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

Goal programming was originated to obtain “constrained regression” estimates for an executive compensation formula which would conform to an organization hierarchy and other company policies prescribed by management. A subsequent history in that context is traced through other uses in personnel planning and in organization designs. Applications to planning advertising strategies are also examined which extend to uses of goal programming that involve fitting frequency functions under a variety of constraints. Finally this is all related to the initial and continuing research on the statistical properties of these estimates.

Goal programming and constrained regression—A comment

Least squares/ridge regression and goal programming/constrained regression alternatives

Analytic relations between the two representations (half-space and finitely generated) of cones in polyhedral cone-ratio DEA models are derived, which, for useful classes of cases in which they are simple, can make available the advantages of both for analysis and computation. We prove that such transfers between the two may be made through, essentially, the inverse of an associated matrix available in the computation and we provide formulae connecting solutions in the two representations.

Relations between half-space and finitely generated cones in polyhedral cone-ratio DEA models

: Management accountability as an added dimension for management science research is examined from the standpoint of possible uses in some of the newer comprehensive auditing approaches to propriety, effectiveness and efficiency evaluations of management and organization behavior Attention is centered on non-market activities and not-for-profit organizations Goal focusing is examined, for example, as a relatively recent extension of goal programming for use in effectiveness evaluation and as an alternative to utility theoretic approaches in national goals accounting systems designed to deal with programs or objectives involving numerous kinds of off-market activities The bulk of the paper, however, is devoted to a new mathematical programming model for deriving analytic representations of extremal frontiers or envelopes from empirical data and for measuring the efficiency of not-for-profit entities An illustrative application to a recently completed large-scale social experiment in educating disadvantaged children in the US public schools is used to show how distinctions may also be drawn between program efficiency and management efficiency The appendix develops a canonical form for the types of statistical distributions involved It also provides a beginning for dealing with statistical properties of the extremal relations obtained by applying these kinds of mathematical programming models to observational data

/pdf/management-science-relations-for-evaluation-and-management-4yhbakv9hn.pdf

Management Science Relations for Evaluation and Management Accountability

Models and measures of efficiency dominance as treated by Free Disposal Hull and Russell Measure approaches to efficiency evaluation are examined as they relate to additive models and MED (Measures of Efficiency Dominance) in DEA.

William W. Cooper

Papers

Goal programming and constrained regression—A comment

Least squares/ridge regression and goal programming/constrained regression alternatives

Relations between half-space and finitely generated cones in polyhedral cone-ratio DEA models

Management Science Relations for Evaluation and Management Accountability

MODELS AND MEASURES FOR EFFICIENCY DOMINANCE IN DEA Part II : Free Disposal Hull (FDH) and Russel Measure (RM) Approaches