Measuring the efficiency of decision making units

In management contexts, mathematical programming is usually used to evaluate a collection of possible alternative courses of action en route to selecting one which is best. In this capacity, mathematical programming serves as a planning aid to management. Data Envelopment Analysis reverses this role and employs mathematical programming to obtain ex post facto evaluations of the relative efficiency of management accomplishments, however they may have been planned or executed. Mathematical programming is thereby extended for use as a tool for control and evaluation of past accomplishments as well as a tool to aid in planning future activities. The CCR ratio form introduced by Charnes, Cooper and Rhodes, as part of their Data Envelopment Analysis approach, comprehends both technical and scale inefficiencies via the optimal value of the ratio form, as obtained directly from the data without requiring a priori specification of weights and/or explicit delineation of assumed functional forms of relations between inputs and outputs. A separation into technical and scale efficiencies is accomplished by the methods developed in this paper without altering the latter conditions for use of DEA directly on observational data. Technical inefficiencies are identified with failures to achieve best possible output levels and/or usage of excessive amounts of inputs. Methods for identifying and correcting the magnitudes of these inefficiencies, as supplied in prior work, are illustrated. In the present paper, a new separate variable is introduced which makes it possible to determine whether operations were conducted in regions of increasing, constant or decreasing returns to scale in multiple input and multiple output situations. The results are discussed and related not only to classical single output economics but also to more modern versions of economics which are identified with "contestable market theories."

http://www.utdallas.edu/~ryoung/phdseminar/BCC1984.pdf

Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis

Fuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. All chapters have been updated. Exercises are included.

https://www.springer.com/productFlyer_978-0-7923-7435-0.pdf?SGWID=0-0-1297-33300503-0

Fuzzy Set Theory - and Its Applications

1. Introduction and Overview. 2. Detecting Influential Observations and Outliers. 3. Detecting and Assessing Collinearity. 4. Applications and Remedies. 5. Research Issues and Directions for Extensions. Bibliography. Author Index. Subject Index.

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

List of Tables. List of Figures. Preface. 1. General Discussion. 2. The Basic CCR Model. 3. The CCR Model and Production Correspondence. 4. Alternative DEA Models. 5. Returns to Scale. 6. Models with Restricted Multipliers. 7. Discretionary, Non-Discretionary and Categorical Variables. 8. Allocation Models. 9. Data Variations. Appendices. Index.

Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software

Preface G. Kozmetsky. Part I: Concepts, Models & Computation. 1. Introduction. 2. Basic DEA Models. 3. Extensions to DEA Models. 4. Computational Aspects of DEA A. Iqbal Ali. 5. DEA Software Packages. Part II: Novel Applications. 6. Evaluating the Impacts of Operating Strategies on Efficiency in the U.S. Airline Industry R.D. Banker, H.H. Johnston. 7. Analyzing Technical and Allocative Efficiency of Hospitals P. Byrnes, V. Valdmanis. 8. A Multi Period Analysis of Market Segments and Brand Efficiency in the Competitive Carbonated Beverage Industry A. Charnes, W.w. Cooper, B. Golanyi, F.Y. Phillips, J.J. Rousseau. 9. Exploring why Some Physicians' Hospital Practices are More Efficient: Taking DEA Inside the Hospital J. Chilingerian. 10. On the Measurement and Monitoring of Relative Efficiency of Highway Maintenance Patrols W.D. Cook, A. Kazakov, Y. Roll. 11. Strategic Leaders in the U.S. Brewing Industry: a Longitudinal Analysis of Outliers D. Day, A.Y. Lewin, R. Salazar, Hongyu Li. 12. A Spatial Efficiency Framework for the Support of Locational Decision A. Desai, K. Haynes, J. Storbeck. 13. Productivity Developments in Swedish Hospitals: a Malmquist Output Index Approach R. Fare, S. Grosskopf, B. Lindgren, P. Roos. 14. Ownership Type, Property Rights and Relative Efficiency G. Ferrier. 15. A Comparative Analysis of Ferry Transport in Norway F.R. Forsund, E. Hernaes. 16. Incorporating Standards via Data Envelopment Analysis B. Golany, Y. Roll. 17.Stratified Models of Education Production Using Modified DEA and Regression Analysis C.A. Knox Lovell, L.C. Walters, L.L. Woods. 18. The Problems of New and Disappearing Commodities in the Construction of Price Indexes C.A. Knox Lovell, K.D. Zieschang. 19. Evaluating the Relative Efficiency of Baseball Players? M.J. Mazur. 20. Sensitivity Analysis of Efficiency Measures with Applications to Kansas Farming and Illinois Coal Mining R. Thompson, P.S. Dharmapala, R.M. Thrall. Part III: Epilogue: Process and Bibliography. 21. The DEA Process, Usages and Interpretations. 22. DEA Bibliography L.M. Seiford. References. Index.

William W. Cooper

Papers

Measuring the efficiency of decision making units

Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis

Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software

"Data Envelopment Analysis: Theory, Methodology, and Applications"

Programming with linear fractional functionals