A New Method of Sensitivity Analysis of Returns to Scale in Two-Stage Network; A Case Study of the Insurance Industry in Iran

Subject Areas : Financial Mathematics

Maryam  Sarparast ¹ (Islamic Azad University, Science and Research Branch)
Farhad  Hosseinzadeh Lotfi ² (Department of Mathematics, Science and Research branch, Islamic Azad University, Tehran, Iran.)
Alireza  Amirteimoori ³ (Department of Applied Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran)
Mohsen  Rostamy-Malkhalifeh ⁴ (Department of Mathematics, science and research Branch, Islamic Azad University, Tehran, Iran)

Received: 2021-11-30 Accepted : 2022-08-14 Published : 2024-04-27

Keywords: Two-Stage Networks , Sensitivity Analysis, Returns to Scale , Data Envelopment Analysis , Insurance Industry,

Abstract :

One important issue in data envelopment analysis (DEA) which has been studied by many researchers is returns to scale (RTS). The authors developed DEA models to evaluate the efficiency of two-stage networks in returns to scale variable and introduced a new definition to determine return to scale classification in two-stage networks. The current article proposed an approach for determining the stability region of returns to scale classification in two-stage network DEA. The data were collected from insurance companies in Iran in 2019. We consider the insurance industry process as a two-stage network; the stage of marketing and that of investment. The effectiveness of insurance companies was evaluated, and, after determining the classification of returns to scale, we found a sustainability interval to classify returns to their scale.

References:

