Abstract
The conventional data envelopment analysis (DEA) models make an assumption of non-negativity in the inputs and outputs data of the decision making units (DMUs) under analysis. In this paper, we present a non-radial measure of efficiency of DMUs by establishing a multi-period additive DEA model taking into consideration both desirable and undesirable inputs and outputs with positive and non-positive values. The proposed efficiency model possesses the requisite features of translation invariance and unit independence, obligatory when dealing with negative values in the data set. Furthermore, this paper contributes with the proposal of a multi-period additive super-efficiency DEA model to discriminate the performance of efficient decision making units. Finally, we present an efficiency evaluation 37 countries worldwide on economic parameters to demonstrate the applicability and efficacy of the proposed models.
Similar content being viewed by others
Notes
The complete data file is provided by Prof. Josef Jablonsky.
References
Ali, A.I., Seiford, L.M.: Translation invariance in data envelopment analysis. Oper. Res. Lett. 10, 403–405 (1990)
Andersen, P., Petersen, N.C.: A procedure for ranking efficient units in data envelopment analysis. Manag. Sci. 39(10), 1261–1264 (1993)
Banker, R.D., Charnes, A., Cooper, W.W.: Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manag. Sci. 30, 1078–1092 (1984)
Briec, W., Kerstens, K.: Multi-horizon Markowitz portfolio performance appraisals: a general approach. Omega 37, 50–62 (2009)
Charnes, A., Cooper, W.W., Rhodes, E.: Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2(6), 429–444 (1978)
Charnes, A., Cooper, W.W., Golany, B., Seiford, L., Stutz, J.: Foundations of data envepoment analysis for Pareto–Koopmans efficient empirical production functions. J. Econ. 30, 91–107 (1985)
Chen, Y.: Measuring super-efficiency in DEA in the presence of infeasibility. Eur. J. Oper. Res. 161, 545–551 (2005)
Du, J., Liang, L., Zhu, J.: A slacks-based measure of super-efficiency in data envelopment analysis: a comment. Eur. J. Oper. Res. 204, 694–697 (2010)
Emrouznejad, A., Yang, G.L.: A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016. Socio-Econ. Plan. Sci. 61, 4–8 (2018). https://doi.org/10.1016/j.seps.2017.01.008
Esmaeilzadeh, A., Hadi-Vencheh, A.: A super-efficiency model for measuring aggregative efficiency of multi-period production systems. Measurement 46(10), 3988–3993 (2013)
Fare, R., Grosskopf, S.: Modelling undesirable factors in efficiency evaluation: comments. Eur. J. Oper. Res. 157, 242–245 (2004)
Guo, I.L., Lee, H.S., Lee, D.: An integrated model for slack-based measure of super-efficiency in additive DEA. Omega 67, 160–167 (2017)
Huang, T.H., Pan, S.C., Wu, P.C.: Country performance evaluation: the DEA model approach. Soc. Indic. Res. 118, 835–849 (2014)
Jablonsky, J.: Efficiency analysis in multi-period systems: an application to performance evaluation in Czech higher education. Cent. Eur. J. Oper. Res. 24, 283–296 (2015)
Koopmans, T.C.: Analysis of production as an efficient combination of activities. In: Koopmans, T.C. (ed.) Activity Analysis of Production and Allocation, pp. 33–97. Wiley, Cowles Commission, New York (1951)
Korhonen, P.J., Luptacik, M.: Eco-efficiency analysis of power plants: an extension of data envelopment analysis. Eur. J. Oper. Res. 154(2), 437–446 (2004)
Lin, R., Chen, Z., Hu, Q., Li, Z.: Multi-period fund performance evaluation: a dynamic network DEA approach with diversification and the directional distance function. OR Spectr. 39, 821–860 (2017)
Liu, W.B., Meng, W., Li, X.X., Zhang, D.Q.: DEA models with undesirable inputs and outputs. Ann. Oper. Res. 173, 117–194 (2010)
Liu, W.B., Meng, W., Sharp, J.: A modified slacks based measure model for data envelopment analysis with natural negative outputs and inputs. J. Oper. Res. Soc. 58, 1672–1677 (2007)
Liu, W., Zhou, Z., Ma, C.X., Liu, D., Shen, W.: Two-stage DEA models with undesirable input-intermediate-outputs. Omega 56, 74–87 (2015)
Lovell, C.A.K., Pastor, J.T., Turner, J.A.: Measuring macroeconomic performance in the OECD: a comparison of European and non-European countries. Eur. J. Oper. Res. 87, 507–518 (1995)
Mahdiloo, M., Noorizadeh, A., Saen, R.F., Tavana, M.: A game theoretic approach to modeling undesirable outputs and efficiency decomposition in data envelopment analysis. Appl. Math. Comput. 244, 479–492 (2014)
Pastor, J.T.: Translation invariance in data envelopment analysis: a generalization. Ann. Oper. Res. 66, 93–102 (1996)
Pastor, J.T., Aparicio, J.: Translation invariance in data envelopment analysis. Int. Ser. Oper. Res. Manag. Sci. 221, 245–268 (2015)
Portela, S., Simpson, G., Thanassoulis, E.: Negative data in DEA: a directional distance approach applied to bank branches. J. Oper. Res. Soc. 55, 1111–1121 (2004)
Seiford, L.M., Zhu, J.: Infeasibility of super-efficiency data envelopment analysis models. Inf. Syst. Oper. Res. 37, 174–187 (1999)
Seiford, L.M., Zhu, J.: Modeling undesirable factors in efficiency evaluation. Eur. J. Oper. Res. 142(1), 16–20 (2002)
Skevas, T., Lansink, A.O., Stefanou, S.E.: Measuring technical efficiency in the presence of pesticide spillovers and production uncertainty: the case of Dutch arable farm. Eur. J. Oper. Res. 223(2), 550–559 (2012)
Tone, K.: A slacks-based measure of efficiency in data envelopment analysis. Eur. J. Oper. Res. 130, 498–509 (2002)
Wei, W., Xia, H.-S.: Undesirable output based evaluation of airports productivity. Syst. Eng. Theory Pract. 34(1), 138–146 (2014)
Wojcik, V., Dyckhoff, H., Gutgesell, S.: The desirable input of undesirable factors in data envelopment analysis. Ann. Oper. Res. 259(1–2), 461–484 (2017)
Zhou, Z., Liu, W.: DEA models with undesirable inputs, intermediates, and outputs. In: Zhu, J. (ed.) Data Envelopment Analysis: A Handbook of Models and Methods, pp. 415–446. Springer, New York (2015)
Zhu, J.: Quantitative Models for Performance Evaluation and Benchmarking Data Envelopment Analysis with Spreadsheets. Kluwer, Boston (2003)
Acknowledgements
The first author is thankful to CSIR (1061440740), India, for financial grant to pursue this research. The authors are thankful to Prof. Josef Jablonsky, Czech Republic, for providing the complete 4 year data used in Sect. 4. The authors are thankful to the esteemed referees for their valuable inputs and comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bansal, P., Mehra, A. Multi-period additive efficiency measurement in data envelopment analysis with non-positive and undesirable data. OPSEARCH 55, 642–661 (2018). https://doi.org/10.1007/s12597-018-0343-z
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12597-018-0343-z