Radojko Lukic, PhD Analysis Of The Efficiency Of Insurance Companies In Serbia DOI: https://doi.org/10.55707/eb.v10i2.128 Original Scientific article UDK 368.03:005.336.1(497.11) KEYWORDS : efficiency, insurance companies, Serbia, DEA Super-Radial models ABSTRACT - It is very challenging to investigate the efficiency of insurance companies in all countries ba- sed on the DEA (Data Envelopment Analysis) model. This is also the case with Serbia. This paper analyzes the efficiency of insurance companies in Serbia ba- sed on the DEA Super-Radial model. According to the results of Super-Radial (Super-CCR-I and Super -CCR-O) in 2021, no insurance company in Serbia was efficient. In the same year, according to the Su- per-Radial (Super-BCC-I) results, only two insuran- ce companies in Serbia were efficient: DUNAV OSI- GURANJE and ĐENERALI OSIGURANJE SERBIA. According to the results of Super-Radial (Super-B- CC-O) in 2021 in Serbia, only two insurance compa- nies were efficient: DDOR RE and SAVA ŽIVOTNO. Other insurance companies were ineffective. In order to improve the efficiency of insurance companies in Serbia, it is necessary, in addition to efficient adap- ting to a dynamic business environment, managing assets, capital, human resources, sales of insurance products and profits as efficiently as possible. Digi- talization of the entire business plays a significant role in this. It significantly mitigated the impact of the Covid-19 pandemic on the efficiency of insurance companies in Serbia. Izvirni znanstveni članek UDK 368.03:005.336.1(497.11) KLJUČNE BESEDE: učinkovitost, zavarovalnice, Srbija, DEA Super-Radial modeli POVZETEK: Raziskovanje učinkovitosti zavaroval- nic v državah po modelu DEA (Data Envelopment Analysis) je zelo zahtevno, enako velja tudi za Srbi- jo. Prispevek analizira učinkovitost zavarovalnic v Srbiji na podlagi modela DEA Super-Radial. Glede na rezultate Super-Radial (Super-CCR-I in Super -CCR-O) v letu 2021 nobena zavarovalnica v Srbiji ni bila učinkovita. Istega leta sta bili po rezultatih Super-Radiala (Super-BCC-I) v Srbiji uspešni le dve zavarovalnici: DUNAV OSIGURANJE in ĐENE- RALI OSIGURANJE SRBIJA. Po rezultatih Super -Radiala (Super-BCC-O) sta bili leta 2021 v Srbiji učinkoviti le dve zavarovalnici: DDOR RE in SAVA ŽIVOTNO. Ostale zavarovalnice so bile neučinkovi- te. Za izboljšanje učinkovitosti zavarovalnic v Srbiji je potrebno poleg učinkovitega prilagajanja dinamič- nemu poslovnemu okolju čim bolj učinkovito uprav- ljati s sredstvi, kapitalom, človeškimi viri, prodajo zavarovalnih produktov in dobičkom, pri čemer ima pomembno vlogo digitalizacija celotnega poslovanja, ki je bistveno omilila vpliv pandemije Covid-19 na učinkovitost zavarovalnic v Srbiji. 1 Introduction It is a very challenging problem to evaluate the efficiency of insurance companies based on the DEA (data envelopment analysis) model. Considering that, the subject of research in this paper is the analysis of the efficiency of insurance companies in Serbia based on the DEA Super-Radial method. The aim and purpose of this is to see as fully as possible the efficiency of insurance companies in Serbia with the aim of future im- Prejeto/Received: 11. 5. 2023 Sprejeto/Accepted: 17. 10. 2023 Besedilo/Text © 2023 Avtor(ji)/The Author(s) To delo je objavljeno pod licenco CC BY Priznanje avtorstva 4.0 Mednarodna. / This work is published under a CC BY Attribution 4.0 International license. https://creativecommons.org/licenses/by/4.0/ Analysis Of The Efficiency Of Insurance ... 