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

The querulous and exaggerated tones which seem to attend so many contemporary activities have now been permitted an entrance to the pages of Management Science where they are amply represented in the article published by A. S. C. Ehrenberg “Models of Fact: Examples from Marketing,” Management Science Vol 16, No. 7 March 1970, pp. 435--445.. The tone of Ehrenberg's article provides a warning that should naturally make anyone reluctant to attempt to reply to any of his criticisms or to question any of his claims. Some possibility for a productive response may be available, however, if one avoids a direct reply to Ehrenberg's claims and criticisms in order to respond by indicating possibilities and considerations other than those which Ehrenberg allows for in modeling, at least in management science.

Communications to the Editor---Models of Fact and Laws of Behavior

: In the first five sections of this paper various properties of a Rao generalized inverse of a matrix are established. A method of computing such an inverse is also given. In order to illustrate the differences between the Rao and other generalized inverses, a survey of results on Penrose-Moore inverses is included. The last three sections are devoted to showing how a generalized inverse can be used in the theoretical development of the simplex and modified simplex methods of linear programming. In particular, it is shown that the fundamental equations and iteration formulas of these methods can be derived using matrix notation without requiring the assumption that the linear programming problem has no redundant constraints.

/pdf/properties-of-a-generalized-inverse-with-applications-to-4n953gq100.pdf

Properties of a generalized inverse with applications to linear programming theory

: This paper shows how to take personally assessed information and use it to develop a continuous unimodal prior density function, perhaps for subsequent Bayesian analysis. The method is completely nonparametric and uses only the furnished information and no other. The technique is easily computerized, and yields a closed analytical formula for the prior. The resulting distribution may be considered to be an inferential distribution. (Author)

A Method for Constructing a Unimodal Inferential or Prior Distribution.

: Media planning has heretofore been restricted, by and large, only to the consideration of average frequency. A recently developed mathematical model explicitly considers both cumulative duplicating audiences over a variety of time periods and the simultaneous selection and scheduling of media. This model thus required the development of methods for handling such nonlinear concave aspects of audience characteristics within a linear programming model and for generating distribution of frequency data within the computational processes of the model. This is done by means of logarithmic transformations and, for the discrete distributions of frequencies, by log-normal approximating devices. Each of these two techniques is important in its own right as a type of method which may be employed in a wide variety of modelling or computational situations. Thus, because neither of these techniques is restricted to the area of media planning per se it seemed worthwhile to present them on their own terms--as in the present paper--instead of treating them only as a detail in developing and interpreting the LPII model.

Abraham Charnes

Papers

Communications to the Editor---Models of Fact and Laws of Behavior

Properties of a generalized inverse with applications to linear programming theory

A Method for Constructing a Unimodal Inferential or Prior Distribution.

Generation and approximation of reach and distribution of frequencies.

A dynamic goal programming model for planning food self-sufficiency in the Middle East