The Quality Of Life As A Complex Dynamic Object Of Management

Multilayer model for rating the life quality as a managed object

In solving the first problem, a system approach is used, according to which a three-level model of the integral indicator of quality of life is proposed (Ilyasov, Martynov, Gerasimova, Makarova, & Zakieva, 2017). This model can be represented differently, in the form of a multilayer structure, if moving from vertical to horizontal bonds (Figure 01 ).

The generalized integral indicator “Quality of Life” (the first layer) is formed by three system integral indicators: Quality of living environment ( $J_{\mathrm{1}}$), Quality of life potential ( $J_{\mathrm{2}}$), Level of life ( $J_{\mathrm{3}}$), which form the second layer. Each system indicator has its own mechanism of self-organization, realized in the form of corresponding coefficients of feedbacks $A_{\mathrm{1}}$, $A_{\mathrm{2}}$, $A_{\mathrm{3}}$.

Each system integral indicator is formed by partial integral indicators (the third layer). Thus the system integral indicator “Quality of living environment” is formed by the following partial integral indicators: “Quality of environment” ( $\mathrm{}{x}_{\mathrm{11}}$), “Quality of working life” ( $\mathrm{}{x}_{\mathrm{12}}$), “Quality of social environment” ( $\mathrm{}{x}_{\mathrm{13}}$); the system integral indicator “Quality of the live potential” is formed by “Level of education” ( $\mathrm{}{x}_{\mathrm{21}}),$ “Status” ( $\mathrm{}{x}_{\mathrm{22}}$), “Level of health” ( $\mathrm{}{x}_{\mathrm{23}}$), the system integral indicator “Life level” is formed by “Income level” ( $\mathrm{}{x}_{\mathrm{31}}$), “Quality of housing conditions” ( $\mathrm{}{x}_{\mathrm{32}}$) , “Food quality” ( $\mathrm{}{x}_{\mathrm{33}}$).

Each partial indicator has its own self-organization mechanism, realized by introducing corresponding feedback coefficient $a_{\mathrm{i}\mathrm{1}},a_{\mathrm{i}\mathrm{2}},a_{\mathrm{i}\mathrm{3}},\mathrm{}\mathrm{}i=\overline{\mathrm{1,3}}$.

The generalized integral indicator “Quality of Life” ( $QoL$) is calculated as the weighted sum of the system integral indicators:

$$QoL={\mathrm{\alpha }}_{\mathrm{1}}{J}_{\mathrm{1}}+{\mathrm{\alpha }}_{\mathrm{2}}{J}_{\mathrm{2}}+{\mathrm{\alpha }}_{\mathrm{3}}{J}_{\mathrm{3}},$$

where ${\mathrm{\alpha }}_{\mathrm{1}},\mathrm{}{\mathrm{\alpha }}_{\mathrm{2}},\mathrm{}{\mathrm{\alpha }}_{\mathrm{3}}$ – weight coefficients characterizing the significance of the indicator $J_i$ and are defined by an expert, while $\underset{i=\mathrm{1}}{\overset{\mathrm{3}}{\sum }}{\alpha }_i=\mathrm{1}.$

The system integral indicator $J_i$ is calculated as the result of interaction with other system indicators:

$$\left\{\begin{array}{c}{J}_{\mathrm{1}}=-A_{\mathrm{1}}\left(z_1\right)J_{\mathrm{1}}+{\mathrm{\lambda }}_{\mathrm{12}}{J}_{\mathrm{2}}+{\mathrm{\lambda }}_{\mathrm{13}}{J}_{\mathrm{3}}+J_{\mathrm{10}},\\ J_{\mathrm{2}}={-A_{\mathrm{2}}\left(z_2\right)J_{\mathrm{2}}+\mathrm{\lambda }}_{\mathrm{21}}{J}_{\mathrm{1}}+{\mathrm{\lambda }}_{\mathrm{23}}{J}_{\mathrm{3}}+J_{\mathrm{20}},\\ J_{\mathrm{3}}=-{A_{\mathrm{3}}\left(z_3\right)J}_{\mathrm{3}}{+\mathrm{\lambda }}_{\mathrm{31}}{J}_{\mathrm{1}}+{\mathrm{\lambda }}_{\mathrm{32}}{J}_{\mathrm{2}}+J_{\mathrm{30}},\end{array}\right.$$

where $J_{i\mathrm{0}},\mathrm{}i=\overline{\mathrm{1,3}}$ – initial values of indicators $J_i$, determined by private integral indicators;