48 Revija za ekonomske in poslovne vede (2, 2023) provement by applying relevant measures. This reflects the scientific and professional contribution of the paper. The literature devoted to the development and application of DEA models is very rich (Andersen & Petersen, 1993; Banker idr., 1984; Chen idr., 2021; Chang & Wang, 2020; Guo & Cai, 2020; Lee idr., 2011; Lin, 2020; Pendharkar, 2021; Tone, 2002; Dobrovič idr., 2021; Podinovski & Bouzdine-Chameeva, 2021; Rostamzadeh idr., 2021; Fenyves & Tarnóczi, 2020; Amini idr., 2019; Tsai idr., 2021; Sıcakyuz, 2023). Likewise, an increasing number of works are devoted to the specifics of the analysis of the efficiency of insurance companies based on the DEA model (Kočović idr., 2010; Lukić, 2010, 2016, 2018a, 2018b, 2021a, 2021b, 2021c, 2021d, 2021e, 2022a, 2022b, 2023; Lukic & Hadrovic Zekic, 2019; Lukic idr., 2017, 2020; Mandić idr., 2017; Ra- konjac-Antić, 2018). In this paper, it serves as a theoretical-methodological and em- pirical basis for evaluating the efficiency of insurance companies in Serbia using the DEA Super-Radial model. Continuous monitoring of the efficiency of insurance companies, in this specific case in Serbia, is the basic assumption for improvement in the future by applying relevant measures. This reflects the primary research hypothesis in this paper. The research methodology of the given hypothesis is based on the application of the DEA Super-Radial model. The application of the DEA Super-Radial model has a significant role in understan- ding the real situation regarding the efficiency of insurance companies in Serbia. Its application clearly indicates which insurance companies are efficient and which are not, and which measures should be taken in order to transform inefficient ones into efficient insurance companies. The necessary empirical data for the research of the problem treated in this work were collected from the National Bank of Serbia. They have been generated in accor- dance with the relevant international standards. In terms of international comparison, there are no restrictions. 2 Methodology The investigation of the efficiency of insurance companies in Serbia in this paper is based on the application of the DEA Super-Radial model. Considering that, we will briefly point out its methodological characteristics. Suppose we have n DMUs {DMU j (j = 1, 2, ..., n)}. Each consumes a set of m inputs, x ij (i =1, 2, ..., m), in the production of a set of s outputs, Y rj (r =1, ..., s). Ba- sed on the VRS (variable return to scale) model (Banker idr., 1984), the input-oriented VRS super-efficient efficiency measurement model can be expressed as: 49 Radojko Lukic, PhD: Analysis Of The Efficiency Of Insurance ... 3 results and discussion When analyzing the efficiency of insurance companies in Serbia based on the DEA Super-Radial model of input and output orientation, with constant and varia- ble returns, the following elements were used as input elements: total assets, capi- tal and salary costs, salary compensation and other personal expenses; and as output elements: business (functional) income and net profit. DMU units are the observed insurance companies in Serbia that operated in 2021. Table 1 shows the input/output elements for 2021. 