Gradual Improving in Network DEA. Case study: 24 non-life insurance companies, in Taiwan

Subject Areas : تحقیق در عملیات

Elahe Mollaeian ¹ , Farhad Hossein Zadeh Lotfi ^{2 *} , abbas toloie eshlaghi ³ , Mohsen Rostami malKhalife ⁴ , Mohammad Ali Afshar Kazemi ⁵

1 - گروه مدیریت صنعتی ، دانشکده مدیریت و اقتصاد، واحد علوم و تحقیقات دانشگاه آزاد اسلامی تهران، ایران
2 - Department of Applied Mathematics, Islamic Azad University, Science and Research Branch, Tehran, Iran
3 - Department Of Industrial Management,Science & Research Branch, Islamic Azad University,Tehran,Iran.
4 - Department of Mathematics, Science and Research Unit, Islamic Azad University, Tehran, Iran
5 - Department of Management, Islamic Azad University, Central Tehran Branch, Tehran, Iran.

Received: 2021-11-14 Accepted : 2024-05-13 Published : 2025-07-29

Keywords: Data Envelopment Analysis (DEA), Two-stage DEA, Target Setting, Gradual Improvement,

Abstract :

Nowadays, performance evaluation and target setting for an organization are unavoidable. In addition, Data Envelopment Analysis is a non-parametric mathematical technique, which utilizes multiple inputs and outputs, which have been proved a usable approach for achieving these goals. The purpose of this paper is to determine a sequence of targets, each one within an appropriate, short distance of the preceding for the two-stage unit. Moreover, it is guaranteed that original unit is dominated by each element sequence of targets. To the best of this paper knowledge, few papers have looked at the sequence target setting in network DEA. From this perspective, this paper discusses a situation where a set of two-stage DMU considered and assumed as given the upper bounds on input and output changes. It is based upon the assumption of constant return to scale (CRS). The larger the bounds, the more changes in the input and output of DMUs as well as the number of steps required to efficiency improvement. This approach is illustrated by an empirical application to 24 non-life insurance companies, in Taiwan. Results determine that inputs always decrease (or stay the same) and final outputs always increase (or stay the same) along each step as well as the number of steps is variable. Moreover, Taiwan Fire, Fubon and Union achieve to the final target after one step as well as Kuo-Hou is in the worst case, and reaches its final goal after thirteen step.

References:

[1] A.Charnes, W. W., Cooper, and E. Rhodes, "Measuring the efficiency of decision-making", European Journal Operation Research. 2, 429-444. 1978.

[2] R. D.Banker, A. Charnes, and w.w. Cooper, "Some method for estimating technical and scale inefficiencies in Data Envelopment Analysis". Management Science. 30, 9, 1078-1092. 1984.

[3] K. Tone, “A Slack-based measure of efficiency in DEA”. European Journal of Operation Research 130 498-509. 2001

[4] R. Fare, S.Grosskopf, “Network DEA”. Socio-Economic Planning Sciences 34 35-49. 2000.

[5] C. Kao, S.N. Hwang, “Efficiency decomposition in two-stage DEA: An application to non-life insurance companies in Taiwan”. European Journal of Operation Research 185 (1) 418-429. 2008.

[6] Y. Chen, WD. Cook , N. Li , J. Zhu, "Additive efficiency decomposition in two-stage DEA". European Journal of Operational Research,196:1170–6 , 2009

[7] K. Tone, M. Tsutsui, “Network DEA: A Slack-based measure approach”. European Journal of Operation Research 197 (1) 243-252. 2009

[8] Y. Chen, D. Wade, Cook , Zhu. "Deriving the DEA frontier for two-stage processes" European Journal of Operational Research 202 , 138–142. 2010.

[9] S. Lozano, "Scale and cost efficiency analysis of networks of processes". Expert Systems with Applications 38 ,6612–6617, 2011.

[10] A. Ebrahimnejad , M.Tavana , F . Hosseinzadeh Lotfi, R. Shahverdi . and M .Yousefpour , "A three-stage Data Envelopment Analysis model with application to banking industry" Measurement 49 ,308–319, 2014.

[11 S .Lozano, "Alternative SBM Model for Network DEA" Computers & Industrial Engineering . S0360-8352(15)00017-0, 2015.

