Document Type : Research Paper


1 Ph.D. Candidate in Mathematics, Department of Mathematics, Guilan Science and Research Branch, Islamic Azad University, Rasht, Iran

2 Professor, Department of Mathematics, Guilan Science and Research Branch, Islamic Azad University, Rasht, Iran

3 Professor, Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.

4 Assisstant Professor, Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran


Data Envelopment Analysis (DEA) is an estimator. This estimator tries to assess a relationship between multiple inputs and multiple outputs, and an identified technology. In traditional DEA models, firms are classified into two divisions, efficient and inefficient. Efficient firms are considered as a reference for inefficient firms. In traditional DEA models, the efficiency improvement has been inspected for inefficient firms and efficient firms are assumed to be unchanged. Since the estimated technology is rationally smaller than the real technology or in other words, the estimated technology is always the subset of the true technology, we can expand it a little. Thus, we can improve efficient firms. This is done by creating some virtual DMUs. In this paper, an algorithm is proposed to expand the Production Possibility Set (PPS) and to improve efficient firms. To illustrate the proposed approach, numerical and applied examples are provided. The results are explained and discussed.



[1] Aigner, D.J., & Chu, S.F. (1968) On Estimating the Industry Production Function. American Economic Review, 58, 826-839.
[2] Aigner, D., Lovell, C. K., & Schmidt, P. (1977). Formulation and estimation of stochastic frontier production function models. Journal of Econometrics, 6(1), 21–37.
[3] Amirteimoori, A., Kordrostami, S., & Nasrollahian, P. A. (2017). Method for solving super-Efficiency infeasibility by adding virtual DMUs with mean values. Iranian journal of management studies, 10(4), 905-916.
[4] Banker, R. D., Charnes, A., &Cooper, W. W. (1984). Some models for estimating technical and scale inefficiency in data envelopment analysis. Management Science, 30, 1078–1092.
[5] Battese, G., & Coelli, T. (1992). Frontier production functions, technical efficiency and panel data: With application to paddy farmers in India. Journal of Productivity Analysis, 3, 153–169.
[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.
[7] Coelli, T., Rao, D.S.P., & Battese, G.E. (1998). An introduction to efficiency and productivity analysis. Boston: Kluwer Academic.
[8] Deprins, D., Simar, L., and Tulkens, H. (1984). Measuring labor-efficiency in post office. In North Holland, editor, The Performance of Public Enterprises. Amsterdam: M. Marchand and P. Pestieau and H. Tulkens.
[9] Didehkhani, H., Hosseinzadeh Lotfi, F., Sadi-Nezhad, S. (2019). Practical benchmarking in DEA using artificial DMUs. Journal of Industrial Engineering International, 15, 293–301.
[10] Fethi, M., Jackson, P. M., & Weyman-Jones, T. G. (2001). European airlines: a stochastic dea study of efficiency with market liberalisation. Tech. rep., University of Leicester Efficiency and Productivity Research Unit
[11] Farrell, M. J. (1957). The measurement of productive efficiency.Journal of the Royal Statistical Society, 120(3), 253–281.
[12] Greene, W. H. (1980). Maximum likelihood estimation of econometric frontier functions. Journal of Econometrics, 13(1), 27–56.
[13] Greene, W. H. (1990). A Gamma-distributed stochastic frontier model. Journal of Econometrics, 46, 141–163.
[14] Greene, W. H. (2008). Econometric Analysis, sixth edn. Pearson Prentice Hall.
[15] Krivonozhko, V. E., Forsund, F. R. and Lychev, A. V. (2015). On comparison of different sets of units used for improving the frontier in DEA models. Ann. Operat. Res. Doi: 10.1007/s10479 - 015- 1875-8
[16] Krivonozhko, V. E., Forsund, F. R. and Lychev, A. V. (2016). Improving the Frontier in DEA Models. Doklady Mathematics, 94(3), 715–719. Doi: 10.1134/S1064562416060181
[17] Land, K. C., Lovel CAK, & Thore, S. (1993). Chance-constrained data envelopment analysis. Managerial and Decision Economics, 14, 541–554.
[18] Lovell CAK (1993). Production Frontiers and Productive Efficiency. In: Fried H, Lovell CAK, Schmidt S (eds) The Measurement of Productive Efficiency. New York: Techniques and Applications, Oxford University Press.
[19] Olesen, O. B., & Petersen, N.C. (1995). Chance Constrained Efficiency Evaluation. Management Science, 41, 442-457.
[20] Bogetoft, P., & Otto, L. (2011). Benchmarking with DEA, SFA, and R. New York: Springer.
[21] Sexton, T.R., Silkman, R.H., & Hogan, A.J. (1986(. Data envelopment analysis: Critique and extensions. In: Silkman, R.H. (Ed.), Measuring Efficiency: An Assessment of Data Envelopment Analysis. Jossey-Bass, San Francisco, CA, 73–105.
[22] Sowlati, T., &Paradi, J. C. (2004). Establishing the “practical frontier” in data envelopment analysis. Omega, 32, 261–272.