zbMATH — the first resource for mathematics

Polyhedral cone-ratio DEA models with an illustrative application to large commercials banks. (English) Zbl 0712.90015
Summary: Polyhedral Cone-Ratio Data Envelopment Analysis Models generalizing the CCR Ratio Model are developed for situations with a finite number of DMUs and employing polyhedral cones of virtual multipliers. They provide improved definitions of efficiency over CCR models whose input-output data and/or numbers of DMUs are inadequate to capture aspects or restrictions which should be involved. The focus here is on the sum form for cones which easily provides for capturing exogenous expert opinion as well as mathematical reduction to the old form with its very powerful software. Transformation from the usual intersection form to it and vice versa is explicitly given. Thereby the advantages of either or both are available. The theory is illustrated with two-dimensional examples and by real banking examples for motivation.

91B66 Multisectoral models in economics
90C90 Applications of mathematical programming
62P20 Applications of statistics to economics
90C05 Linear programming
Full Text: DOI
[1] Bessent, A.; Bessent, W.; Charnes, A.; Cooper, W.W.; Thorogood, N., Evaluation of educational proposals by means of DEA, Educational administration quarterly, 19, 82-92, (1983)
[2] Ben-Israel, A.; Charnes, A.; Kortanek, K.O., Duality and asymptotic solvability over cones, Bulletin of American mathematical society, 75, 318-324, (March 1969)
[3] Charnes, A.; Cooper, W.W., Preface to topics in data envelopment analysis, Annals of operations research, 2, 59-94, (1985)
[4] Charnes, A.; Golany, B.; Halek, R.; Klopp, G.; Schmitz, E.; Thomas, D., Data analysis approaches to policy evaluation and management of army recruiting activities I: tradeoffs between joint services and army advertising, ()
[5] Charnes, A.; Seiford, L.; Stutz, J., Foundations of Pareto-koopmans optimality efficiency analysis and empirical production functions, Journal of econometrics, 30, 91-107, (1985) · Zbl 0582.90007
[6] Charnes, A.; Huang, Z.M.; Sun, D.B., Relations between half-space and finitely generated cones in polyhedral cone-ratio DEA models, () · Zbl 0747.93007
[7] Charnes, A.; Rhodes, E., Measuring the efficiency of decision making units, European journal of operations research, 2, 429-444, (1978) · Zbl 0416.90080
[8] Charnes, A., Data envelopment analysis as an approach for evaluating program and managerial efficiency - with an illustrative application to the program follow thr ough experiment in U.S. public school education, Management science, 27, 668-697, (1981)
[9] Charnes, A.; Rousseau, J.; Semple, J., Data envelopment analysis and axiomatic notions of efficiency and reference sets, (), forthcoming · Zbl 0786.90035
[10] Charnes, A.; Wei, Q.L.; Huang, Z.M., Cone-ratio data envelopment analysis and multi-objective programming, (), 1099-1118 · Zbl 0678.90083
[11] Charnes, A.; Seiford, L.; Stutz, J., Invariant multiplicative efficiency and piecewise cobb-Douglas envelopments, Operations research letters, 2, 101-103, (1983) · Zbl 0521.90066
[12] Divine, J.D., Efficiency analysis and management of not-for-profit and governmentally regulated organizations, ()
[13] Huang, Z.M., The second order conditions of nondominated solutions for generalized multiobjective mathematical programming, Journal of systems science and mathematical science, 5, 172-184, (1985) · Zbl 0591.90087
[14] Seiford, L.; Thrall, R., Recent developments in DEA: the mathematical programming approach to frontier analysis, Journal of econometrics, (1989), this issue.
[15] Sun, D.B., Evaluation of managerial performance of large commercial banks by data envelopment analysis, ()
[16] Thomas, D.L., Auditing the efficiency of regulated companies: an application of data envelopment analysis to electric cooperatives, (1986), IC^2 Institute, University of Texas Austin, TX
[17] Thompson, R.G.; Singleton, F.D.; Thrall, R.M.; Smith, B.A., Comparative site evaluations for locating a high energy physics lab in Texas, Interfaces, 16, 35-49, (December 1985)
[18] Yu, P.L., Cone convexity, cone extreme point, and nondominated solutions in decision problems with multi-objectives, Journal of optimization theory and application, 14, 319-377, (1974) · Zbl 0268.90057
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.