Abstract
This paper describes how the recent, published DEA/AR theory, in conjunction with software, provides measures of radial efficiency and profit ratios, This new DEA theory does not require use of the non-Archimedean principle, i.e., positive infinitesimals, and it allows for analysis of zero data entries. Further, this theory provides a comprehensive classification of the measures for both the efficient and inefficient decision-making units (DMUs). As programmed in the software, the efficiency principles are relative to the Charnes-Cooper-Rhodes ratio model and the Banker-Charnes-Cooper convex model, and the profitability principles are relative to the Thompson-Thrall profit ratio model. An illustrative application to 48 large U.S. banks illustrates some of the most fundamental computations, which are developed for a base option. Additional options may be exercised by the user to more fully utilize the theory. Additions to the software are being made to computer “analytic centers” and to make multiplier sensitivity analyses. Software utility updates and new DEA theory contributions continue to complement this computational capability.
Similar content being viewed by others
References
A.I. Ali and W.M. Seiford, The mathematical approach to efficiency analysis, in:The Measurement of Productive Efficiency, H.O. Fried, C.A.K. Lovell and S.S. Schmidt, eds., Oxford University Press, New York, 1993, pp. 120–159.
R.D. Banker, Estimating most productive scale size using data envelopment analysis, European Journal of Operational Research 17(1984)35–44.
R.D. Banker, A. Charnes and W.W. Cooper, Some models for estimating technical and scale efficiencies in Data Envelopment Analysis, Management Science 30(1984)1078–1092.
R.D. Banker and R.M. Thrall, Estimation of returns to scale dusing Data Envelopment Analysis,European Journal of Operational Research 62(1992)74–84.
R.F. Barr, L. Seiford and T. Siems, Envelopment analysis approach to measuring managerial quality of banks, Annals of Operations Research 45(1993)1–19.
P.W. Bauer, A.N. Berger and D.B. Humphrey, Efficiency and productivity growth in U.S. banking, in:The Measurement of Productive Efficiency, H.O. Fried, C.A.K. Lovell and S.S. Schmidt, eds., Oxford University Press, New York, 1993, pp. 386–414.
S.A. Berg, F.R. Forsund and E.S. Jansen, Technical efficiency of Norwegian banks: The nonparametric approach to efficiency measurements, Journal of Productivity Analysis 2(1992) 127–142.
A.N. Berger and D.B. Humphrey, Measurement and efficiency issues in commercial banking, in:Output Measurement in the Service Sectors, Z. Grilisches, ed., National Bureau of Economic Research, University of Chicago Press, Chicago, 1992).
A. Charnes and W.W. Cooper, Preface to Topicsd in data Envelopment Analysis, Annals of Operations Research 2(1985)59–94.
A. Charnes, W.W. Cooper and E. Rhodes, Measuring the efficiency of decision making units, European Journal of Operational Research 2 (1978)429–444.
A. Charnes, W.W. Cooper and E. Rhodes, Short Communication: Measuring the efficiency of decision making units, European Journal of Operational Research 3(1979) 339.
A. Charnes, W.W. Cooper, Z.M. Huang and D.B. Sun, Polyhedral cone-ratio models with an illustrative application to large commercial banks, Journal of Economtris 46(1990)73–91.
A. Charnes, W.W. Cooper, A.Y. Lewin and L.M. Seiford, Basic DEA models, in:Data Envelopment Analysis: Theory, Methodology and Applications, Kluwer Academic, Boston, 1994.
A. Charnes, W.W. Cooper and R.M. Thrall, A structure for classifying and characterizing efficiencies and inefficiencies in Data Envelopment Analysis, Journal of Productivity Analysis 2(1991)197–237.
A. Charnes, W.W. Cooper and R.M. Thrall, Classifying and characterizing efficiencies and inefficiencies in Data Envelopment Analysis, Operations Research Letters 5(1986)105–110.
W.W. Cooper, S. Kumbhaker, R.M. Thrall and X. Yu, DEA and stochastic frontier analysis of the 1978 Chinese economic reforms, Journal of Socio-Economic Planning Sciences (1995); see also IC2 Working Paper 92-05-01.
E. Elyasiani and S. Mehdian, Efficiency in the commercial banking industry, a production frontier approach, Applied Economics 22(1990)1–13.
