A variant of radial measure capable of dealing with negative inputs and outputs in data envelopment analysis
AbstractData envelopment analysis (DEA) is a linear programming methodology to evaluate the relative technical efficiency for each member of a set of peer decision making units (DMUs) with multiple inputs and multiple outputs. It has been widely used to measure performance in many areas. A weakness of the traditional DEA model is that it cannot deal with negative input or output values. There have been many studies exploring this issue, and various approaches have been proposed. In this paper, we develop a variant of the traditional radial model whereby original values are replaced with absolute values as the basement to quantify the proportion of improvements to reach the frontier. The new radial measure is units invariant and can deal with all cases of the presence of negative data. In addition, the VRM model preserves the property of proportionate improvement of a traditional radial model, and provides the exact same results in the cases that the traditional radial model can deal with. Examples show the advantages of the new approach.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 30951.
Date of creation: 17 May 2011
Date of revision:
Data Envelopment Analysis; Negative data in DEA; Variant of radial measure; Unit invariance;
Other versions of this item:
- Cheng, Gang & Zervopoulos, Panagiotis & Qian, Zhenhua, 2013. "A variant of radial measure capable of dealing with negative inputs and outputs in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 225(1), pages 100-105.
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-05-30 (All new papers)
- NEP-ECM-2011-05-30 (Econometrics)
- NEP-EFF-2011-05-30 (Efficiency & Productivity)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Seiford, Lawrence M. & Zhu, Joe, 2002. "Modeling undesirable factors in efficiency evaluation," European Journal of Operational Research, Elsevier, vol. 142(1), pages 16-20, October.
- Emrouznejad, Ali & Anouze, Abdel Latef & Thanassoulis, Emmanuel, 2010. "A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA," European Journal of Operational Research, Elsevier, vol. 200(1), pages 297-304, January.
- Lamb, John D. & Tee, Kai-Hong, 2012. "Data envelopment analysis models of investment funds," European Journal of Operational Research, Elsevier, vol. 216(3), pages 687-696.
- Shawna Grosskopf & Kathy J. Hayes & Lori L. Taylor & William L. Weber, 1999. "Anticipating the Consequences of School Reform: A New Use of DEA," Management Science, INFORMS, vol. 45(4), pages 608-620, April.
- Charnes, A. & Cooper, W. W. & Golany, B. & Seiford, L. & Stutz, J., 1985. "Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 91-107.
- Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
- Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
- Scheel, Holger, 2001. "Undesirable outputs in efficiency valuations," European Journal of Operational Research, Elsevier, vol. 132(2), pages 400-410, July.
- R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
- Portela, Maria Conceicao A. Silva & Thanassoulis, Emmanuel, 2007. "Comparative efficiency analysis of Portuguese bank branches," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1275-1288, March.
- Edirisinghe, N.C.P. & Zhang, X., 2007. "Generalized DEA model of fundamental analysis and its application to portfolio optimization," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3311-3335, November.
- Emrouznejad, Ali & Amin, Gholam R. & Thanassoulis, Emmanuel & Anouze, Abdel Latef, 2010. "On the boundedness of the SORM DEA models with negative data," European Journal of Operational Research, Elsevier, vol. 206(1), pages 265-268, October.
- Cordero Ferrera, Jose Manuel & Alonso Morán, Edurne & Nuño Solís, Roberto & Orueta, Juan F. & Souto Arce, Regina, 2013. "Efficiency assessment of primary care providers: A conditional nonparametric approach," MPRA Paper 51926, University Library of Munich, Germany.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).
If references are entirely missing, you can add them using this form.