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

This chapter discusses returns to scale (RTS) in data envelopment analysis (DEA). The BCC and CCR models described in Chap. 1 of this handbook are treated in input-oriented forms, while the multiplicative model is treated in output-oriented form. (This distinction is not pertinent for the additive model, which simultaneously maximizes outputs and minimizes inputs in the sense of a vector optimization.) Quantitative estimates in the form of scale elasticities are treated in the context of multiplicative models, but the bulk of the discussion is confined to qualitative characterizations such as whether RTS is identified as increasing, decreasing, or constant. This is discussed for each type of model, and relations between the results for the different models are established. The opening section describes and delimits approaches to be examined. The concluding section outlines further opportunities for research and an Appendix discusses other approaches in DEA treatment of RTS.

Returns to Scale in DEA

Evaluating solvency versus efficiency performance and different forms of organization and marketing in US property - Liability insurance companies

New Perspectives in Organization Research

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.

Duality, haar programs, and finite sequence spaces.

Publisher Summary Chance-constrained programming is an extension of statistical method. Chance-constrained programming was originated in the context of developing a planning and operations model for the Standard Oil of New Jersey for the scheduling of heating oil manufacture, storage, and distribution with weather-dependent demand. The constrained game approach was not entirely satisfactory as an extension of statistical method. While the constraints on permissible (mixed) strategies of nature were substantially better than none at all, the remnant clairvoyant malevolence of nature implicit in the minimax solution did not seem appropriate to the behavior of weather. Another important consideration was that while the policy of the company as the major supplier of a product tinged with the national interest was to supply all emergent demand, one could determine random combinations of weather whose associated demand would be impossible for the company to meet from its available mechanisms or resources. It is clear that within these prescriptions, chance-constrained programming may be considered a method of tremendous flexibility with innumerable individual possible variations or models.

William W. Cooper

Papers

Returns to Scale in DEA

Evaluating solvency versus efficiency performance and different forms of organization and marketing in US property - Liability insurance companies

New Perspectives in Organization Research

Duality, haar programs, and finite sequence spaces.

Chance-constrained programming: an extension of statistical method