50 Revija za ekonomske in poslovne vede (2, 2023) Table 1 Input / Output data DMU (I) Total assets (I) Capital (I) Salary expenses, salary compensation and other personal expenses (O) Business (functional) income (O)Net profit AMS 8164 2921 105 4255 522 DDOR NEW USA 23713 7825 269 12376 703 DDOR RE 1293 667 16 14 3 DUNA V IN- SURANCE 60772 18501 1017 27833 2519 DANUBE-RE 10053 2520 77 2325 351 GENERALI IN- SURANCE OF SERBIA 74708 17243 493 19495 3393 GENERALI RE- OSIGURANJE SERBIA 5167 773 32 187 132 GLOBOS IN- SURANCE 4750 1165 53 3077 382 GRA VES 37212 10171 143 4447 751 MERKUR IN- SURANCE 5340 686 43 773 48 MILLENNIUM 6740 2048 66 3310 284 OTP INSURANCE 1860 677 684 100 99 SA V A LIFELESS 4617 1435 1664 155 65 ALL LIFE 1545 535 545 31 3 SOGAZ 1679 947 169 61 43 THREE-HEADED 11642 3106 5276 271 481 UNIQA NON-LIFE INSURANCE 6754 1368 2725 254 19 UNIQA LIFE IN- SURANCE 11643 1024 in 1823 95 59 WINER RE 8041 880 1021 55 62 WINER STADTSCHE 48338 6580 9401 322 1178 IN TOTAL 334043 81084 101409 3669 11108 Note: Data are expressed in millions of dinars. I - input, O - output Source: National Bank of Serbia Table 2 shows the statistics of input / output elements. (In this paper, all calculati- ons and results are the author's.) 51 Radojko Lukic, PhD: Analysis Of The Efficiency Of Insurance ... Table 2 Statistics of Input / Output elements Statistics Total assets Capital Salary expen- ses, salary compensation and other perso- nal expenses Business (functional) income Net gain N Valid 20 20 20 20 20 Missing 0 0 0 0 0 Mean 16701.5500 4053.6000 1281.1000 3971.8000 554.8500 Median 7397.5000 1401.5000 381.0000 296.5000 208.0000 Std. Deviation 21377.83981 5418.97381 2295.78288 7458.75665 889.80975 The minimum 1293.00 535.00 16.00 14.00 3.00 Maximum 74708.00 18501.00 9401.00 27833.00 3393.00 Correlations Total assets Capital Salary expen- ses, salary com- pensation and other personal expenses Business (functional) income Net gain Total assets Pearson Cor- relation 1 .951 ** .278 .793 ** .948 ** Sig. (2-tailed) .000 .236 .000 .000 N 20 20 20 20 20 Capital Pearson Cor- relation .951 ** 1 .067 .917 ** .943 ** Sig. (2-tailed) .000 .779 .000 .000 N 20 20 20 20 20 Salary expen- ses, salary compensation and other per- sonal expenses Pearson Cor- relation .278 .067 1 -.163 .115 Sig. (2-tailed) .236 .779 .492 .629 N 20 20 20 20 20 Business (functional) income Pearson Cor- relation .793 ** .917 ** -.163 1 .872 ** Sig. (2-tailed) .000 .000 .492 .000 N 20 20 20 20 20 Net gain Pearson Cor- relation .948 ** .943 ** .115 .872 ** 1 Sig. (2-tailed) .000 .000 .629 .000 N 20 20 20 20 20 **. Correlation is significant at the 0.01 level (2-tailed). In this case, there is therefore a strong correlation between the observed variables at the level of statistical significance, except for salary expenses, salary allowances and other personal expenses. 52 Revija za ekonomske in poslovne vede (2, 2023) Table 3 and figures 1 and 2 show the results of the application of the DEA Super -Radial model of input and output orientation with constant return in the assessment of the efficiency of insurance companies in Serbia. Table 3 Efficiency of insurance companies in Serbia: Super-Radial (Super-CCR-I) Returns to Scale = Constant and Super-Radial (Super-CCR-O) Returns to Scale = Constant Model Name = DEA-Solver LV(V7)/ Super-Ra- dial(Super-CCR-I) Returns to Scale = Constant (0 =< Sum of Lambda < Infinity) Model Name = DEA-Solver LV(V7)/ Super-Ra- dial(Super-CCR -O) Returns to Sca- le = Constant (0 =< Sum of Lambda < Infinity) No. DMU Score Rank Score Rank 1 AMS 0.804568 5 0.804568 5 2 DDOR NEW USA 0.805675 4 0.805675 4 3 DDOR RE 2.89E-02 20 2.89E-02 20 4 DUNA V INSURANCE 0.707005 7 0.707005 7 5 DANUBE-RE 0.632454 9 0.632454 9 6 GENERALI OSIGURANJE SERBIA 0.954881 2 0.954881 2 7 GENERALI REOSIGURANJE SERBIA 0.572317 10 0.572317 10 8 GLOBOS INSURANCE 1.828092 1 1.828092 1 9 GRA VES 0.728646 6 0.728646 6 10 MERKUR INSURANCE 0.426632 13 0.426632 13 11 MILLENNIUM 0.863838 3 0.863838 3 12 OTP INSURANCE 0.661839 8 0.661839 8 13 SA V A LIFELESS 0.175059 17 0.175059 17 14 ALL LIFE 3.10E-02 19 3.10E-02 19 15 SOGAZ 