M.J. Farrell, The mesurement of productive efficiency, Journal of the Royal Statistical Society A120(1957)251–281.
G.D. Ferrier and C.A.K. Lovell, Measuring cost efficiency in banking: Econometric and linear programming evidence, Journal of Econometrics 46(1990)229–245.
M.D. González-Lima, R.A. Tapia and R.M. Thrall, On the construction of strong complementarity slackness solutions for DEA linear programming problems using a primal-dual interior-point method, Annals of Operations Research 66(1996)139–162.
T.C. Koopmans, Efficient allocation of resources, Econometrica 19(1951)455–465.
C.A.K. Lovell, Production frontiers and productive efficiency, in:The Measurement of Productive Efficiency, H.O. Fried, C.A.K. Lovell and S.S. Schmidt, eds., Oxford University Press, New York, 1993.
N. Rangan, R. Grabowski, H.Y. Aly and C. Pasurka, The technical efficiency of U.S. Banks, Economic Letters 28(1988)169–175.
L.H. Seiford and R.M. Thrall, Recent developments in DEA: The mathematical programming approach, Journal of Econometrics 46(1990)7–38.
D.B. Sun, Evaluation of managerial performance in large commercial banks by Data Envelopment Analysis, Ph.D. Dissertation, University of Texas at Austin, 1988, unpublished.
R.G. Thompson, P.S. Dharmapala and R.M. Thrall, DEA sensitivity analysis of efficiency measures with applications to Kansas farming and Illinois coal mining, in:Data Envelopment Analysis: Theory, Methodology and Applications, A. Charnes, W.W. Cooper, L. Seiford and A. Lewin, eds., Kluwer Academic, Boston, 1994.
R.G. Thompson, P.S. Dharmapala and R.M. Thrall, Importance for DEA of zeros in data and multipliers, Journal of Productivity Analysis 4(1993)337–348.
R.G. Thompson, P.S. Dharmapala and R.M. Thrall, DEA linked-cone efficiency and profitability potential with application to Illinois coal mines, International Journal of Production Economics (1994) 1–17.
R.G. Thompson, P.S. Dharmapala, J. Diaz, M.D. González-Lima and R.M. Thrall, DEA multiplier analytic center sensitivity with an illustrative application to independent oil companies, Annals of Operations Research 66(1996)163–177.
R.G. Thompson, C.-T. Lee and R.M. Thrall, Fixed weights and DEA, Applications in Management Science 7(1993)171–191.
R.G. Thompson, L. Langemeier, C.-T. Lee, E. Lee and R.M. Thrall, The role of multiplier bounds in efficiency analysis with an application to Kansas farming, Journal of Econometrics 46(1990) 93–108.
R.G. Thompson, F.D. Singleton, Jr., B.A. Smith and R.M. Thrall, Comparative site evaluations for locating high energy lab in Texas, TIMS Interfaces (1986) 1380–1395.
R.G. Thompson, P.S. Dharmapala, D.B. Humphrey, W.M. Taylor and R.M. Thrall, DEA/AR efficiency and profitability of the U.S. 48 largest commercial banks, 1980–1990, Working Paper No. 107, Jones School of Administration, Rice University, February 1994.
R.G. Thompson and R.M. Thrall, Polyhedral assurance regions with linked constraints, In:New Directions in Computational Economics, W.W. Cooper and A.B. Whinston, eds., Kluwer Academic, Boston, 1994, pp. 121–133.
R.M. Thrall, Duality, classification and slacks in DEA, Annals of Operations Research 66(1996) 109–138.
H.R. Varian, Goodness-of-fit in optimizing models, Journal of Econometrics 46(1990)125–140.
Author information
Authors and Affiliations
Additional information
DEA is an advanced operations research method called Data Envelopment Analysis, and AR is an assurance region method used to bound the multipliers in the DEA model. Underlying data have been deposited with the editors.
Rights and permissions
About this article
Cite this article
Thompson, R.G., Dharmapala, P.S., Humphrey, D.B. et al. Computing DEA/AR efficiency and profit ratio measures with an illustrative bank application. Ann Oper Res 68, 301–327 (1996). https://doi.org/10.1007/BF02207220
Issue Date:
DOI: https://doi.org/10.1007/BF02207220