An Efficiency Measurement and Benchmarking Model Based on Tobit Regression, GANN-DEA and PSOGA

Document Type : Original Article


1 Ph.D. Candidate, Department of industrial management, Central Tehran Branch, Islamic Azad University, Tehran, Iran.

2 Associated professor, Department of industrial management, Central Tehran Branch, Islamic Azad University, Tehran, Iran (Corresponding author).

3 Professor, Department of Industrial Management, Science and Research Branch, Islamic Azad University, Tehran, Iran.


The purpose of this study is designing a model based on Tobit regression, DEA, Artificial Neural Network, Genetic Algorithm and Particle Swarm Optimization to evaluate the efficiency and also benchmarking the efficient and inefficient units. This model has three stages, and it uses the data envelopment analysis combined model with neural network, optimized by genetic algorithm, to evaluate the relative efficiency of 16 regional electric companies of Tavanir. A two-staged approach of data envelopment analysis and Tobit regression has been used to measure the effects of environmental variables on the mean efficiency of companies. Finally we use a hybrid model of particle swarm algorithm and genetic algorithm to benchmark the efficient and inefficient units. The mean efficiency of regional electric companies have increased from 0.8934 to 0.9147, during 2012 to 2017, and regional electric companies of Azarbayjan, Isfahan, Tehran, Khorasan, Semnan, Kerman, Gilan and Yazd, had the highest mean efficiency of 1, and west regional electric companies and Fars had the lowest efficiency of 0.7047 and 0.6025, respectively.