0.318455 14 0.318455 14 16 THREE-HEADED 0.513745 12 0.513745 12 17 UNIQA NON-LIFE INSURANCE 7.03E-02 18 7.03E-02 18 18 UNIQA LIFE INSURANCE 0.175717 16 0.175717 16 19 WINER RE 0.214868 15 0.214868 15 20 WINER STADTSCHE 0.545987 11 0.545987 11 SD 0.408445 0.408445 Maximum 1.828092 1.828092 The minimum 0.02885 0.02885 Average of scores = 0.552995 0.552995 No. of efficient DMUs = 0 0 No. of inefficient DMUs = 20 20 No. of over iteration DMUs = 0 0 53 Radojko Lukic, PhD: Analysis Of The Efficiency Of Insurance ... Figure 1 Super-Radial (Super-CCR-I) Source: Author's picture 54 Revija za ekonomske in poslovne vede (2, 2023) Figure 2 Super-Radial (Super-CCR-O) Source: Author's picture A DMU unit is considered efficient if the score value is equal to one. If, however, the score value is greater or less than one, the DMU unit is inefficient. The score value of the DMU unit – AMS in both input and output orientation models with constant yield (CCR-I and CCR-O) – is 0.804568. The given DMU unit is 80% efficient and 20% inefficient. The analysis of results is similar for other DMU units. According to the results of the Super-Radial (Super-CCR-I and Super-CCR-O) model in 2021, no insurance company in Serbia was efficient. 55 Radojko Lukic, PhD: Analysis Of The Efficiency Of Insurance ... Table 4 and figures 3 and 4 show the results of applying the DEA Super-Radial model of input and output orientation with variable yield in the evaluation of the effi- ciency of insurance companies in Serbia. Table 4 Efficiency of insurance companies in Serbia: Super-Radial(Super-BCC-I) Returns to Scale = Variable and Super-Radial(Super-BCC-O) Returns to Scale = Variable Model Name = DE- A-Solver LV(V7)/ Super-Radial(Su- per-BCC-I) Returns to Scale = Variable (Sum of Lambda = 1) Model Name = DEA-Solver LV(V7)/ Super -Radial(Super-B- CC-O) Returns to Scale = Variable (Sum of Lambda = 1) No. DMU Score Rank Score Rank 1 AMS 1.004944 8 1.00316 8 2 DDOR NEW USA 1.384294 3 1.321771 7 3 DDOR RE 3.517881 1 1 9 4 DUNA V INSURANCE 1 9 1.58597 5 5 DANUBE-RE 0.649006 16 0.642579 16 6 GENERALI OSIGURANJE SERBIA 1 9 2.325551 3 7 GENERALI REOSIGURANJE SERBIA 1.069234 7 1.413699 6 8 GLOBOS INSURANCE 1.907679 2 2.562415 2 9 GRA VES 0.747708 14 0.752591 14 10 MERKUR INSURANCE 1.143267 6 4.539957 1 11 MILLENNIUM 0.885033 12 0.910175 11 12 OTP INSURANCE 1.168235 5 1.854022 4 13 SA V A LIFELESS 0.438112 19 0.176163 19 14 ALL LIFE 1.247512 4 1 9 15 SOGAZ 0.948227 11 0.812396 13 16 THREE-HEADED 0.605582 17 0.708778 15 17 UNIQA NON-LIFE INSURANCE 0.424346 20 7.54E-02 20 18 UNIQA LIFE INSURANCE 0.603928 18 0.196513 18 19 WINER RE 0.70712 15 0.286075 17 20 WINER STADTSCHE 0.823016 13 0.843784 12 SD 0.656669 1.00754 Maximum 3.517881 4.539957 The minimum 0.424346 0.075441 Average of scores = 1.063756 1.200552 No. of efficient DMUs = 2 2 No. of inefficient DMUs = 18 18 No. of over iteration DMUs = 0 0 56 Revija za ekonomske in poslovne vede (2, 2023) Figure 3 Super-radial (Super-BCC-1) Source: Author's picture 57 Radojko Lukic, PhD: Analysis Of The Efficiency Of Insurance ... Figure 4 Super-Radial (Super-BCC-O) Source: Author's picture According to the results of Super-Radial (Super-BCC-I) in Serbia in 2021, only two insurance companies were efficient: DUNA V OSIGURANJE and ĐENERALI OSIGURANJE SERBIA. Other insurance companies were ineffective. The same is the case with the results of applying Super-Radial (Super-BCC-O). In the specific case, according to this method in Serbia in 2021, only two insurance companies were effective: DDOR RE and SA V A ŽIVOTNO. Other insurance companies were ine- ffective. 