Cheng, Gang and Zervopoulos, Panagiotis and Qian, Zhenhua (2011): A variant of radial measure capable of dealing with negative inputs and outputs in data envelopment analysis.
Download (200kB) | Preview
Data 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.
|Item Type:||MPRA Paper|
|Original Title:||A variant of radial measure capable of dealing with negative inputs and outputs in data envelopment analysis|
|Keywords:||Data Envelopment Analysis; Negative data in DEA; Variant of radial measure; Unit invariance|
|Subjects:||C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C67 - Input-Output Models
|Depositing User:||Panagiotis Zervopoulos|
|Date Deposited:||17. May 2011 23:16|
|Last Modified:||15. Feb 2013 22:46|
 Charnes A., Cooper W.W.,Rhodes E., Measuring the efficiency of decision making units, European Journal of Operational Research, 2(1978) 429-444.
 Scheel H., Undesirable outputs in efficiency valuations, European Journal of Operational Research, 132(2001) 400-410.
 Zhu J., Quantitative Models for Performance Evaluation and Benchmarking: DEA with Spreadsheets, Springer, 2009.
 Ali A.I.,Seiford L.M., Translation-Invariance in Data Envelopment Analysis, Operations Research Letters, 9(1990) 403-405.
 Cooper W.W., Seiford L.M.,Tone K., Data envelopment analysis: a comprehensive text with models, applications, references and DEA-Solver software, Springer Science + Business Media, 2007.
 Charnes A., Cooper W.W., Seiford L.,Stutz J., Invariant Multiplicative Efficiency and Piecewise Cobb-Douglas Envelopments, Operations Research Letters, 2(1983) 101-103.
 Lovell C.A.K.,Pastor J.T., Units invariant and translation invariant DEA models, Operations Research Letters, 18(1995) 147-151.
 Seiford L.M.,Zhu J., Modeling undesirable factors in efficiency evaluation, European Journal of Operational Research, 142(2002) 16-20.
 Charnes A., Cooper W.W., Golany B., Seiford L.,Stutz J., Foundations of Data Envelopment Analysis for Pareto-Koopmans Efficient Empirical Production-Functions, Journal of Econometrics, 30(1985) 91-107.
 Pastor J.T., Translation invariance in data envelopment analysis: A generalization, Annals of Operations Research, 66(1996) 93-102.
 Portela M.C.A.S., Thanassoulis E.,Simpson G., Negative data in DEA: a directional distance approach applied to bank branches, Journal of the Operational Research Society, 55(2004) 1111-1121.
 Sharp J.A., Meng W.,Liu W., A modified slacks-based measure model for data envelopment analysis with 'natural' negative outputs and inputs, Journal of the Operational Research Society, 58(2007) 1672-1677.
 Emrouznejad A., Anouze A.L.,Thanassoulis E., A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA, European Journal of Operational Research, 200(2010) 297-304.
 Emrouznejad A., Amin G.R., Thanassoulis E.,Anouze A.L., On the boundedness of the SORM DEA models with negative data, European Journal of Operational Research, 206(2010) 265-268.
 Banker R.D., Charnes A.,Cooper W.W., Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science, 30(1984) 1078-1092.
 Chambers R.G., Chung Y.,Färe R., Benefit and Distance Functions, Journal of Economic Theory, 70(1996) 407-419.
 Chung Y.H., Färe R.,Grosskopf S., Productivity and undesirable outputs: A directional distance function approach, Journal of Environmental Management, 51(1997) 229-240.
 Chambers R.G., Chung Y.,Färe R., Profit, directional distance functions, and Nerlovian efficiency, Journal of Optimization Theory and Applications, 98(1998) 351-364.
Available Versions of this Item
- A variant of radial measure capable of dealing with negative inputs and outputs in data envelopment analysis. (deposited 17. May 2011 23:16) [Currently Displayed]