[1] Banker. R. D., Charnes. A. W.W., Some Methods for Estimating Technical and scale Inefficiencies in Data Envelopment Analysis, Management science, 1984; 30(9):1078-1092. Doi: 10.1287/mnsc.30.9.1078.
[2] Banker, R. D., & Thrall, R. M. , Estimation Of Returns To Scale Using Data Envelopment Analysis, European Journal of Operational Research, 1992; 62(1): 74-84. Doi: 10.1016/0377-2217(92)90178-C.
[3] Charnes, A., Cooper, WW. And Rhodes, E., Measurement The Efficiency Of Decision Making Unit, European Journal of Operational Research, 1978; 2: 429-444., Doi: 10.1016/0377-2217(78)90138-8
[4] Du, J., Liang, L., Chen, Y., Cook, W. D., Zhu, J., Bargaining Game Model Or Measuring Performance Of Two-Stage Network Structures, European Journal of Operational Research, 2011; 210: 390–397. Doi: 10.1016/ j.ejor.2010.08.025.
[5] Fare, R., and Grosskopf, S., Network DEA, Socio-economic planning science, 2000; 34: 35-49. Doi: 10.1016/S0038-0121(99)00012-9.
[6] Färe, R., and Grosskopf, S., Productivity And Intermediate Products: A Frontier Approach., Economics letters, 1996; 50(1): 65-70. Doi: 10.1016/0165-1765(95)00729-6.
[7] Kang. C., Fengb. C., Choub. P., Weyc. W. and Khand. H., Mixed Network DEA Models With Shared Resources For Measuring And Decomposing Performance Of Public Transportation Systems, Research in Transportation Business and Management, 2022, In press. Doi: 10.1016/j.rtbm.2022.100828.
[8] Kao C, Hwang S-N., Efficiency Decomposition In Two-Stage Data Envelopment Analysis: An Application To Non-Life Insurance Companies In Taiwan, European Journal of Operation Research, 2008; 185(1):418-29. Doi: 10.1016/j.ejor.2006.11.041.
[9] Kao, C., Efficiency Decomposition For General Multi-Stage Systems In Data Envelopment Analysis, European Journal of Operational Research, 2014; 232: 117–124. Doi: 10.1016/j.ejor.2013.07.012.
[10] Kao, C., Efficiency Decomposition For Parallel Production Systems, Journal of the Operational Research Society, 2012; 63: 64-71. Doi: 10.1057/jors.2011.16.
[11] Kao. C., Efficiency Decomposition In Network Data Envelopment Analysis: A Relational Model, European Journal of Operation Research, 2009; 192: 949-962. Doi:10.1016/j.ejor.2007.10.008.
[12] Khaleghi. M, Jahanshahloo. Gh. R., Zohrehbandian. M., and Hosseinzadeh Lotfi. F., Returns to Scale and Scale Elasticity in Two-Stage Dea , Math. Comput, 2012; 17(3): 193-202. Doi: 10.3390/mca17030193.
[13] Khodabakhshi, M., Gholamy, Y., Kheyrollahi. H., Additive Model Approach For Estimating Returns To Scale In Imprecise Data Envelopment Analysis, Applied Mathematical Modelling, 2010; 5:1247-1257. Doi: 10.1016/j.apm.2009.08.011.
[14] Khodakarami. M., Shabani. A., Farzipoor Saen. R., Concurrent Estimation Of Efficiency, Effectiveness And Returns To Scale, International Journal of Systems Science, 2016; 47(5): 1202–1220. Doi: 10.1080/ 00207721.2014.919073.
[15] Khoveynia. M. and Eslamib. R., Two-Stage Network DEA With Shared Resources: Illustrating The Drawbacks And Measuring The Overall Efficiency, Knowledge-Based Systems, 2022, In Press, 250. Doi: 10.1016/j.knosys.2022.108725.
[16] Lianga. S., Yangb. J and Dingb. T., Performance Evaluation Of Ai Driven Low Carbon Manufacturing Industry In China: An Interactive Network Dea Approach, Computers & Industrial Engineering, 2022;170. Doi: 10.1016/j.cie.2022.108248.
[17] Lo, S. F., Performance Evaluation For Sustainable Business: A Profitability And Marketability Framework, Corporate Social Responsibility and Environmental Management, 2010; 17: 311–319. Doi: 10.1002/csr.214 .
[18] Lu, W. C., The Evolution Of R&D Efficiency And Marketability: Evidence From Taiwan’s IC-Design Industry, Asian Journal of Technology Innovation, 2009; 17: 1–26. Doi: 10.1080/19761597.2009.9668671.
[19] Michalia. M., Emrouznejad. A., Dehnokhalajia. A., Clegga. B., Sub Sampling Bootstrap In Network DEA, European Journal of Operational Research, 2022; In Press. Doi: 10.1016/j.ejor.2022.06.022.
[20] Nasution. N. H., Efendi. S., Tulus. T., Sensitivity Analysis In Data Envelopment Analysis For Interval Data, The International Conference on Computer Science and Applied Mathematics, Journal of Physics: Conf. Series 1255, 2019; 012084. Doi: 10.1088/1742-6596/1255/1/012084.
[21] Nasution. N., Zamsuri. A., Lisnawita. L., and Wanto. A., Polak-Ribiere Updates Analysis With Binary And Linear Function In Determining Coffee Exports In Indonesia, IOP Conference Series: Materials Science and Engineering, 2018; 420(12089): 1–9. Doi: 10.1088/1757-899X/420/1/012088.
[22] Neralic. L., and Wendell. R., Enlarging The Radius Of Stability And Stability Regions In Data Envelopment Analysis, European Journal of Operational Research, 2018; 278(2):430-441. Doi:10.1016/j. ejor.2018.11.019.
[23] Peykani. P., Mohammadi. E. and Esmaeili. F. S., Stock Evaluation Under Mixed Uncertainties Using Robust DEA Model, Journal of Quality Engineering and Production Optimization, 2019; 4(1): 73-84.Doi: 10.22070/jqepo.2019.3652.1080.
[24] Peykani. P., Mohammadi. E. and Emrouznejad A., An AdjusTable Fuzzy Chance-Constrained Network DEA Approach With Application To Ranking Investment Firms, Expert Systems with Applications, Expert Systems With Applications, 2021; 166: 113938. Doi: 10.1016/j.eswa.2020.113938.
[25] Peykani. P., Mohammadi. E., Interval Network Data Envelopment Analysis Model For Classification Of Investment Companies In The Presence Of Uncertain Data, Journal of Industrial and Systems Engineering, 11 (Special issue: 14th International Industrial Engineering Conference),2018; 63-72. Doi:10.22070/ 2019.3652.1080.
[26] Peykani. P., Mohammadi. E., Window Network Data Envelopment Analysis: An Application To Investment Companies, International Journal of Industrial Mathematics, 2020l; 12(1): 89-99.

[27] Peykani. P., Mohammadi. E., Emrouznejad. A., Pishvaee. M. S., and Rostamy-Malkhalifeh. M., Fuzzy Data Envelopment Analysis: An AdjusTable Approach, Expert Systems with Applications, 2019; 136: 439-452. Doi: 10.1016/j.eswa.2019.06.039.
[28] Sarparast, M., Hosseinzadeh Lotfi, F., and Amirteimoori, A., Sensitivity Analysis Of Returns To Scale In Two-Stage Network: Based On DEA Models, Accepted by Journal of “Discrete Dynamics in Nature and Society, 2022.
[29] Tavassoli, M., Ketabi. S., and chandehari. M., A Novel Fuzzy Network DEA Model To Evaluate Efficiency Of Iran’s Electricity Distribution Network With Sustainability Considerations., Sustainable Energy Technologies and Assessments, 2022; 52. Doi: 10.1016/j.seta.2022.102269.
[30] Zhou. Zh., Lin. L., Xiao. H., Ma. Ch. and Wu. Sh., Stochastic Network DEA Models For Two-Stage Systems Under The Centralized Control Organization Mechanism, Computers & Industrial Engineering, 2017; 110: 404-412. Doi: 10.1016/j.cie.2017.06.005.