58 Revija za ekonomske in poslovne vede (2, 2023) The projection of the input / output element shows the percentage deviation of the realized values from the projected values. Table 5 shows, for the sake of illustration, the projection of input / output elements only for Super-Radial (Super-BCC-O). The same is true for other Super-Radial models. Table 5 Projection of Input / Output elements: Super-Radial (Super-BCC-O) Model Name = DEA-Solver LV(V7)/ Super-Radial(Super-BCC-O) Returns to Scale = V ariable (Sum of Lambda = 1) (I) Total assets ((I) Capital I) Salary expenses, salary compensation and other personal expenses (O) Business (functio- nal) income (O)Net profit No. DMU Score Projecti- on Chan- ge(%) Projecti- on Chan- ge(%) Projecti- on Chan- ge(%) Projecti- on Change(%) Projecti- on Chan- ge(%) 1 AMS 1.00316 8164 0.00% 2089.257 -28.47% 93.61905 -10.84% 4241.597 -0.31% 520.3558 -0.31% 2 DDOR NEW USA 1.321771 23713 0.00% 6228.624 -20.40% 269 0.00% 9363.198 -24.34% 1154.806 64.27% 3 DDOR RE 1 1293 0.00% 667 0.00% 16 0.00% 14 0.00% 3.000321 0.01% 4 DUNA V INSURAN- CE 1.58597 60772 0.00% 14669.23 -20.71% 431.7849 -57.54% 17549.51 -36.95% 2657.872 5.51% 5 DANUBE -RE 0.642579 8565.891 -14.79% 2041.982 -18.97% 77 0.00% 3972.527 70.86% 546.2364 55.62% 6 GENERALI OSIGU- RANJE SERBIA 2.325551 46646.78 -37.56% 13506.81 -21.67% 493 0.00% 13812.1 -29.15% 1459.009 -57.00% 7 GENERALI REOSI- GURANJE SERBIA 1.413699 3271.886 -36.68% 773 0.00% 32 0.00% 869.8802 365.18% 93.37206 -29.26% 8 GLOBOS INSURAN- CE 2.562415 4750 0.00% 1165 0.00% 53 0.00% 1200.82 -60.97% 149.0781 -60.97% 9 GRA VES 0.752591 19059.59 -48.78% 4453.682 -56.21% 143 0.00% 6435.227 44.71% 997.8864 32.87% 10 MERKUR INSURAN- CE 4.539957 1480.41 -72.28% 686 0.00% 43 0.00% 170.2659 -77.97% 22.23564 -53.68% 11 MIL- LENNIUM 0.910175 5891.292 -12.59% 1565,833 -23.54% 66 0.00% 3636.662 9.87% 401.3194 41.31% 12 OTP IN- SURANCE 1.854022 1860 0.00% 677 0.00% 246.2049 -64.01% 428.5414 328.54% 53.39741 -46.06% 13 S AVA LIFELESS 0.176163 4617 0.00% 1142.538 -20.38% 82.0282 -95.07% 2940.014 999.90% 368,977 467.66% 14 ALL LIFE 1 1544.974 0.00% 535 0.00% 544.9731 0.00% 31 0.00% 3.000067 0.00% 15 SOGAZ 0.812396 1679 0.00% 706.4799 -25.40% 169 0.00% 262.3746 330.12% 52.92983 23.09% 16 THREE-HE- ADED 0.708778 11642 0.00% 2748.944 -11.50% 96.34715 -98.17% 4694.44 999.90% 678.6324 41.09% 17 UNIQA NON-LIFE INSURAN- CE 7.54E-02 5406.003 -19.96% 1368 0.00% 64.28819 -97.64% 3366.886 999.90% 407.0237 999.90% 18 UNIQA LIFE IN- SURANCE 0.196513 3915.001 -66.37% 1024 0.00% 235.302 -87.09% 2216.883 999.90% 300.2345 408.87% 19 WINER RE 0.286075 3062.214 -61.92% 880 0.00% 421.4988 -58.72% 1338.423 999.90% 216.7263 249.56% 20 WINER STADTSCHE 0.843784 28311.55 -41.43% 6580 0.00% 201.1901 -97.86% 8606.511 999.90% 1396.092 18.51% 59 Radojko Lukic, PhD: Analysis Of The Efficiency Of Insurance ... In the specific case, in order to improve efficiency (i.e., equalize the realized values of input/output elements with the projected ones) it is necessary, for example, for the DMU unit DUNA V OSIGURANJE to reduce capital by 20.71%; salary expenses, salary compensation and other personal expenses by 57.54%; business (functional) revenues by 36.95%; and increase net profit by 5.51%. The analysis of the projection of input/output elements is similar for the other DMU units observed. Slack shows how to transform inefficient DMU units into efficient ones. In Table 6, for the sake of illustration, slack is shown only for the Super-Radial (Super-BCC-O) model. The analysis is similar for the other Super-Radial models. Table 6 Slack: Super-Radial(Super-BCC-O) Returns to Scale = Variable Model Name = DEA-Solver