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

: In contrast to classical econometric work which only tests data for consistency with a special class of production functions, new theory and explicit construction by Data Envelopment Analysis of the empirical Pareto-Koopmans efficient production function is developed for data sets which satisfy two conditions met in all previous real applications of DEA known to the authors The construction requires no additional computation beyond that of the DEA tests In section 2, we bring forth the differences in key preoccupations of research in economic production theory with those of DEA by references to papers of Hanoch and Rothschild (1972), of Diewert and Parkan (1983) and, in still another direction by Fare, Grosskopf and Lovell (1985) and Debreu (1951) In section 3, we develop basic concepts of and theorems for geometric elucidation and analysis of the empirical efficient production functions of DEA including a new lemma on optimal solutions to the general linear programming problem (for arbitrary ordered fields of scalars) Then, restricting ourselves to two conditions on empirical data which have held in every DEA application we have made, we show that the mathematical structure of the efficient empirical function is so simplified that it is available immediately in analytic form without further computational work on top of the DEA tests The efficient empirical production is then, moreover, piece-wise linear and continuous from piece to piece

/pdf/explicit-construction-and-analysis-of-some-efficient-4d5u3aj32q.pdf

Explicit Construction and Analysis of Some Efficient Empirical Production Functions in Data Envelopment Analysis.

This paper provides a theoretical framework for application of Chance-Constrained Programming (CCP) in situations where the coefficient matrix is random and its elements are not normally distributed. Much of the CCP literature proceeds to derive deterministic equivalent in computationally implementable form on the assumption of “normality”. However, in many applications, such as air pollution control, right skewed distributions are more likely to occur. Two types of models are considered in this paper. One assumes an exponential distribution of matrix coefficients, and another one uses an empirical approach. In case of exponential distributions, it is possible to derive exact “deterministic” equivalent to the chance-constrained program. Each row of the coefficient matrix is assumed to consist of independent, exponentially distributed random variables and a simple example illustrates the complexities associated with finding a numerical solution to the associated deterministic equivalent. In our empirical approach, on the other hand, simulated data typically encountered in air pollution control are provided, and the data-driven (empirical) solution to the implicit form of deterministic equivalent is obtained. Post-optimality analyses on model results are performed and risk implications of these decisions are discussed. Conclusions are drawn and directions for future research are indicated.

Chance-constrained programming with skewed distributions of matrix coefficients and applications to environmental regulatory activities

Remarks on graduate education in management sciences reflecting opinions at the Carnegie-Mellon University.

Remarks on Graduate Education in the Management Sciences

This paper develops a general theoretical model for the measurement of strategic performance. The concepts are universal and, by applying the methodology through specific quantitative analytic methods, measurable for all forms of strategic activity. The model distinguishes three aspects of strategic performance: (i) strategy itself relative to its goals; (ii) specific executions relative to the strategy itself; and (iii) competing or alternative strategies per se. The methodology for quantifying these aspects of strategic performance is: (i) estimate a strategy’s best potential from its actual best performances; (ii) evaluate individual executions by comparing their results to their strategies’ potentials; and (iii) compare different strategies per se based on their best potentials. These general steps can be implemented by different quantitative analytic methods; one is outlined and others are indicated.The conceptual framework and derived methods address two problems. First, they provide practicable means of evaluating the three aspects of strategic performance in practice to diagnose the causes of strategic success and failure, to identify efficacious from futile strategies and effectual from unavailing execution, and to compare competing strategies. Second, they supply a fundamental theoretical deficiency common to both academic and practitioner studies which evaluate either strategy performance or execution performance while failing to control or account for the simultaneous effect of the other. These methods can also be applied to investigate broader economic issues, like risk theory or market completeness.

Evaluating Strategic Performance: Concepts and Methodology

The title of this talk is intended to indicate the dates (approximately) on which we have been, or may be, reporting to TIMS audiences in meetings such as this one. The first three are past history, naturally, while the last one refers to “futurology”, as practiced by George Orwell and perhaps others who, like us, are also eager to influence the futures that can materialize from ingredients presently at hand.

William W. Cooper

Papers

Explicit Construction and Analysis of Some Efficient Empirical Production Functions in Data Envelopment Analysis.

Chance-constrained programming with skewed distributions of matrix coefficients and applications to environmental regulatory activities

Remarks on Graduate Education in the Management Sciences

Evaluating Strategic Performance: Concepts and Methodology

TIMS in Perspective 1954, 1964, 1974; 1984?