Abstract
Data Envelopment Analysis (DEA) is a mathematical programming approach for measuring efficiency of Decision Making Units (DMUs). In traditional DEA, a ratio of weighted outputs to inputs is examined and, for each DMU, some optimal weights are obtained. The method of cross-efficiency is an extension to DEA by which a matrix of scores is computed. The elements of the matrix are computed by means of the weights obtained via usual models of DEA. The cross-efficiency may have some drawbacks, e.g., the cross-efficiency scores may be multiple due to the presence of several optima. To overcome this issue, secondary goals are used. However, this method has never been used for peer evaluation of DMUs with undesirable outputs. In this paper, our objective is to bridge this gap. For this end, we introduce a new secondary goal, test it on an empirical example with undesirable outputs, report the results, and finally, we give some concluding remarks.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Banker, R.D., Charnes, A., Cooper, W.W.: Some models for estimating technical and scale inefficiences in data envelopment analysis. Management Science 30, 1078–1091 (1984)
Beasley, J.E.: Allocating fixed costs and resources via data envelopment analysis. European Journal of Operational Research 147, 198–216 (2003)
Charnes, A., Cooper, W.W., Rhodes, E.: Measuring the efficiency of decision making units. European Journal of Operational Research 1, 429–444 (1987)
Chen, T.Y.: An assessment of technical efficiency and cross-efficiency in Taiwan’s electricity distribution sector. European Journal of Operational Research 137, 421–433 (2002)
Cook, W.D., Seiford, L.M.: Data envelopment analysis (DEA): Thirty years on. European Journal of Operational Research 2, 1–17 (2009)
Cooper, W.W., Ramon, N., Ruiz, J.L., Sirvent, I.: Avoiding Large Differences in Weights in Cross-Efficiency Evaluations: Application to the Ranking of Basketball Players. Journal of CENTRUM Cathedra 4(2), 197–215 (2011)
Doyle, J., Green, R.: Efficiency and cross efficiency in DEA: Derivations, meanings and the uses. Journal of the Operational Research Society 54, 567–578 (1994)
Ehrgott, M.: Multicriteria Optimization. Springer (2005)
Fare, R., Grosskopf, S., Lovel, C.A.K.: Multilateral productivity comparisons when some outputs are undesirable: a nonparametric approach. The Review of Economics and Statistics 66, 90–98 (1989)
Fare, R., Grosskopf, S., Lovel, C.A.K., Yaiswarng, S.: Deviation of shadow prices for undesirable outputs: a distance function approach. The Review of Economics and Statistics 218, 374–380 (1993)
Gulpinar, N., Le Thi, H.A., Moeini, M.: Robust Investment Strategies with Discrete Asset Choice Constraints Using DC Programming. Optimization 59(1), 45–62 (2010)
Hailu, A., Veeman, T.: Non-parametric productivity analysis with undesirable outputs: an application to Canadian pulp and paper industry. American Journal of Agricultural Economics, 605–616 (2001)
Kuosmanen, T.: Weak Disposability in Nonparametric Productivity Analysis with Undesirable Outputs. American Journal of Agricultural Economics 37, 1077–1082 (2005)
Kuosmanen, T., Poidinovski, V.: A Weak Disposability in Nonparametric Productivity Analysis with Undesirable Outputs: Reply to Fare and Grosskopf. American Journal of Agricultural Economics 18 (2009)
Liang, L., Wu, J., Cook, W.D., Zhu, J.I.: Alternative secondary goals in DEA cross efficiency evaluation. International Journal of Production Economics 36, 1025–1030 (2008)
Rodder, W., Reucher, E.: A consensual peer-based DEA-model with optimized cross-efficiencies: input allocation instead of radial reduction. European Journal of Operational Research 36, 148–154 (2011)
Rodder, W., Reucher, E.: Advanced X-efficiencies for CCR- and BCC-models: towards Peer-based DEA controlling. European Journal of Operational Research 219, 467–476 (2012)
Seiford, L.M., Zhu, J.: Modeling undesirable factors in efficiency evaluation. European Journal of Operational Research 48, 16–20 (2002)
Sexton, T.R., Silkman, R.H., Hogan, A.J.: Data envelopment analysis: Critique and extensions. In: Silkman, R.H. (ed.) Measuring Efficiency: An Assessment of Data Envelopment Analysis, vol. 3, pp. 73–105. Jossey-Bass, San Francisco (1986)
Tone, K.: Dealing with undesirable outputs in DEA: a slacks-based measure (SBM) approach. Presentation at NAPWIII, Toronto (2004)
Wang, Y.M., Chin, K.S.: Some alternative models for DEA cross efficiency evaluation. International Journal of Production Economics 36, 332–338 (2010)
Wu, C., Li, Y., Liu, Q., Wang, K.: A stochastic DEA model considering undesirable outputs with weak disposability. Mathematical and Computer Modeling (2012), doi:10.1016/j.mcm.2012.09.022
Wu, J., An, Q., Xiong, B., Chen, Y.: Congestion measurement for regional industries in China: A data envelopment analysis approach with undesirable outputs. Energy Policy 57, 7–13 (2013)
Wu, J., An, Q., Ali, S., Liang, L.: DEA based resource allocation considering environmental factors. Mathematical and Computer Modelling 58(5-6), 1128–1137 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Moeini, M., Karimi, B., Khorram, E. (2015). A Cross-Efficiency Approach for Evaluating Decision Making Units in Presence of Undesirable Outputs. In: Le Thi, H., Pham Dinh, T., Nguyen, N. (eds) Modelling, Computation and Optimization in Information Systems and Management Sciences. Advances in Intelligent Systems and Computing, vol 360. Springer, Cham. https://doi.org/10.1007/978-3-319-18167-7_42
Download citation
DOI: https://doi.org/10.1007/978-3-319-18167-7_42
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18166-0
Online ISBN: 978-3-319-18167-7
eBook Packages: EngineeringEngineering (R0)