LV(V7)/ Super-Radial(Super-BCC-O) Returns to Scale = Variable (Sum of Lambda = 1) Excess Excess Excess Shortage Shortage No. DMU Score Total assets Capital salary expenses, wage compensation and other personal expenses Business (functi- onal) in- come Net gain S-(1) S-(2) S-(3) S+(1) S+(2) 1 AMS 1.00316 0 831.7433 11.38095 0 0 2 DDOR NEW USA 1.321771 0 1596.376 0 0 622.9437 3 DDOR RE 1 0 0 0 0 3.21E-04 4 DUNA V INSURANCE 1.58597 0 3831.767 585.2151 0 1069.57 5 DANUBE-RE 0.642579 1487.109 478.0182 0 354.2949 0 6 GENERALI OSIGURANJE SERBIA 2.325551 28061.22 3736.188 0 5429.143 0 7 GENERALI REOSIGURA- NJE SERBIA 1.413699 1895.114 0 0 737.6031 0 8 GLOBOS INSURANCE 2.562415 0 0 0 0 0 9 GRA VES 0.752591 18152.41 5717.318 0 526.305 0 10 MERKUR INSURANCE 4.539957 3859.59 0 0 0 11.66285 11 MILLENNIUM 0.910175 848.7083 482.1667 0 0 89.29164 12 OTP INSURANCE 1.854022 0 0 437.7951 374.6046 0 13 SA V A LIFELESS 0.176163 0 292.4618 1581.972 2060.146 0 14 ALL LIFE 1 2.57E-02 0 2.69E-02 0 6.67E-05 15 SOGAZ 0.812396 0 240.5201 0 187.2881 0 16 THREE-HEADED 0.708778 0 357.0557 5179.653 4312.092 0 17 UNIQA NON-LIFE IN- SURANCE 7.54E-02 1347.997 0 2660.712 0 155.17 18 UNIQA LIFE INSURANCE 0.196513 7727.999 0 1587.698 1733.454 0 19 WINER RE 0.286075 4978.786 0 599.5012 1146.166 0 20 WINER STADTSCHE 0.843784 20026.45 0 9199.81 8224.896 0 Slack: Super-Radial (Super-BCC-O) Returns to Scale = Variable So, for example, in order to transform the inefficient DMU unit DUNA V OSI- GURANJE into an efficient DMU unit, the capital and salary costs should be reduced by 3,831.767 monetary units, salary compensation and other personal expenses by 585.2151 monetary units, and the net profit increased by 1,069.57 monetary units. The analysis is similar for the other DMU units observed. 60 Revija za ekonomske in poslovne vede (2, 2023) All in all, in order to improve the efficiency of insurance companies in Serbia, it is necessary, in addition to efficiently adapting to the business environment, to manage assets, capital, human resources, sales of insurance products, and profits as efficiently as possible. The digitalization of the entire business plays a significant role in this. The increased digitalization of business significantly mitigated the impact of the CO- VID-19 pandemic on the efficiency of insurance companies in Serbia. 4 Conclusion Based on the results obtained from the application of the DEA Super-Radial model in the evaluation of the efficiency of insurance companies in Serbia, the following can be concluded: According to the results of the Super-Radial (Super-CCR-I and Super -CCR-O) model, no insurance company was efficient in Serbia in 2021. According to the results of the Super-Radial (Super-BCC-I) model in Serbia in 2021, only two insurance companies were efficient: DUNA V OSIGURANJE and ĐENERALI OSI- GURANJE SERBIA. According to the results of the Super-Radial (Super-BCC-O) model in Serbia in 2021, only two insurance companies were efficient: DDOR RE and SA V A ŽIVOTNO. Other insurance companies were inefficient. In the specific case, in order to improve the efficiency of insurance companies in Serbia, it is necessary, in addition to efficiently adapting to the business environment, to manage assets, capital, human resources, sales of insurance products, and profits as efficiently as possible. The digitalization of the entire business plays a significant role in this. It significantly mitigated the impact of the COVID-19 pandemic on the efficiency of insurance companies in Serbia. Dr. Radojko Lukic Analiza učinkovitosti zavarovalnic v Srbiji Raziskovanje učinkovitosti zavarovalnic v državah