[12] Ch .Kao, "Efficiency decomposition and aggregation in network data envelopment analysis" European Journal of Operational Research. S0377-2217(16)30339-3. 2016

[13] M. Izadikhah, M.Tavana, D. Caprio and J. Francisco Santos-Arteaga. " A novel two-stage DEA production model with freely distributed initial inputs and shared intermediate outputs". Expert Systems With Applications 0 0 0 1–18, 2017.

[14] N.Adler, V.Liebert, and E.Yazhemsky. "Benchmarking airports from a managerial perspective”, Omega, 41(2), 442-458, 2013.

[15] A.Zanella, A.S.Camanho, and T.G.Dias,. "Benchmarking countries' environmental performance", Journal of the Operational Research Society, 64(3), 426-438, 2013.

[16] J.Krüger, "Direct targeting of efficient DMUs for benchmarking" International Journal of Production Economics S0925-5273(18)30098-7, 2016.

[17] J.L. Ruiz , I.Sirvent, "Common benchmarking and ranking of units with DEA", Omega, 65, 1-9. 2017.

[18] S. Lozano, N. Soltani and A.Dehnokhalaji, " A compromise programming approach for target setting in DEA." Annals of operation Research , 288, 363-390. 2019.

[19] J.L. Ruiz, J.V. Segura, I.Sirvent. "Benchmarking and target setting with expert preferences: An application to the evaluation of educational performance of Spanish universities", European Journal of Operational Research, 242(2), 594-605. 2015

[20] J.L. Ruiz, I.Sirvent, "Common benchmarking and ranking of units with DEA", Omega, 65, 1-9. 2016.

[21] J.Aparicio, J.M.Cordero and J.T.Pastor. "The determination of the least distance to the strongly efficient frontier in Data Envelopment Analysis oriented models". Modelling and computational aspects, Omega 2016.

[22] W.D.Cook, J.L.Ruiz, , I.Sirvent, and J. Zhu. "Within-group common benchmarking using DEA". European Journal of Operational Research, 256, 901-910. 2017

[23] J.Zhu, "Quantitative models for performance evaluation and benchmarking: data envelopment analysis with spreadsheets", Springer International Series. 2003.

[24] S.Lozano, G. Villa. “Determining a sequence of targets in DEA”. Journal of the Operational
Research Society, 56(12), 1439–1447. 2005

[25] S.Lozano, G. Villa,. “Gradual technical and scale efficiency improvement in DEA”. Annals of
Operations Research, 173, 123–136. 2010

[26] S.Lim, H.Bar, and L.H. Lee, “A study on the selection of benchmarking paths in DEA”, Expert Systems with Applications, 38(6), 7665-7673. 2011

[27] G.R. Jahanshahloo, F.Hosseinzadeh Lotfi, M .Rostamy-Malkhalife and A.Haseli. "A New Gradual Efficiency Improvement Model for Environmental Assessment Projects Decision Making Units on the Scale Efficiency Frontier in DEA". J. Appl. Environ. Biol. Sci., 4(1)1-8, 2014

[28] N.Ramon, , j L.Ruiz, I.Sirvent. "Two-step benchmarking: Setting more realistically achievable targets in DEA". Expert Systems With Applications, S0957-4174(17)30648-6. 2017

[29] N.NasrAbadi, "A sequence of targets toward a common best practice frontier in DEA". Journal of Industrial Engineering International 15:695–707. 2019
[30] Q. An, X.Tao, B.Dai, " Bounded-change target-setting approach: Selection of a realistic benchmarking path". Journal of the Operation Research Society. 1700185, 2019.

[31] A.DehnoKhalaji, N.Soltani, " Gradual efficiency improvement through a sequence of target." Journal of the Operational Research Society, 70, 2143-2152. 2019.

[32] K.Rashidi, "AHP versus DEA: a comparative analysis for the gradual improvement of unsustainable suppliers", Benchmarking: An International Journal, Vol. 27 No. 8, pp. 2283-2321. 2020

[33] غلامرضا جهانشاهلو، فرهاد حسین زاده لطفی، هاشم نیکو مرام." تحلیل پوششی داده ها و کاربرد های آن ". 1387.