1)     Abd-El-Wahed, W., Mousa, A., & El-Shorbagy, M. (2011). Integrating particle swarm optimization with genetic algorithms for solving nonlinear optimization problems. Journal of Computational and Applied Mathematics, 235(5), 1446-1453.
2)     Angeline, P. J. (1998). Using selection to improve particle swarm optimization. Paper presented at the Evolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence., The 1998 IEEE International Conference on.
3)     Athanassopoulos, A. D., & Curram, S. P. (1996). A Comparison of Data Envelopment Analysis and Artificial Neural Networks as Tools for Assessing the Efficiency of Decision Making Units. Journal of the Operational Research Society, 47(8), 1000-1016.
4)     Bagdadioglu, N., Price, C. M. W., & Weyman-Jones, T. G. (1996). Efficiency and ownership in electricity distribution: a non-parametric model of the Turkish experience. Energy Economics, 18(1-2), 1-23.
5)     Bongo, M. F., Ocampo, L. A., Magallano, Y. A. D., Manaban, G. A., & Ramos, E. K. F. (2018). Input–output performance efficiency measurement of an electricity distribution utility using super-efficiency data envelopment analysis. Soft Computing.
6)     Çelen, A. (2013). Efficiency and productivity (TFP) of the Turkish electricity distribution companies: An application of two-stage (DEA&Tobit) analysis. Energy Policy, 63, 300-310.
7)     Charnes, A., Cooper, W., Lewin, A., & Seiford, L. (1995). Data Envelopment Analysis: Theory, Methodology and Applications, Kluwer Publications.
8)     Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429-444.
9)     Cook, W. D., & Green, R. H. (2005). Evaluating power plant efficiency: a hierarchical model. Computers & Operations Research, 32(4), 813-823.
10)  Costa, Á., & Markellos, R. N. (1997). Evaluating public transport efficiency with neural network models. Transportation Research Part C: Emerging Technologies, 5(5), 301-312.
11)  Cullmann, A., & von Hirschhausen, C. (2008). Efficiency analysis of East European electricity distribution in transition: legacy of the past. Journal of Productivity Analysis, 29(2), 155.
12)  De Jong, K. A. (1975). Analysis of the behavior of a class of genetic adaptive systems.
13)  Debreu, G. (1951). The Coefficient of Resource Utilization, Econometric, 19, Economics: Principles and Applications: Zaria: AGTAB Publishers Ltd.
14)  Dreyfus, G. (2005). Neural networks: methodology and applications: Springer Science & Business Media.
15)  Eberhart, R., & Kennedy, J. (1995). A new optimizer using particle swarm theory. Paper presented at the Micro Machine and Human Science, 1995. MHS'95., Proceedings of the Sixth International Symposium on.
16)  Emrouznejad, A., & Shale, E. (2009). A combined neural network and DEA for measuring efficiency of large scale datasets. Computers & Industrial Engineering, 56(1), 249-254.
17)  Fallahi, M., & Ahmadi, V. (2005). Cost efficiency analysis of electricity distribution companies in Iran. Journal of Economic Researches, 71, 297-320.
18)  Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society. Series A (General), 120(3), 253-290.
19)  Garg, H. (2016). A hybrid PSO-GA algorithm for constrained optimization problems. Applied Mathematics and Computation, 274, 292-305.
20)  Goldberg, D. E., & Holland, J. H. (1988). Genetic algorithms and machine learning. Machine learning, 3(2), 95-99.
21)  Goto, M., & Tsutsui, M. (2008). Technical efficiency and impacts of deregulation: An analysis of three functions in US electric power utilities during the period from 1992 through 2000. Energy Economics, 30(1), 15-38.
22)  Hattori, T., Jamasb, T., & Pollitt, M. G. (2003). A comparison of UK and Japanese electricity distribution performance 1985-1998: lessons for incentive regulation.
23)  Hess, B., & Cullmann, A. (2007). Efficiency analysis of East and West German electricity distribution companies–Do the “Ossis” really beat the “Wessis”? Utilities Policy, 15(3), 206-214.
24)  Hjalmarsson, L., & Veiderpass, A. (1992). Efficiency and ownership in Swedish electricity retail distribution International Applications of Productivity and Efficiency Analysis (pp. 3-19): Springer.
25)  Holland, J. (1975). Adaptation in natural and artificial systems: an introductory analysis with application to biology. Control and artificial intelligence.
26)  Koopmans, T. C. (1951). Efficient allocation of resources. Econometrica: Journal of the Econometric Society, 455-465.
27)  Li, J., Li, J., & Zheng, F. (2014). Unified efficiency measurement of electric power supply companies in China. Sustainability, 6(2), 779-793.
28)  McDonald, J. (2009). Using least squares and tobit in second stage DEA efficiency analyses. European Journal of Operational Research, 197(2), 792-798.
29)  Meibodi, A. E. (1998). Efficiency considerations in the electricity supply industry: The case of Iran: university of Surrey.
30)  Mostafa, M. M. (2009). Modeling the efficiency of top Arab banks: A DEA–neural network approach. Expert systems with applications, 36(1), 309-320.
31)  Munakata, T. (1998). Fundamentals of the new artificial intelligence (Vol. 2): Springer.
32)  Ouenniche, J., Xu, B., & Tone, K. (2017). DEA IN PERFORMANCE EVALUATION OF CRUDE OIL PREDICTION MODELS. Advances in DEA Theory and Applications: With Extensions to Forecasting Models, 381-403.
33)  Pérez-Reyes, R., & Tovar, B. (2009). Measuring efficiency and productivity change (PTF) in the Peruvian electricity distribution companies after reforms. Energy Policy, 37(6), 2249-2261.
34)  Russell, R. R. (1985). Measures of technical efficiency. Journal of Economic Theory, 35(1), 109-126.
35)  Sadjadi, S., & Omrani, H. (2008). Data envelopment analysis with uncertain data: An application for Iranian electricity distribution companies. Energy Policy, 36(11), 4247-4254.
36)  Samoilenko, S., & Osei-Bryson, K.-M. (2010). Determining sources of relative inefficiency in heterogeneous samples: Methodology using Cluster Analysis, DEA and Neural Networks. European Journal of Operational Research, 206(2), 479-487.
37)  Shokrollahpour, E., Lotfi, F. H., & Zandieh, M. (2016). An integrated data envelopment analysis–artificial neural network approach for benchmarking of bank branches. Journal of Industrial Engineering International, 12(2), 137-143.
38)  Tobin, J. (1958). Estimation of Relationships for Limited Dependent Variables. Econometrica, 26(1), 24-36.
39)  Toloie-Eshlaghy, A., Alborzi, M., & Ghafari, B. (2012). Assessment of the personnel’s efficiency with Neuro/DEA combined model.
40)  Tone, K. (2001). A slacks-based measure of efficiency in data envelopment analysis. European Journal of Operational Research, 130(3), 498-509.
41)  Wu, D. D., Yang, Z., & Liang, L. (2006). Using DEA-neural network approach to evaluate branch efficiency of a large Canadian bank. Expert systems with applications, 31(1), 108-115.
Wu, Y., Hu, Y., Xiao, X., & Mao, C. (2016). Efficiency assessment of wind farms in China using two-stage data envelopment analysis. Energy Conversion and Management, 123, 46-55.