po modelu DEA je zelo zahtevno, enako velja tudi za Srbijo. Prispevek analizira učinkovitost zavarovalnic v Srbiji na podlagi modela DEA Super-Radial. Glede na rezultate Super-Radial (Super-CCR-I in Super-CCR-O) v letu 2021 nobena zavarovalnica v Srbiji ni bila učinkovita. Istega leta sta bili po rezultatih Super-Radiala (Super-BCC-I) v Srbiji uspešni le dve zavarovalnici: DUNAV OSIGURANJE in ĐENERALI OSIGURANJE SRBIJA. Po rezultatih Super-Ra- diala (Super-BCC-O) sta bili leta 2021 v Srbiji učinkoviti le dve zavarovalnici: DDOR RE in SAVA ŽIVOTNO, medtem ko so bile ostale zavarovalnice neučinkovite. Za izbolj- šanje učinkovitosti zavarovalnic v Srbiji je potrebno poleg učinkovitega prilagajanja dinamičnemu poslovnemu okolju čim bolj učinkovito upravljati s sredstvi, kapitalom, človeškimi viri, prodajo zavarovalnih produktov in dobičkom, pri čemer ima pomembno 61 Radojko Lukic, PhD: Analysis Of The Efficiency Of Insurance ... vlogo digitalizacija celotnega poslovanja, ki je bistveno omilila vpliv pandemije Co- vid-19 na učinkovitost zavarovalnic v Srbiji. Ocenjevanje učinkovitosti zavarovalnic po modelu DEA je zelo zahteven problem. Glede na to je predmet raziskave v tem prispevku analiza učinkovitosti zavarovalnic v Srbiji na podlagi metode DEA Super-Radial. Cilj in namen te raziskave je čim bolj celovit pregled nad učinkovitostjo zavarovalnic v Srbiji z namenom izboljšanja v priho- dnosti z uporabo ustreznih ukrepov, kar odraža znanstveni in strokovni prispevek tega prispevka. Na razpolago je številna literatura, posvečena razvoju in uporabi modelov DEA, poleg tega pa je vse več del posvečenih posebnostim analize učinkovitosti zavarovalnic po modelu DEA. V tem prispevku služi kot teoretično-metodološka in empirična podlaga za oceno učinkovitosti zavarovalnic v Srbiji z uporabo modela DEA Super-Radial. Stalno spremljanje učinkovitosti zavarovalnic, v konkretnem primeru v Srbiji, je osnovna predpostavka za izboljšanje v prihodnosti z uporabo ustreznih ukrepov. To od- raža primarno raziskovalno hipotezo v tem dokumentu. Raziskovalna metodologija po- dane hipoteze temelji na uporabi modela DEA Super-Radial. Uporaba modela DEA Super-Radial ima pomembno vlogo pri razumevanju de- janskega stanja glede učinkovitosti zavarovalnic v Srbiji. Njegova uporaba jasno kaže, katere zavarovalnice so učinkovite in katere ne ter katere ukrepe je treba sprejeti, da se neučinkovite preoblikujejo v učinkovite zavarovalnice. Potrebne empirične podatke za raziskavo obravnavanega problema v tem delu smo zbrali pri Narodni banki Srbije. Pripravljeni so v skladu z ustreznimi mednarodnimi standardi. Z vidika mednarodne primerjave ni nobenih omejitev. Pri analizi učinkovitosti zavarovalnic v Srbiji na podlagi modela DEA Super-Radial input and output orientation, s stalnimi in variabilnimi donosi, so bili kot vhodni upo- rabljeni naslednji elementi: bilančna vsota, stroški kapitala in plač, nadomestila plače in drugi osebni odhodki, kot output elementi pa poslovni (funkcionalni) dohodek in čisti dobiček. Enote DMU so opazovane zavarovalnice v Srbiji, ki so poslovale v letu 2021. V tem primeru gre torej za močno korelacijo med opazovanimi spremenljivkami na ravni statistične pomembnosti, razen pri odhodkih za plače, nadomestilih plač in drugih osebnih stroških. Enota DMU velja za učinkovito, če je vrednost rezultata enaka ena. Če pa je vrednost rezultata večja ali manjša od enote, je enota DMU neučinkovita. Vrednost ocene enote DMU – AMS v modelih vhodne in izhodne orientacije s stalnim donosom (CCR-I in CCR-O) je 0,804568. Določena enota DMU je 80 % učinkovita in 20 % neu- činkovita. Analiza rezultatov je