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

: The Cobb-Douglas function is widely used in production economics in the following form: A = AL sub alpha K sub beta, where alpha and beta along with A are positive constants that relate the inputs L (=Labor) and K (=Capital) to the amount of output Q. A variety of supposed alternatives and generalizations have been suggested in place of the Cobb-Douglas form for use in production economics. These alternatives and generalizations are here shown to be representable in an extended Cobb-Douglas form in which A, alpha and beta are functions of L an K rather than constants. This extension is then formally related to other general forms, such as the minimum discrimination information statistics, and used to explain the successful uses of the Cobb-Douglas function for the empirical applications in many different countries and contexts. Keywords: Production function; Aggregation; Homogenous functions.

An Extended Cobb-Douglas Form for Use in Production Economics.

The Efficiency of Joint Versus Service-Specific Advertising

“Small sample properties of ML, COLS and DEA estimators of frontier models in the presence of heteroscedasticity” by A.N. Bojanic, S.B. Caudill and J.M. Ford, European Journal of Operational Research 108, 1998, 140–148: A comment

Rapid Urbanization and Its Problems

: The construction and analysis of Pareto-optimal frontier production functions by a new Data Envelopment Analysis method is developed in the context of new theoretical characterizations of the inherent structure and capabilities of such empirical production functions. Contrasts and connections with other developments, including solutions of some remaining problems, are made re aspects such as informatics, economies of scale, isotonicity and non-concavity, discretionary and nondiscretionary inputs, piecewise linearity, partial derivatives and Cobb-Douglas properties of the functions. Non-Archimedean constructs are not required. (Author)

/pdf/pareto-optimality-efficiency-analysis-and-empirical-5gtwdmye97.pdf

William W. Cooper

Papers

An Extended Cobb-Douglas Form for Use in Production Economics.

The Efficiency of Joint Versus Service-Specific Advertising

“Small sample properties of ML, COLS and DEA estimators of frontier models in the presence of heteroscedasticity” by A.N. Bojanic, S.B. Caudill and J.M. Ford, European Journal of Operational Research 108, 1998, 140–148: A comment

Rapid Urbanization and Its Problems

Pareto-Optimality, Efficiency Analysis and Empirical Production Functions.