Abstract
The appearance of strictly positive slack variables in DEA solutions causes well known computational and analytical problems studied by Olesen and Petersen (1996) and Green et al. (1996) under constant returns to scale. This paper discusses variable returns to scale and suggests the use of efficient facets (EFs) in the reference technology. It is found to give a lower bound of the efficiency scores. Most importantly, efficiency measured with respect to EFs—the EF based efficiency index—may decrease if additional variables are introduced but are disposed in production. Thus, units are penalized for disposal of incoming variables, and the EF based efficiency index captures the net efficiency of a unit. EF is found to be a useful tool also to search a suitable set of variables for efficiency measurement. Its use is demonstrated with Finnish university data and it is found to change the measured performance of the university sector quite significantly.
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References
Agha, I. A. and L. M. Seiford. (1993a). “Computational Accurancy and Infinitesimals in Data Envelopment Analysis.” INFOR 31(4), 290-297.
Agha, I. A. and L. M. Seiford. (1993b). “The Mathematical Programming Approach to Efficiency Analysis.” In The Measurement of Productive Efficiency, Techniques and Applications. pp. 120-159, Oxford University Press.
Banker, R. D., A. Charnes and W. W. Cooper. (1984). “Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis.” Management Science 30(9), 1078-1092.
Bessent, A., W. Bessent, J. Elam and T. Clark. (1988). “Efficiency Frontier Determination by Constrained Facet Analysis.” Operations Research 36(5), 785-796.
Charnes, A., W. W. Cooper and E. Rhodes. (1978). “Measuring the Efficiency of Decision Making Units.” European Journal of Operational Research 2(6), 429-444.
Charnes, A., W. W. Cooper and R. M. Thrall. (1991). “A Structure for Classifying and Characterizing Efficiency and Inefficiency in Data Envelopment Analysis.” The Journal of Productivity Analysis 2(3), 197-237.
Färe, R. (1988). Fundamentals of Production Theory,Volume 311 of Lecture Notes in Economics and Mathematical Systems. Springer-Verlag.
Green, R. H., J. R. Doyle and W. D. Cook. (1996). “Efficiency Bounds in Data Envelopment Analysis.” European Journal of Operational Research 89, 482-490.
Mäkilä, A. (1995). Korkeakoulujen tehokkuuden arviointi data envelopment analysis-menetelmällä. Korkeakouluneuvoston julkaisuja 2/95, Opetusministeriö.
Nemhauser, G. L. and L. A. Wolsey. (1988). Integer and Combinatorial Optimization. Wiley Interscience Series in Discrete Mathematics and Optimization. John Wiley & Sons.
Olesen, O. B. and N. C. Petersen. (1991). “Collinearity in Data Envelopment Analysis: An Extended Facet Approach.” Working Paper 1, Department of Management, Odense University.
Olesen, O. B. and N. C. Petersen. (1996). “Indicators of Ill-Conditioned Data Sets and Model Misspecification in Data Envelopment Analysis: An Extended Facet Approach.” Management Science 42(2), 205-219.
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Räty, T. Efficient Facet Based Efficiency Index: A Variable Returns to Scale Specification. Journal of Productivity Analysis 17, 65–82 (2002). https://doi.org/10.1023/A:1013584203829
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DOI: https://doi.org/10.1023/A:1013584203829