Application of PROMETHEE Method in Evaluation of Insurance Efficiency in Serbia

– The issue of evaluating the efficiency of insurance based on the methods of multi-criteria analysis is very current, complex and significant. It provides a basis for improving the efficiency of in - surance by applying adequate measures in the future. With this in mind, the paper analyzes the efficiency of insurance in Serbia using the PROMETHEE method. The results obtained from the empirical research of insurance efficiency in Serbia using the PRO - METHEE method show that it was most efficient in 2020. Recently, the efficiency of insurance in Serbia has been increasing continuously. This has been posi - tively influenced by numerous factors: economic cli - mate; living standard; employment; modern concepts of cost, income and profit management; electronic sa - les of insurance products; digitalization of the entire business. The negative impact of the COVID-19 pan - demic on insurance efficiency in Serbia is negligible (compared to other production activities, such as tou - rism and hospitality) and is partly offset by increased sales of insurance products online and infrastructure (property) insurance. There is a growing understan - ding of the importance of insuring against potential risks of all kinds.


Introduction
The importance of evaluating the efficiency of insurance based on the methods of multi-criteria analysis is growing (Beiragh, 2020). Starting from that, the subject of this research paper is the analysis of insurance efficiency in Serbia based on the PROMETHEE method. The goal and purpose of this is to address this issue as complexly as possible using qualitative and especially quantitative methods in order to gain knowledge about the real efficiency of insurance companies in Serbia, as a star-ting point for future improvement by taking appropriate measures. This, among other things, reflects the scientific and professional contribution of this paper.
Lately, there is increasingly rich literature dedicated to evaluating the efficiency of all companies, which includes insurance companies, based on multi-criteria analysis. In this context, the role and importance of the PROMETHEE method is growing. In the relevant literature, there is, as far as we know, no comprehensive work dedicated to the evaluation of insurance efficiency in Serbia using the PROMETHEE method (Kočović, 2010;Lukić, 2016Lukić, , 2018Lukić, , 2021Mandić, 2017;Rakonjac Antić, 2018). This gap should be somewhat filled by this paper, which, among other things, reflects its scientific and professional contribution.
The basic research hypothesis in this paper is based on the fact that continuous analysis and control of critical factors is a prerequisite for improving the efficiency of insurance in Serbia in the future by taking appropriate measures and effectively controlling their implementation. The application of the PROMETHEE method also plays a significant role in this.
The research methodology is based on the application of the AHP and PRO-METHEE methods. In order to make the quantitative analysis of the researched problem as complex as possible, statistical analysis is used to some extent.
For the purpose of researching the problem addressed by this paper using the given methodology, empirical data were collected from the Serbian Business Registers Agency. They have been generated in accordance with the relevant international standards, so there are no restrictions on international comparison.

PROMETHEE method
The PROMETHEE method is based on the comparison of paired alternatives according to each criterion. For each criterion, the decision maker considers a particular function of preference (Brans, 2010(Brans, , 2016Podvezko, 2010;Stanitsas, 2021). The preference can take a value in the range from 0 to 1. Different variants of the PROMETHEE method have been developed (I, II, III, IV, V, VI). There is also a visual interactive modulation of GAIA that represents a graphical interpretation of the PROMETHEE method. The PROMETHEE method is simple, allows partial and complex ranking of alternatives (PROMETHEE I and PROMETHEE II, respectively), and has wide practical application (in banking, investment, medicine, chemistry, trade, tourism, etc.).
where P j (a, b) represents the function of the difference between the evaluation of alternative a in relation to alternative b for each criterion in the interval from 0 to 1. A smaller number of functions indicates the indifference of decision makers. Conversely, values closer to 1 indicate greater preference. □ Step 6: Define the multi-criteria preference index where wj indicates the weight of the criterion. The symbol π (a, b) shows the degree of preference of a in relation to b for all criteria.
π (a, b) ≈ 0 implies a weak preference of a over b. π (a, b) ≈ 1 implies a strong preference of a over b. □ Step 7: Obtain the order of preferences. in this step, the ranking can be performed partially or completely. Partial ranking can be obtained using PROMETHEE I. In case a complete ranking is needed, it includes an additional step by applying PROMETHEE II.
Partial ranking of alternatives (PROMETHEE I): where represents a positive output flow (how many alternatives a dominate over other alternatives), and represents a negative input flow (how many alternatives are preferred by all the other alternatives). An alternative with a high value and a lower value is the best alternative. Preferential ratio and partial rankings are performed as follows: However, not all alternatives are comparable. It is therefore necessary to calculate the net flow in the next step.
(b) Complex ranking of alternatives (PROMETHEE II). The complex ranking of alternatives can avoid incomparability.
where denotes the net flow for each alternative. Relationship preferences are as follows: Thus, all alternatives are capable of being comparable based on the value . The highest value indicates the most desirable alternative. In the calculation procedure, most of the steps are fixed, except for step 5. In this step, the choice of the preference function is arbitrary depending on the characteristics of the criteria and the preference of the decision makers. Special attention is paid to the choice of the preference function because it can affect the final net value.