${\mathrm{\lambda }}_{ij},\mathrm{}i\ne j$ – weight coefficients characterizing the mutual influence of indicators $J_i$ and are determined by expert modes. If ${\mathrm{\lambda }}_{ij}$=0.05, then it is a weak influence, if ${\mathrm{\lambda }}_{ij}$=0.1, then it is a strong influence;

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$A_i\left(z_i\right)$ – feedback coefficients of system integral indicators, which depend on organizational-administrative control actions $z_i$ at the level of federal management structures.

The initial value of $J_{i\mathrm{0}}$ can be calculated as the weighted sum of the corresponding partial indicators $x_{i\mathrm{1}},\mathrm{}{x}_{i\mathrm{2}},x_{i\mathrm{3}}$:

$$J_{i\mathrm{0}}={\beta }_{i\mathrm{1}}{x}_{i\mathrm{1}}+{\beta }_{i\mathrm{2}}{x}_{i\mathrm{2}}+{\beta }_{i\mathrm{3}}{x}_{i\mathrm{3}},$$

where ${\beta }_{ij}$ – weight coefficients characterizing the degree of significance of partial indicators $x_{i\mathrm{1}},\mathrm{}{x}_{i\mathrm{2}},x_{i\mathrm{3}}$ are determined by expert modes, while $\underset{j=\mathrm{1}}{\overset{\mathrm{3}}{\sum }}{\beta }_{ij}=\mathrm{1}$.

To calculate the partial indicators $x_{i\mathrm{1}},\mathrm{}{x}_{i\mathrm{2}},x_{i\mathrm{3}}$ the system of equations is calculated:

$$\left\{\begin{array}{c}{x}_{i\mathrm{1}}={-a_{i\mathrm{1}}\left(z_{i1}\right)x_{i\mathrm{1}}+k}_{\mathrm{12}}{x}_{i\mathrm{2}}+k_{\mathrm{13}}{x}_{i\mathrm{3}}+u_{i\mathrm{1}},\\ x_{i\mathrm{2}}=-a_{i\mathrm{2}}{\left(z_{i2}\right)x}_{i\mathrm{2}}+k_{\mathrm{21}}{x}_{i\mathrm{1}}+k_{\mathrm{23}}{x}_{i\mathrm{3}}+u_{i\mathrm{2}},\\ x_{i\mathrm{3}}=-a_{i\mathrm{3}}{\left(z_{i3}\right)x}_{i\mathrm{3}}+k_{\mathrm{31}}{x}_{i\mathrm{1}}+k_{\mathrm{32}}{x}_{i\mathrm{2}}+u_{i\mathrm{3}},\end{array}\right.$$

where $k_{ij},\mathrm{}i\ne j$ – weight coefficients characterizing the mutual influence of indicators $x_{i\mathrm{1}},\mathrm{}{x}_{i\mathrm{2}},\mathrm{}{x}_{i\mathrm{3}}$, the numerical values of which are determined by experts;

$a_{ij}\left(z_{ij}\right)$ – feedback coefficients of partial integral indicators, which depend on organizational-administrative control actions $z_{ij}$ at the level of regional management structures;

$u_{i\mathrm{1}},\mathrm{}{u}_{i\mathrm{2}},\mathrm{}{u}_{i\mathrm{3}}$ – financial-economic control actions.

Thus, the multilayer model of the quality of life as a complex multi-connected dynamic object is proposed. The features of the proposed model are as follows. First, each layer is a multi-connected system, which significantly complicates the analysis of the influence of the lower-level indicators on the integral indicator. Secondly, each partial and each system integral indicator has a self-organization mechanism realized by the introduction of feedbacks. Thirdly, all components of the generalized integral indicator vary in time, which makes it necessary to consider the quality of life as a dynamic object.

Two-channel quality of life control system

In solving the second problem – the development of the quality of life control system – the principle of feedback is applied. To manage the quality of life as a complex dynamic object developed a two-channel system (Figure 02 ).

According to the feedback principle, the actual (current) value of the quality of life ( $QoL$) is measured at each time and compared with the target value ( ${QoL}^0$). The social standards of life quality and living standards developed by government departments should be considered as a target value of the quality of life indicator.

