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

Marginal rates and elasticities of substitution are derived from the optimal slack values obtained from modified versions of additive DEA models. Projection formulas are used to ensure that all points are on the efficient frontier as required for conformance with assumptions in micro-economics. The models used differ from standard versions in that slack values are allowed to be negative as well as positive in these additive models. This makes movement possible on efficiency frontiers, where improvement in some inputs or outputs requires worsening other inputs or outputs. A new definition is therefore introduced in which efficiency is attained only if the value of the worsenings is exactly offset by the value of the improvements. This includes, but is not restricted to, the case in which all slacks must be zero for full attainment of efficiency—as in standard versions of additive models.

Marginal Rates and Elasticities of Substitution with Additive Models in DEA

Kohler's Dictionary for accountants

Two-stage financial risk tolerance assessment using data envelopment analysis

Using data obtained from Chinese sources for the period 1966–1988, this paper reports results from a study of the impact of the 1978 economic reforms for the period 1966–1988 on the Textiles, Chemicals and Metallurgical Industries. In all three, the effects were found to be dramatic and manifested almost immediately in: (1) drastic changes in capital-to-labor ratios; (2) large increases in output; and (3) significant increases in efficiency. DEA (Data Envelopment Analysis) and SF (Stochastic Frontier Analysis) provide analytic frameworks which are interpreted as follows. Via its single optimization over all observations, SF estimates are addressed to behavior across all periods while n optimizations used in DEA (one for each observation) are addressed to performances in each of the periods that are applicable for effecting its evaluations. Although based on different principles and treating the data in different ways, these two different approaches to performance evaluation, as used here, provide confirmation of each other's findings. The adjustments to the data obtained from efficiency evaluations in these two approaches are also used to show that trends underlying the observed behavior would have accelerated under fully efficient production. The joint use made here of DEA and SF contrasts with points of view that have regarded these two approaches as mutually exclusive alternatives. A new ratio measure of efficiency is also introduced in furtherance of DEA as a body of concepts in its own right.

William W. Cooper

Papers

Marginal Rates and Elasticities of Substitution with Additive Models in DEA

Kohler's Dictionary for accountants

Two-stage financial risk tolerance assessment using data envelopment analysis

DEA and stochastic frontier analyses of the 1978 Chinese economic reforms

Origins, uses of, and relations between goal programming and data envelopment analysis