Preference functions
The PROMETHEE method uses preference functions to define deviations between alternatives for each criterion. The PROMETHEE method uses six preference functions to express the significance of the alternative for each criterion/factor, as well as the difficulty to express the relative importance of each criterion. These functions are: Type I -The usual preference function is a basic type of function that does not contain any parameters and is used very rarely ( Figure 1).
Type II -The U-shape function contains only the indifference threshold ( Figure 2) Parameter q.
Type III -The V-shape function contains only the preference threshold ( Figure 3). It differs from the previous one because the preference is defined as the proportional deviation of the alternatives in the value range from 0 to m.

Parameter p.
Type IV -The Level function contains the indifference threshold n and the preference threshold m.
Type V -The Linear function contains the indifference threshold n and the preference threshold m. It is proportional to the deviation of alternatives in the interval from -n -m to + n + m ( Figure 5).
Parameters p, q. Type VI -The Gaussian function contains only the Gaussian threshold σ and is used less frequently ( Figure 6).

Method of analytic hierarchy process (AHP)
Considering that the weighting coefficients (weights) of the criterion when applying the PROMETHEE method are determined using the AHP method, we will briefly look at its theoretical and methodological characteristics.
The Analytic Hierarchy Process (AHP) method takes place through the following steps (Saaty, 2008):

Measuring insurance efficiency in Serbia based on AHP/ PROMETHEE methods: results and discussion
When measuring the efficiency of insurance in Serbia on the basis of the PRO-METHEE method, the following criteria were used: C1 -number of employees, C2 -assets, C3 -capital, C4 -business (functional) income, C5 -net profit. Alternatives were observed in the following years: A1 -2013, A2 -2014, A3 -2015, A4 -2016, A5 -2017, A6 -2018, A7 -2019 and A8 -2020. Table 1 shows the initial data for measuring the efficiency of insurance in Serbia for the period 2013 -2020. Source: Serbian Business Registers Agency Table 2 shows the statistics of the initial data. The data in the table above show that the values of all observed variables from 2016 were above average. This had a positive effect on the efficiency of insurance in Serbia. Seeing that Asymp. Sig. = .000 < .05, the hypotheithat the differences between the variables (measurements) are equal to zero is rejected, i.e., the hypothesis that the differences between them are statistically significant is accepted. Table 3 shows the correlation matrix of the initial data. The correlation matrix shows that there is a strong correlation between the analyzed variables at the level of statistical significance (Sig. (2-tailed) = .000 < .05), except for the number of employees. Improving the efficiency of insurance through a more efficient management of assets, capital, business (functional) revenues and profits can have a significant impact. In this regard, it is also necessary to significantly improve the efficiency of human resource management through training, career advancement, flexible employment and working hours, and an adequate remuneration system. The sale of insurance products via the Internet also plays a significant role in all this.
The weighting coefficients (weights) of the criteria were determined using the AHP method (Saaty, 2008). They are shown in Table 4 and Figure 7.  Ranked in first place is the criterion of the number of employees. It is followed by the criteria of assets, operating (functional) income, net profit and capital. This indicates that more efficient human capital management can, among other things, significantly influence the achievement of the target insurance efficiency in Serbia. Table 5 shows the initial matrix of the PROMETHEE method.  Table 6 shows the flows of the PROMETHEE method.  Table 7 shows the summary result of the PROMETHEE method -ranking of alternatives.
Note: Author's presentation of results Figure 8 shows the flows of the PROMETHEE method.

Figure 8 Flows
Source: Author's picture The results obtained from the empirical research of insurance efficiency in Serbia in the period 2013 -2020 using the PROMETHEE method show that it has been continuously increasing in recent years. It was the most efficient in 2020. Such a trend of insurance efficiency in Serbia was influenced by numerous macro and micro factors, such as: economic climate; employment; interest rate; exchange rate; inflation; a growing understanding of the importance of insurance against potential risks of all kinds; digitalization of the entire business, etc. The impact of the COVID-19 pande-mic on insurance efficiency in Serbia is negligible. It is largely neutralized by selling insurance products electronically.

Conclusion
Based on the results obtained from the empirical research of insurance efficiency in Serbia in the period 2013 -2020 using the PROMETHEE method, it can be concluded that it has been continuously increasing in recent years. It was the most efficient in 2020. Such a trend of insurance efficiency in Serbia was influenced by numerous macro and micro factors, such as: economic climate; employment; interest rate; exchange rate; inflation; a growing understanding of the importance of insurance against potential risks of all kinds; digitalization of the entire business, etc. The impact of the COVID-19 pandemic on insurance efficiency in Serbia is negligible. It is largely neutralized by selling insurance products electronically.
In order to increase the efficiency of insurance in Serbia in the future, it is necessary to manage human resources, assets, capital, sales of insurance products, and profits as efficiently as possible. The digitalization of the entire business also plays an important role in this.
The application of the PROMETHEE method in analyzing insurance efficiency in Serbia provides more reliable results in relation to the ratio analysis as a basis for future improvements by taking appropriate measures and adequately controlling their implementation. Therefore, it should be used especially in combination with other methods of multi-criteria decision making (TOPSIS, ARAS, AHP, etc.).