Abraham Charnes

Bio: Abraham Charnes is an academic researcher from University of Texas at Austin. The author has contributed to research in topics: Linear programming & Data envelopment analysis. The author has an hindex of 57, co-authored 222 publications receiving 63459 citations. Previous affiliations of Abraham Charnes include Carnegie Institution for Science & Northwestern University.

Basic DEA Models

Abstract: Data Envelopment Analysis (DEA) is a body of concepts and methodologies that have now been incorporated in a collection of models with accompanying interpretive possibilities as follows: 1. the CCR ratio model (1978) (i) yields an objective evaluation of overall efficiency and (ii) identifies the sources and estimates the amounts of the thusidentified inefficiencies 2. the BCC model (1984) distinguishes between technical and scale inefficiencies by (i) estimating pure technical efficiency at the given scale of operation and (ii) identifying whether increasing decreasing, or constant returns to scale possibilities are present for further exploitation 3. the Multiplicative models (Charnes et al., 1982, 1983) provide (i) a log-linear envelopment or (ii) a piecewise Cobb- Douglas interpretation of the production process (by reduction to the antecedent 1981 additive model of Charnes, Cooper, and Seiford); and 4. the Additive model (as better rendered in Charnes et al., 1985) and the extended Additive model (Charnes et al., 1987) (i) relate DEA to the earlier Charnes-Cooper (1959) inefficiency analysis and in the process (ii) relate the efficiency results to the economic concept of Pareto optimality as interpreted in the still earlier work of T. Koopmans (1949) in the volume that published the proceedings of the first conference on linear programming.1

An Extremal and Information-Theoretic Characterization of some Interzonal Transfer Models.

Abstract: : The paper develops a method of deriving gravity models from extremal principles. The prototype result yields the most popular gravity flow model characterized by an extremal principle. This principle is also for the first time elucidated as an information-theoretic one of choosing the distribution of interzonal transfers which gives least information (in the technical sense) for discrimination against a distribution reflecting the facility (reciprocal of the difficulty) of travel between zones. (Author)

Constrained Generalized Medians and Hypermedians as Deterministic Equivalents for Two-Stage Linear Programs under Uncertainty

Abstract: In linear programming under uncertainty the two-stage problem is handled by assuming that one chooses a first set of constrained decision variables; this is followed by observations of certain random variables after which another set of decisions must be made to adjust for any constraint violations. The objective is to optimize an expected value functional defined relative to the indicated choices. This paper shows how such problems may always be replaced with either constrained generalized medians or hypermedians in which all random elements appear only in the functional. The resulting problem is called a deterministic equivalent for the original problem since (a) the originally defined objective replaces all random variables by corresponding expected values and (b) the remaining constraints do not contain any random terms. Significant classes of cases are singled out and special attention is devoted to the structure of the constraint matrices for these purposes. Numerical examples are supplied and relat...

Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis

Abstract: 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."

Fuzzy Set Theory - and Its Applications

Abstract: 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.

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

Abstract: 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.

Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software

Abstract: 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.