As a result of comparing the current and target values of the quality of life indicator, a deviation (control error) $\mathrm{\epsilon }={QoL}^0-QoL$ is calculated (block “Quality of life analysis”). There are two components of the control error: error $\mathrm{}{\mathrm{\epsilon }}_{\mathrm{u}}$, associated with the financing of the social system, and error $\mathrm{}{\mathrm{\epsilon }}_{\mathrm{z}}$, associated with organizational changes in the social system, the elimination of which requires financial-economic impact on partial indicators and organizational-administrative measures.

At the output of the block “Decision-making algorithms” formed two channels of control: organizational-administrative, which reduces the error $\mathrm{}{\mathrm{\epsilon }}_{\mathrm{z}}$ and financial-economic, which reduces the error $\mathrm{}{\mathrm{\epsilon }}_{\mathrm{u}}$.

To reduce the organizational-administrative components of control error $\mathrm{}{\mathrm{\epsilon }}_{\mathrm{z}}$ the management decisions Z (the first control channel) are taken for changing organizational structures, for example, by changing the feedback coefficients $A_{\mathrm{1}}$, $A_{\mathrm{2}}$, $A_{\mathrm{3}}$ responsible for stabilizing the system integral indicators at the federal level, as well as the feedback coefficients $a_{ij}$, responsible for stabilizing the partial integral indicators at the regional level.

To reduce the financial-economic component of error $\mathrm{}{\mathrm{\epsilon }}_{\mathrm{u}}$ the management decisions U (the second control channel) are taken to change the amount of financial resources invested in the growth of partial integral indicators.

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Thus, the two-channel quality of life control system is developed. The first channel is intended for the implementation of organizational-administrative management by changing the structure of the management object, and the second channel – for the implementation of financial-economic management through the redistribution of additional allocated financial resources.

Simulation results

On the basis of the developed models the efficiency of control actions on the first and second control channels is estimated.

When assessing the efficiency of control actions on the second channel (U), it is first necessary to determine the so-called screening parameters, that are most sensitive to the perception of control actions.

Let’s define the most sensitive indicator for the partial integral indicator “Quality of health”. The structure of this indicator was suggested by the authors of this article (Ilyasov et al., 2017). Let’s analyze the impact of control actions in the form of increasing allocated resources on lower-level indicators, such as “Level of medical personnel qualification”, “Level of equipment, technologies and drug supply in medical institutions” and others. The results of the analysis made it possible to reveal that the most sensitive to the perception of control actions is the partial indicator “Level of medical personnel qualification”. If this indicator increased by 5%, the integral indicator “Quality of health” in this model increased by 1.27%.

Similarly, the most sensitive indicators are determined for other partial integral indicators. Thus, for the indicator “Quality of environment” the most sensitive indicator is “Air quality”, for the indicator “Quality of working life” – “Quality of labour potential”, for the indicator “Quality of social environment” – “Security of living”, for the indicator “Level of education” – “Supply with educational facilities”, for the indicator “Status” – “Social status”, for the indicator “Income level” – “Wages”, for the indicator “Quality of housing conditions” – “Provision of comfortable housing”, for the indicator “Food quality” – “Healthy food index”.

After determining the screening parameters, the efficiency of control actions on the second channel (U) was evaluated. In the course of the research it was found that with an increase in the amount of financial resources invested in the growth of each of the screening parameters of the partial integral indicators by 1%, the generalized integral indicator ( $QoL$) increased by 0.85%.

The estimation of efficiency of control actions on the first control channel (Z) is carried out. The results of estimation showed, that with a decrease the feedback coefficients of the partial indicators by 1%, at constant values of other parameters, the generalized integral indicator increased by 1.1%; with a decrease the feedback coefficients of the system integral indicators by 1%, the $QoL$ increased by 1%; with a simultaneous decrease the feedback coefficients of partial and system integral indicators by 1%, the $QoL$ increased by 2.2%.

In the case of simultaneous impact through two control channels, i.e. with an increase in the amount of financial resources invested in the growth of each partial indicator by 1%, and a decrease the feedback coefficients of partial and system integral indicators by 1%, the value of the quality of life indicator increased by 3.22%.

Thus, for the greatest efficiency is achieved with the simultaneous impact on the two control channels.