Efficiency study with undesirable inputs and outputs in DEA

Document Type: Research Paper


1 Department of Mathematics, Islamic Azad University of Central Tehran Branch, Iran.

2 Islamic Azad University of Central Tehran Branch, Iran.


Data Envelopment Analysis (DEA) is one of the well-known methods for calculating efficiency, determining efficient boundaries and evaluating efficiency that is used in specific input and output conditions. Traditional models of DEA do not try to reduce undesirable outputs and increase undesirable inputs. Therefore, in this study, in addition to determining the efficiency of Decision-Making Units (DMU) with the presence of some undesirable input and output components, its effect has also been investigated on the efficiency limit. To do this, we first defined the appropriate production possibility set according to the problem assumptions, and then we presented a new method to determine the unfavorable performance of some input and output components in decision-making units. And we determined the impact of unfavorable inputs and outputs on the efficient boundary. We also showed the model result by providing examples for both unfavorable input and output states and solving them and determining the efficiency score and driving them to the efficient boundary by plotting those boundaries.


Main Subjects

[1]   Walheer, B. (2020). Output, input, and undesirable output interconnections in data envelopment analysis: convexity and returns-to-scale. Annals of operations research284(1), 447-467.
[2]   Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research2(6), 429-444.
[3]   Chen, Y., & Ali, A. I. (2002). Output–input ratio analysis and DEA frontier. European journal of operational research142(3), 476-479.
[4]    Jahanshahloo, G. R., Lotfi, F. H., & Zohrehbandian, M. (2005). Finding the piecewise linear frontier production function in data envelopment analysis. Applied mathematics and computation163(1), 483-488.
[5]   Wu, J., Xia, P., Zhu, Q., & Chu, J. (2019). Measuring environmental efficiency of thermoelectric power plants: a common equilibrium efficient frontier DEA approach with fixed-sum undesirable output. Annals of operations research275(2), 731-749.
[6]   Kao, H. Y., Wu, D. J., & Huang, C. H. (2017). Evaluation of cloud service industry with dynamic and network DEA models. Applied mathematics and computation315, 188-202.
[7]    Gómez-Calvet, R., Conesa, D., Gómez-Calvet, A. R., & Tortosa-Ausina, E. (2020). European energy efficiency evaluation based on the use of super-efficiency under undesirable outputs in SBM models. In Advances in efficiency and productivity II (pp. 193-208). Springer, Cham.
[8]    Yu, S., Liu, J., & Li, L. (2020). Evaluating provincial eco-efficiency in China: an improved network data envelopment analysis model with undesirable output. Environmental science and pollution research27(7), 6886-6903.
[9]   Song, M., Wang, J., Zhao, J., Baležentis, T., & Shen, Z. (2020). Production and safety efficiency evaluation in Chinese coal mines: accident deaths as undesirable output. Annals of operations research, 291, 827–845.