podobna tudi za druge enote DMU. Po rezultatih Super-Radiala (Super-BCC-I) sta bili v Srbiji v letu 2021 uspešni samo dve zavarovalnici: DUNAV OSIGURANJE in ĐENERALI OSIGURANJE SRBIJA. Os- tale zavarovalnice so bile neučinkovite. Enako je z rezultati Super-Radial (Super-BCC -O). V konkretnem primeru sta bili po tej metodi v Srbiji v letu 2021 učinkoviti le dve za - varovalnici: DDOR RE in SAVA ŽIVOTNO. Ostale zavarovalnice so bile neučinkovite. Projekcija vhodno/izhodnega elementa prikazuje odstotek odstopanja realiziranih vrednosti od predvidenih vrednosti. 62 Revija za ekonomske in poslovne vede (2, 2023) V konkretnem primeru je potrebno zaradi izboljšanja učinkovitosti (tj. izenačitve re- aliziranih vrednosti vhodnih/izhodnih elementov s predvidenimi) na primer DMU enoto DUNAV OSIGURANJE dokapitalizirati za 20,71 %, stroške plač, nadomestil plač oz. druge osebne odhodke za 57,54 %, poslovne (funkcionalne) prihodke za 36,95 % in čisti dobiček povečati za 5,51 %. Analiza projekcije vhodno/izhodnih elementov je podobna tudi za ostale opazovane enote DMU. Slack pokaže, kako pretvoriti neučinkovite enote DMU v učinkovite. Tako je na pri- mer za preoblikovanje neučinkovite enote DMU DUNAV OSIGURANJE v učinkovito enoto DMU treba zmanjšati kapital za 3831.767, stroške plač, nadomestil in drugih osebnih stroškov za 585.2151 ter povečati čisti dobiček za 1069,57 denarnih enot. Ana- liza je podobna za ostale opazovane enote DMU. Tako je na primer za preoblikovanje neučinkovite enote DMU DUNAV OSIGURA- NJE v učinkovito enoto DMU treba zmanjšati kapital za 3831.767, stroške plač, na- domestil in drugih osebnih stroškov za 585.2151 ter povečati čisti dobiček za 1069,57 denarnih enot. Analiza je podobna za ostale opazovane enote DMU. Zaključek - Na podlagi rezultatov, pridobljenih z uporabo modela DEA Super-Radi- al glede ocene učinkovitosti zavarovalnic v Srbiji je mogoče ugotoviti naslednje: Glede na rezultate Super-Radial (Super-CCR-I in Super-CCR -O) ni bila leta 2021 v Srbiji učinkovita nobena zavarovalnica. Po rezultatih Super-Radiala (Super-BCC-I) sta bili v Srbiji v letu 2021 uspešni samo dve zavarovalnici: DUNAV OSIGURANJE in ĐENE- RALI OSIGURANJE SRBIJA. Po rezultatih Super-Radiala (Super-BCC-O) sta bili v Srbiji v letu 2021 uspešni le dve zavarovalnici: DDOR RE in SAVA ŽIVOTNO. Ostale zavarovalnice so bile neučinkovite. V konkretnem primeru je za izboljšanje učinkovitosti zavarovalnic v Srbiji poleg učinkovitega prilagajanja poslovnemu okolju potrebno čim bolj učinkovito upravljanje sredstev, kapitala, človeških virov, prodaje zavarovalnih produktov in dobička. Pri tem ima pomembno vlogo digitalizacija celotnega poslovanja, ki je bistveno omilila vpliv pandemije Covid-19 na učinkovitost zavarovalnic v Srbiji. LITErATurE 1. Amini, A., Alinezhad, A., & Yazdipoor, F. (2019). A TOPSIS, VIKOR and DEA integrated evaluation method with belief structure under uncertainty to rank alternatives. International Journal of Advanced Operations Management, 11(3), 171–188. https://doi.org/10.1504/IJAOM.2019.100708 2. Andersen, P., & Petersen, N.C. (1993). A procedure for ranking efficient units in data envelopment analysis. Management Science, 39, 1261-1264. https://doi.org/10.1287/mnsc.39.10.1261 3. Banker, R.D., Charnes, A., & Cooper, W.W. (1984). 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A New Fuzzy DEA Model for Solving the MCDM Problems in Supplier Selection. Journal of Marine Science and Technology, 29(1) , Article 7. https://doi.org/10.51400/2709-6998.1006 Radojko Lukić PhD, full professor at the Faculty of Economics, University of Belgrade E-naslov: radojko.lukic@ekof.bg.ac.rs