Document Type : Original Article

Authors

1 Department of Mathematics, Tafresh University, Tafresh, Iran.

2 Department of Industrial Engineering, Tafresh University, Tafresh, Iran.

10.22105/dmor.2021.266696.1300

Abstract

Purpose: The paper addresses the star network structures with centralized management and provides models for evaluating the performance of such structures. Despite the wide range of applications and importance, such structures have not been studied in data envelopment analysis before.
Methodology: The Data Envelopment Analysis (DEA) method is used for modeling the problem, and a two-level method for efficiency evaluation is proposed.
Findings: The proposed models are developed in both multiplicative and envelopment forms. The required formulas for efficiency decomposition and benchmarking are provided. Some results are proved by mathematical discussions and numerical experimentation.
Originality/Value: The star structure is seen in many real-world applications. A new method for modelling and evaluation of such structures is introduced and established. The proposed technique, discussions and analytical examinations have a significant contribution to the field of data envelopment analysis and its applications.




 

Keywords

Main Subjects

Akther, S., Fukuyama, H., & Weber, W. L. (2013). Estimating two-stage network slacks-based inefficiency: an application to Bangladesh banking. Omega, 41(1), 88-96. https://doi.org/10.1016/j.omega.2011.02.009
Amani, N., & Bagherzadeh Valami, H. (2018). Efficiency evaluation of regional electronic companies in Iran by network DEA: A based on the conversion of the structures into a uniform structure. Journal of decisions and operations research, 3(3), 249-280. (In Persian). DOI: 10.22105/DMOR.2018.81213
Amirteimoori, A. & Yang, F. (2014). A DEA model for two-stage parallel-series production processes. RAIRO-operations research, 48(1), 123-134. https://doi.org/10.1051/ro/2013057
Amirteimoori, A. (2013). A DEA two-stage decision processes with shared resources. Central European journal of operations research, 21(1), 141-151. https://doi.org/10.1007/s10100-011-0218-3
Amirteimoori, A., Shahroodi, K., & Shaker Mahmoodkiani, F. (2015). Network data envelopment analysis: application to gas companies in Iran. International journal of applied operational research, 5(1), 1-16. http://ijorlu.liau.ac.ir/article-1-440-fa.html
Castelli, L., Pesenti, R., & Ukovich, W. (2004). DEA-like models for the efficiency evaluation of hierarchically structured units. European journal of operational research, 154(2), 465-476. https://doi.org/10.1016/S0377-2217(03)00182-6
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429-444. https://doi.org/10.1016/0377-2217(78)90138-8
Chen, Y., Cook, W. D., Li, N., & Zhu, J. (2009). Additive efficiency decomposition in two-stage DEA. European journal of operational research, 196(3), 1170-1176. https://doi.org/10.1016/j.ejor.2008.05.011
Cook, W. D., Zhu, J., Bi, G., & Yang, F. (2010). Network DEA: Additive efficiency decomposition. European journal of operational research, 207(2), 1122-1129. https://doi.org/10.1016/j.ejor.2010.05.006
Färe, R., & Grosskopf, S. (1996). Productivity and intermediate products: a frontier approach. Economics letters, 50(1), 65-70. https://doi.org/10.1016/0165-1765(95)00729-6
Färe, R., & Grosskopf, S. (2000). Network DEA. Socio-economic planning sciences, 34, 35-49. https://doi.org/10.1016/S0038-0121(99)00012-9
Fukuyama, H. & Mirdehghan, S. M. (2012). Identifying the efficiency status in network DEA. European journal of operational research, 220(1), 85-92. https://doi.org/10.1016/j.ejor.2012.01.024
Kao, C., & Hwang, S. N. (2008). Efficiency decomposition in two-stage data envelopment analysis: an application to non-life insurance companies in Taiwan. European journal of operational research, 185(1), 418-429. https://doi.org/10.1016/j.ejor.2006.11.041
Kaveh, M., Ardakani, S. S., Shafiee, M., & Tabataba’i Nasab, S. M. (2020). Predicting and benchmarking the factors of customer attraction in insurance companies by the model of network data envelopment analysis and the theory of dynamics of bass publishing. Journal of decisions and operations research, 5(3), 382-401. (In Persian). DOI: 10.22105/DMOR.2020.237734.1188
Lewis, H. F., & Sexton, T. R. (2004). Network DEA: Efficiency analysis of organizations with complex internal structure. Computers & operations research, 31(9), 1365-1410. https://doi.org/10.1016/S0305-0548(03)00095-9
Liang, L., Cook, W. D., & Zhu, J. (2008). DEA models for two-stage processes: game approach and efficiency decomposition. Naval research logistics, 55(7), 643-653. https://doi.org/10.1002/nav.20308
Maghbouli, M., Amirteimoori, A., & Kordrostami, S. (2014). Two-stage network structures with undesirable outputs: A DEA based approach, Measurement, 48, 109-118. https://doi.org/10.1016/j.measurement.2013.10.032
Rahimi, A., & Hosseinzadeh Saljooghi, F. (2018). Multi-objective programming model for determining the efficiency and returns to scale in supply chain management of two-stage: a case study of resin companies in Iran. Journal of decisions and operations research, 2(3), 213-227. (In Persian). DOI: 10.22105/DMOR.2018.57124
Tone, K., & Tsutsui, M. (2009). Network DEA: a slacks-based measure approach. European journal of operational research, 197(1), 243-252. https://doi.org/10.1016/j.ejor.2008.05.027
Vaezi, H., & Memarpour, M. (2018). Evaluation of the performance and ranking of the efficiency of Tehran branches of a private bank using two-stage data envelope analysis and Borda ranking technique. Journal of decisions and operations research, 2(2), 116-129. (In Persian). DOI: 10.22105/DMOR.2018.55774
Yan, Q., Zhao, F., Wang, X., Yang, G., Baležentis, T., & Streimikiene, D. (2019). The network data envelopment analysis models for non-homogenous decision making units based on the sun network structure. Central European journal of operations research27(4), 1221-1244. https://doi.org/10.1007/s10100-018-0560-9