Document Type : Original Article
Author
Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Abstract
Classic Data Envelopment Analysis methods ignore the internal interactions and consider the systems as a ‘black box’. Most of the network analysis models are nonlinear and it is feasible that these point may cause a considerable amount of modification to occur in the efficiency results. Amidst which, models, such as, the Wang Model, takes the intermediate variables into account, but in order to prevent intricacies in resolving models, it has an inconclusive approach, between two outlooks, of the black box and the network. Hence, in this paper, we consider a three-stage network with additional, desirable and undesirable inputs and outputs and the three abovementioned approaches are analyzed by contemplating on the optimistic and pessimistic views. The goals of this paper are to put together the results of the three mentioned approaches in order to attain the final conclusions. We generalize and use of Wang’s approach for the three levels, with additional inputs and outputs, as well as a heuristic solution to solve the network’s view. Finally, this paper considers a genuine world example, in the form of a dynamic network, for model application and analyzes it from three perspectives.
Keywords
Akbari, S., Heydari, J., Keramati, M. A., & Keramati, A. (2020). A mixed system of network data envelopment analysis to evaluate the performance of bank branches: An illustration with Iranian banks. International Journal of Business Excellence, 22(2), 198-212.
Afzalinejad, M., & Abbasi, Z. (2018). A slacks-based model for dynamic data envelopment analysis. Journal of Industrial & Management Optimization, 429-444.
Amirteimoori, A., Kordrostami, S., & Sarparast, M. (2006). Modeling undesirable factors in data envelopment analysis. Applied Mathematics and Computation, 180(2), 444-452.
An, Q., Liu, X., Li, Y., & Xiong, B. (2019). Resource planning of Chinese commercial banking systems using two-stage inverse data envelopment analysis with undesirable outputs. PLoS One, 14(6), e0218214.
An, Q., Yang, M., Chu, J., Wu, J., & Zhu, Q. (2017). Efficiency evaluation of an interactive system by data envelopment analysis approach. Computers & Industrial Engineering, 103, 17-25.
Azizi, H. (2012). Efficiency assessment in data envelopment analysis using efficient and inefficient frontiers. Management Research in Iran, 16(3), 153-173.
Azizi, H., & Wang, Y. M. (2013). Improved DEA models for measuring interval efficiencies of decision-making units. Measurement, 46(3), 1325-1332.
Badiezadeh, T., Saen, R. F., & Samavati, T. (2018). Assessing sustainability of supply chains by double frontier network DEA: A big data approach. Computers & Operations Research, 98, 284-290.
Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management science, 30(9), 1078-1092.
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429-444.
Chen, C., & Yan, H. (2011). Network DEA model for supply chain performance evaluation. European journal of operational research, 213(1), 147-155.
Cook, W. D., Zhu, J., Bi, G., & Yang, F. (2010). Network DEA: Additive efficiency decomposition. European journal of operational research, 207(2), 1122-1129.
Doyle, J. R., Green, R. H., & Cook, W. D. (1995). Upper and lower bound evaluation of multiattribute objects: Comparison models using linear programming. Organizational Behavior and Human Decision Processes, 64(3), 261-273.
Du, J., Zhu, J., Cook, W. D., & Huo, J. (2015). DEA models for parallel systems: Game-theoretic approaches. AsiaPacific Journal of Operational Research, 32(02), 1550008.
Ebrahimnejad, A., Tavana, M., & Mansourzadeh, S. M. (2015). An interactive MOLP method for solving output-oriented DEA problems with undesirable factors. Journal of Industrial & Management Optimization, 11(4), 1089-1110.
Fare, R., & Grosskopf, S. (2000). Network DEA. socio-economic planning science. 34: 35-49
Fare, R., Grosskopf, S., Lovell, C. K., & Pasurka, C. (1989). Multilateral productivity comparisons when some outputs are undesirable: a nonparametric approach. The review of economics and statistics, 90-98.
Fukuyama, H., & Weber, W. L. (2010). A slacks-based inefficiency measure for a two-stage system with bad outputs. Omega, 38(5), 398-409.
Jafarian-Moghaddam, A. R., & Ghoseiri, K. (2011). Fuzzy dynamic multi-objective Data Envelopment Analysis model. Expert Systems with Applications, 38(1), 850-855.
Jahed, R., Amirteimoori, A., & Azizi, H. (2015). Performance measurement of decision-making units under uncertainty conditions: An approach based on double frontier analysis. Measurement, 69, 264-279.
Kabnurkar, A. (2001). Mathematical Modeling for Data Envelopment Analysis with Fuzzy Restrictions on Weights (Doctoral dissertation, Virginia Tech).
