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

A new application of DEA (Data Envelopment Analysis) is examined for evaluating the efficiency of occupational-technicalprograms in a comprehensive community college. This includes extensions of DEA for use in evaluating new programs that might be introduced along with possible combinations of old programs. Emphasis is placed on the relative efficiency aspects of DEA so that consequences for the efficiency ofprograms other than those being considered can be taken into account. Uses by the director of San Antonio College are described and placed in a context of the other elements that entered into her decisions. In conclusion, possible further improvements in DEA are discussed along with the kinds of research needed to achieve them.

Evaluation of Educational Program Proposals by Means of DEA

By constructing a new infinite dimensional space for which the extreme point—linear independence and opposite sign theorems of Charnes and Cooper continue to hold, and, building on a little-known work of Haar (herein presented), an extended dual theorem comparable in precision and exhaustiveness to the finite space theorem is developed. Building further on this a dual theorem is developed for arbitrary convex programs with convex constraints which subsumes in principle all characterizations of optimality or duality in convex programming. No differentiability or constraint qualifications are involved, and the theorem lends itself to new computational procedures.

Duality in Semi-Infinite Programs and some Works of Haar and Caratheodory

Sensitivity analysis of the additive model in data envelopment analysis

This paper will be concerned with formulating the optimum allocation of search effort as a problem in convex programming so that their solutions may be made amenable to treatment by the adjacent extreme point methods of linear programming. Attention will be concentrated on discrete (statistical) distributions because this class of cases admits of the easiest and most straight-forward treatment. A sketch will then be given of how extensions may also be effected to continuous distributions.

The Theory of Search: Optimum Distribution of Search Effort

SUMMARY THE TECHNIQUES of linear programming are here explained in a commercial application-blending aviation gasolines. Blending is critically important to almost all other areas of programming in an integrated oil company. Intelligent programming of production, transportation, manufacturing, or marketing generally requires solution of blending problems as an initial or integral part of the whole process for it is in blending that the final outputs are determined. In the first part of the paper, questions of optimum programming in a given technological and institutional structure are explored. Computations are executed primarily by means of the simplex technique of Dantzig [4]. Because of the presence of multiple degeneracy and the absence of a general method (at the time these computations were made)2 of handling such problems, it was not possible to rest securely on the simplex method. Alternative methods of computation were, therefore, explored and bounding techniques were employed to discover possible divergences from optimality. Finally, to test the validity of the results, calculations undertaken by a company programming official were obtained for purposes of check and comparison. A relatively simple program is first calculated and more than one optimal program obtained. These results are then extended to more complex problems. Finally, the sensitivity of the matrix to possible changes in the coefficients is studied. The problem of linear programming may be sta-ted as follows: A

Abraham Charnes

Papers

Evaluation of Educational Program Proposals by Means of DEA

Duality in Semi-Infinite Programs and some Works of Haar and Caratheodory

Sensitivity analysis of the additive model in data envelopment analysis

The Theory of Search: Optimum Distribution of Search Effort

Blending aviation gasolines-a study in programming interdependent activities in an integrated oil company'