Yr = -283.17+0.44Х1+13.13Х2+0.02Х3 The overall coefficient of determination R2=0.83. The general coefficient of determination indicates the average relationship between the investigated factors and the indicator, the variation of the labor productivity of the 1st average annual employee is determined by 82.75% of the investigated factors entered into the correlation model. The factors were selected successfully and have a significant impact on the studied indicator.
- PE “named after Kalashnikov” of the Poltava district,
Yr = -101.77+3.20Х1+2.85Х2+0.03Х3 The overall coefficient of determination R2=0.98. The general coefficient of determination indicates the average relationship between the investigated factors and the indicator, the variation of the labor productivity of the 1st average annual employee is determined by 97.75% of the investigated factors entered into the correlation model. The factors were selected successfully and have a significant impact on the studied indicator.
In order to determine the quality of the calculated models, it is necessary to conduct an analysis of Fisher’s F-criterion. If the calculated value of Fisher’s F-criterion is greater than its tabular value, then the multiple linear econometric model with a reliability of Р = 0.95 can be considered adequate experimental data, and based on the accepted models, economic analysis and forecasting of the effective labor productivity indicator of the 1st average annual employee can be carried out. In our study of the influence of the main factors of personnel management on the productivity of the 1st average annual employee over the past seven years, the estimated value of Fisher’s F-criterion is greater than the tabular value, the model is adequate to the experimental data.
The next stage is a comparative characterization of statistical parameters and coefficients of production linear regressions of the influence of the main factors of personnel management on the productivity of the 1st average annual employee of the studied enterprises using the built-in statistical function LINEST (Table 7).
Table 7 Calculation of statistical parameters and coefficients of production linear regressions of the influence of the main factors of personnel management on the labor productivity of the 1st average annual employee of the studied agricultural enterprises using the built-in statistical function LINEST
| Statistical parameters and coefficients of production linear regressions | а3 | а2 | а1 | а0 | ||
| The multiple of the production function of the influence of the main factors of personnel management on the labor productivity of the 1st average annual employee of the SE EF “Stepne” Poltava District, 2016-2022. Yr=151.26+3.01Х1+4.81Х2+0.03Х3. | ||||||
| 0.03 | 4.81 | 3.01 | -151.26 | |||
| Se ai | 0.03 | 3.75 | 3.99 | 328.44 | ||
| R2→ | 0.67 | 61.40 | no data | no data | ||
| Fp→ | 1.99 | 3.00 | no data | no data | ||
| SSR→ | 22,456.15 | 11,309.80 | no data | no data | ||
| The multiple of the production function of the influence of the main factors of personnel management on the productivity of the 1st average annual employee of PAC “Zlagoda” of Poltava district, 2016-2022. Yr=283.17+0.44Х1+13.13Х2+0.02Х3 | ||||||
| а3 | а2 | а1 | а0 | |||
| 0.02 | 13.13 | 0.44 | -283.17 | |||
| Se ai | 0.04 | 9.50 | 3.74 | 504.54 | ||
| R2→ | 0.83 | 42.44 | no data | no data | ||
| Fp→ | 4.80 | 3.00 | no data | no data | ||
| SSR→ | 25,914.43 | 5,402.75 | no data | no data | ||
| The multiple of the production function of the influence of the main factors of personnel management on the productivity of the 1st average annual employee of the PE “named after Kalashnikov” of the Poltava district, 20162022. Yr=-101.77+3.20Х1+2.85Х2+0.03Х3 | ||||||
| а3 | а2 | а1 | а0 | |||
| 0.03 | 2.85 | 3.20 | -101.77 | |||
| Se ai | 0.01 | 1.52 | 3.86 | 256.98 | ||
| R2→ | 0.98 | 9.89 | no data | no data | ||
| Fp→ | 43.47 | 3.00 | no data | no data | ||
| SSR→ | 12,754.91 | 293.40 | no data | no data | ||
Source: developed by the authors
Therefore, it can be concluded that the use of the built-in statistical function LINEST of Microsoft Excel spreadsheets for automation, optimization of processing and analysis of the influence of the main factors of personnel management on the effective indicator of labor productivity of the 1st average annual employee is an alternative in economic and mathematical modeling and management decision-making.
Next, we forecast the main factors of personnel management and labor productivity of the 1st average annual employee of the three studied enterprises for 2024. The forecast was made for the short-term period of 2024.
SE EF “Stepne” Poltava district: staff stability level 57.30%; staff turnover rate 55.74% (built-in TREND statistical function, accurately calculates factor characteristics in dynamics); the amount of monetary incentive is UAH 5,000. (predetermined using game theory).
PAC “Zlagoda” of Poltava district: staff stability level 53.78%; staff turnover rate
45.13% (built-in TREND statistical function, accurately calculates factor characteristics in dynamics); the amount of monetary incentive is 5,100 UAH. (predetermined using game theory).
