Quarterly Publication

Document Type : Original Article


Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran.


In this paper, we present an Additive Slacks-Based Measure (ASBM) model for measuring efficiency Decision-Making Unit (DMU) in the presence of undesirable outputs based on DEA Ratio based (DEA-R) model. In order to obtain a reasonable measure of efficiency, this paper proposes a concept for determining the minimum number of undesirable outputs that a DMU is allowed to generate based on the assertion of weak disposability. We show the
effect of producing excessive amounts of undesirable outputs on efficiency. We propose an alternative form of the ASBM model to measure efficiency based on DEA-R models. In the first stage, we introduce counterpart (hypothetic) units corresponding to each DMUs. We obtain the true efficiency scores and slack variables regarding the input and output components of each of the DMUs. In the second stage, we obtain the efficiency scores in the presence of undesirable outputs based on ASBM-DEA-R model. In the following, we illustrate the proposed approach with a numerical example. At the end, the results of the research are given.


  1. Scheel, H. (2001). Undesirable outputs in efficiency valuations. European journal of operational research132(2), 400-410.
  2. Färe, 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, 71(1), 90-98.
  3. Liu, W. B., Meng, W., Li, X. X., & Zhang, D. Q. (2010). DEA models with undesirable inputs and outputs. Annals of operations research173(1), 177-194.
  4. Zhou, P., Ang, B. W., & Poh, K. L. (2008). A survey of data envelopment analysis in energy and environmental studies. European journal of operational research189(1), 1-18.
  5. Kao, C. (2020). Measuring efficiency in a general production possibility set allowing for negative data. European journal of operational research282(3), 980-988.
  6. Song, M., An, Q., Zhang, W., Wang, Z., & Wu, J. (2012). Environmental efficiency evaluation based on data envelopment analysis: a review. Renewable and sustainable energy reviews16(7), 4465-4469.
  7. Dakpo, K. H., Jeanneaux, P., & Latruffe, L. (2016). Modelling pollution-generating technologies in performance benchmarking: recent developments, limits and future prospects in the nonparametric framework. European journal of operational research250(2), 347-359.
  8. Murty, S., Russell, R. R., & Levkoff, S. B. (2012). On modeling pollution-generating technologies. Journal of environmental economics and management64(1), 117-135.
  9. Sueyoshi, T., & Goto, M. (2012). DEA radial and non-radial models for unified efficiency under natural and managerial disposability: theoretical extension by strong complementary slackness conditions. Energy economics34(3), 700-713.
  10. Kao, C., & Hwang, S. N. (2021). Measuring the effects of undesirable outputs on the efficiency of production units. European journal of operational research292(3), 996-1003.
  11. Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision-making units. European journal of operational research2(6), 429-444.
  12. Green, R. H., Cook, W., & Doyle, J. (1997). A note on the additive data envelopment analysis model. Journal of the operational research society48(4), 446-448.
  13. Chen, K., & Zhu, J. (2020). Additive slacks-based measure: computational strategy and extension to network DEA. Omega91, 102022. https://doi.org/10.1016/j.omega.2018.12.011
  14. Gerami, J., Mozaffari, M. R., Wanke, P. F., & Correa, H. L. (In press). Improving information reliability of non-radial value efficiency analysis: An additive slacks-based measure approach. European journal of operational research. https://doi.org/10.1016/j.ejor.2021.07.036
  15. Despić, O., Despić, M., & Paradi, J. C. (2007). DEA-R: Ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications. Journal of productivity analysis28(1), 33-44.
  16. Emrouznejad, A., & Amin, G. R. (2009). DEA models for ratio data: convexity consideration. Applied mathematical modelling33(1), 486-498.
  17. Wei, C. K., Chen, L. C., Li, R. K., & Tsai, C. H. (2011). A study of developing an input-oriented ratio-based comparative efficiency model. Expert systems with applications38(3), 2473-2477.
  18. Wei, C. K., Chen, L. C., Li, R. K., & Tsai, C. H. (2011). Exploration of efficiency underestimation of CCR model: Based on medical sectors with DEA-R model. Expert systems with applications38(4), 3155-3160.
  19. Wei, C. K., Chen, L. C., Li, R. K., & Tsai, C. H. (2011). Using the DEA-R model in the hospital industry to study the pseudo-inefficiency problem. Expert systems with applications38(3), 2172-2176.
  20. Mozaffari, M. R., Gerami, J., & Jablonsky, J. (2014). Relationship between DEA models without explicit inputs and DEA-R models. Central European journal of operations research22(1), 1-12.
  21. Mozaffari, M. R., Kamyab, P., Jablonsky, J., & Gerami, J. (2014). Cost and revenue efficiency in DEA-R models. Computers & industrial engineering78, 188-194.
  22. Olesen, O. B., Petersen, N. C., & Podinovski, V. V. (2015). Efficiency analysis with ratio measures. European journal of operational research245(2), 446-462.
  23. Olesen, O. B., Petersen, N. C., & Podinovski, V. V. (2017). Efficiency measures and computational approaches for data envelopment analysis models with ratio inputs and outputs. European journal of operational research261(2), 640-655.
  24. Hatami-Marbini, A., & Toloo, M. (2019). Data envelopment analysis models with ratio data: a revisit. Computers & industrial engineering133, 331-338.
  25. Mozaffari, M. R., Dadkhah, F., Jablonsky, J., & Wanke, P. F. (2020). Finding efficient surfaces in DEA-R models. Applied mathematics and computation386, 125497. https://doi.org/10.1016/j.amc.2020.125497
  26. Gerami, J., Mavi, R. K., Saen, R. F., & Mavi, N. K. (2020). A novel network DEA-R model for evaluating hospital services supply chain performance. Annals of operations research, 1-26.
  27. Gerami, J., Mozaffari, M. R., & Wanke, P. F. (2020). A multi-criteria ratio-based approach for two-stage data envelopment analysis. Expert systems with applications158, 113508. https://doi.org/10.1016/j.eswa.2020.113508