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

Once again we show that the analysis of a very simple artificial example contrived by its authors for a general indictment of all chance constrained programming is itself in error. Proofs and further references are supplied below along with a discussion of other deficiencies and ambiguities in an article authored by A. J. Hogan, J. G. Morris and H. E. Thompson in Management Science, Vol. 27, No. 6 June 1981.

Response to Decision Problems Under Risk and Chance Constrained Programming: Dilemmas in the Transition

Constrained Games and Linear Programming.

Minimization of non-linear separable convex functionals†

THEOREM 0. Let En -En X be a homogeneous line bundle over a C-space of complex dimension n. Suppose that the first Chern class ci(Eo) is given by a negative semi-definite quadratic form of index k < n. Then HI(X, E*) = 0 for q < k. (If k = n, we have again Kodaira's theorem.) To apply Theorem 0 to C-spaces, a fairly extensive study of the differential geometry of homogeneous vector bundles is useful; these results may be of independent interest. The reason is that the Atiyah construction of the Chern classes in terms of forms does not work in the non-Kahler case and so one must use a curvature tensor in order to construct the forms. Using Theorem 0 and the fact that H*(X, E*) may be written in terms of Lie algebra cohomology, Theorem 1 is completed using several spectral sequences in Lie algebra cohomology. The Leray spectral sequence used by Bott does not seem to give the complete information here. As mentioned above, the details of the proofs together with other results and applications will appear later.

Abraham Charnes

Papers

Response to Decision Problems Under Risk and Chance Constrained Programming: Dilemmas in the Transition

Constrained Games and Linear Programming.

Minimization of non-linear separable convex functionals†

Duality, haar programs, and finite sequence spaces.

Robustly efficient parametric frontiers via Multiplicative DEA for domestic and international operations of the Latin American airline industry.