PE “named after Kalashnyka” of Poltava district: staff stability level 61.27%; staff turnover rate 42.73% (built-in TREND statistical function, accurately calculates factor characteristics in dynamics); the amount of monetary incentive is UAH 4,900 (predetermined using game theory).
In the studied agricultural enterprises, we observe an increase in the level of staff stability and the amount of monetary incentives and a decrease in the staff turnover rate in the short-term forecast period.
We will graphically present the actual values of the main personnel management factors and the received forecast for 2024 (Fig. 2-4).
Fig. 2. The actual and forecast value of the main factors of personnel management of the SE EF “Stepne” Poltava District, 2016-2022, 2024. Source: developed by the authors
As a result of the predicted factor characteristics, the effective indicator of the labor productivity of the 1st average annual employee of the three studied agricultural enterprises in 2024 is also increasing, but it should be emphasized about the influence of other factors of an external and internal nature and take into account that the data of the study are based on economic and mathematical methods and models.
The actual, theoretical and forecast levels of labor productivity of the 1st average annual employee of the three researched agricultural enterprises, 2016-2022, 2024, are presented in the table. 8.
Graphically, multiple linear regressions of labor productivity of the 1st average annual employee of the studied agricultural enterprises are presented in fig. 5-7, which shows the actual, theoretical and forecast levels of labor productivity of the 1st average annual employee of the studied agricultural enterprises, 2016-2022, 2024.
Fig. 3. The actual and forecast value of the main personnel management factors of PAC “Zlagoda” of Poltava district, 2016-2022, 2024. Source: developed by the authors
Fig. 4. The actual and forecast value of the main personnel management factors of PE “named after Kalashnikov” of Poltava district, 2016-2022, 2024.
Source: developed by the authors
Table 8
Actual, theoretical and forecast levels of labor productivity of the 1st average annual employee of the three researched agricultural enterprises, 2016-2022, 2024
| Years | Labor productivity of the 1st average annual employee, thousand UAH, Y |
Theoretical level of labor productivity of the 1st average annual employee, thousand UAH, Ŷi |
Forecast level of labor productivity of the 1st average annual employee, thousand UAH, Ŷi |
| SE EF “Stepne” Poltava district | |||
| 2016 | 149.36 | 224.94 | |
| 2017 | 254.53 | 231.55 | |
| 2018 | 327.60 | 318.63 | |
| 2019 | 319.43 | 285.39 | |
| 2020 | 344.57 | 295.35 | |
| 2021 | 354.67 | 356.84 | |
| 2022 | 353.78 | 391.24 | |
| 2024 | 451.51 | ||
| PAC “Zlagoda” of Poltava district | |||
| 2016 | 182.24 | 231.17 | |
| 2017 | 234.17 | 203.87 | |
| 2018 | 262.13 | 273.16 | |
| 2019 | 314.40 | 306.99 | |
| 2020 | 352.54 | 321.62 | |
| 2021 | 367.63 | 350.50 | |
| 2022 | 364.88 | 390.66 | |
| 2024 | 434.00 | ||
| PE “named after Kalashnikov” of the Poltava district | |||
| 2016 | 223.21 | 229.04 | |
| 2017 | 252.05 | 241.02 | |
| 2018 | 267.03 | 269.62 | |
| 2019 | 295.00 | 300.34 | |
| 2020 | 320.04 | 327.24 | |
| 2021 | 332.67 | 326.93 | |
| 2022 | 352.41 | 348.21 | |
| 2024 | 377.40 | ||
Source: developed by the authors
Fig. 5. Actual, theoretical, and forecast levels of labor productivity of the 1st average annual employee of the SE EF “Stepne” Poltava district, 2016-2022, 2024.
Source: developed by the authors
Fig.6. Actual, theoretical and forecast levels of labor productivity of the 1st average annual employee of PAC “Zlagoda” of Poltava district, 2016-2022, 2024. Source: developed by the authors
Fig. 7. Actual, theoretical and forecast levels of labor productivity of the 1st average annual employee of PE “named after Kalashnikov” of Poltava district, 2016-2022, 2024. Source: developed by the authors
Conclusions. With the help of game theory, we will determine and analyze the size of the optimal monetary incentive depending on the type of additional payments, using the example of specific socially oriented personnel management of highly adaptive enterprises. In continuation of the study, research, analysis, modeling and forecasting of the impact of the main personnel management factors on the productivity of the 1st average annual employee of three agricultural enterprises, we will conduct a detailed forecasting of the performance indicator taking into account the level of staff stability and the staff turnover rate based on previous statistical data. Research and forecasting will be carried out using linear and non-linear production functions.
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