Kao, C. (2009). Efficiency decomposition in network data envelopment analysis: A relational model. European Journal of Operational Research. 192 (3): 949-962
Kao, C., & Hwang, S.N. (2008). Efficiency de composition in two-stage data envelopment analysis: an application to non-life insurance companies in Taiwan. European Journal of Operational Research. 185 (1): 418-429.
Kawaguchi, H., Tone, K., & Tsutsui, M. (2014). Estimation of the efficiency of Japanese hospitals using a dynamic and network data envelopment analysis model. Health care management science, 17(2), 101-112.
Khalafi, S., Khalilzadeh, M., Razaghi, S., & Vaezi, E. (2021). Investigating the impact of the internet of things on the performance of knowledge areas of project management. International Journal of Internet Manufacturing and Services, 8(2), 89-102.
Korhonen, P. J., & Luptacik, M. (2004). Eco-efficiency analysis of power plants: An extension of data envelopment analysis. European journal of operational research, 154(2), 437-446.
Liu, J. S., Lu, L. Y., & Lu, W. M. (2016). Research Fronts and Prevailing Applications in Data Envelopment Analysis. In Data Envelopment Analysis (pp. 543-574). Springer, Boston, MA.
Lu, W. M., & Lo, S. F. (2007). A closer look at the economic-environmental disparities for regional development in China. European Journal of Operational Research, 183(2), 882-894.
Saati, S., Hatami-Marbini, A., Agrell, P. J., & Tavana, M. (2012). A common set of weight approach using an ideal decision-making unit in data envelopment analysis. Journal of Industrial and Management Optimization, 8(3), 623-637.
Shi, X., Emrouznejad, A., & Yu, W. (2021). Overall efficiency of operational process with undesirable outputs containing both series and parallel processes: A SBM network DEA model. Expert Systems with Applications, 178, 115062.
Shahriari, S. (2013). A Network Data Envelopment Analysis (NDEA) Model to evaluate firm’s Strategic Entrepreneurship. (Unpublished doctoral dissertation). Tehran University, Tehran, Iran. (in Persian)
Sengupta, J.K. (1995). Dynamic of Data Envelopment Analysis: Theory of Systems Efficiency. Springer Science & Business Media. Netherlands
Tavana, M., Kaviani, M. A., Di Caprio, D., & Rahpeyma, B. (2016). A two-stage data envelopment analysis model for measuring performance in three-level supply chains. Measurement, 78, 322-333.
Tone, K., & Tsutsui, M. (2009). Network DEA: a slacks-based measure approach. European Journal of Operational Research. 197 (1): 243-252
Vaezi, E. (2021). Measuring the performances of Medical Diagnostic Laboratories based on interval efficiencies. Journal of Optimization in Industrial Engineering, 14(2), 153-170.
Vaezi, E. (2022). Performance measurement in the health care sector: A leader-follower network DEA model based on double frontier analysis. Scientia Iranica, 29(3), 1662-1684.
Vaezi, E., Najafi, S., Hajimolana, S., Hosseinzadeh Lotfi, F., Ahadzadeh Namin, M. (2020). Production planning and efficiency evaluation of a three-stage network. Journal of Industrial and Systems Engineering, 13(Issue 2), 155-178.
Wang, K., Yu, S., & Zhang, W. (2013). China’s regional energy and environmental efficiency: A DEA window analysis based dynamic evaluation. Mathematical and Computer Modelling, 58(5-6), 1117-1127.
Wang, W. K., Lu, W. M., & Liu, P. Y. (2014). A fuzzy multi-objective two-stage DEA model for evaluating the performance of US bank holding companies. Expert Systems with Applications, 41(9), 4290-4297.
Wang, Y. M., & Chin, K. S. (2009). A new approach for the selection of advanced manufacturing technologies: DEA with double frontiers. International Journal of Production Research, 47(23), 6663-6679.
Wang, Y. M., & Chin, K. S. (2010). Some alternative DEA models for two-stage process. Expert Systems with Applications, 37(12), 8799-8808.
Wang, Y. M., Chin, K. S., & Yang, J. B. (2017). Measuring the performances of decision-making units using geometric average efficiency. Journal of the Operational Research Society, 58(7), 929-937.
Wu, J., Lv, L., Sun, J., & Ji, X. (2015). A comprehensive analysis of China's regional energy saving and emission reduction efficiency: from production and treatment perspectives. Energy Policy, 84, 166-176.
Wu, J., Zhu, Q., Ji, X., Chu, J., & Liang, L. (2016). Two-stage network processes with shared resources and resources recovered from undesirable outputs. European Journal of Operational Research, 251(1), 182-197.
Zhou, X., Luo, R., Tu, Y., Lev, B., & Pedrycz, W. (2018). Data envelopment analysis for bi-level
systems with multiple followers. Omega, 77, 180-188.
)