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.

Preface to Management Science, Ecology and the Quality of Life

Abstract: Most of the articles that follow are the papers that formed the Distinguished Lecturer Series---i.e., the invited, thematic series---at the XIX International Meetings of The Institute of Management Sciences in Houston, Texas, on April 4--8,1972. There are two exceptions: 1 “The ORSA New Orleans Address on 'Compact City'” by G. B. Dantzig and 2 “A Model to Study Revenue Sharing and Account for Regionalized Economic Activity and Social Goals” by A. Charnes, C. Colantoni, W. W. Cooper and K. O. Kortanek. The former, as its title suggests, was the basis of Dr. Dantzig's plenary lecture on April 27, 1972, to the 41st National Meeting of the Operations Research Society of America in New Orleans---to which he has added “An Agenda for Research on Urban Development”. The latter paper is intended to complement “Measuring, Monitoring and Modeling Quality of Life” which was presented by A. Charnes, W. W. Cooper and G. Kozmetsky, as the final Distinguished Lecture in the TIMS series at Houston.

A two-segment approximation algorithm for separable convex programming with linear constraints

Abstract: We discuss a new algorithm for the separable convex programming with linear constraints. This is based on the approximation of the objective function by at most two linear pieces in the neighborhood of the current feasible solution. The two segments will be adaptively defined rather than predecided fixed grids. If3 furthermore, the objective function is differentiable, and one introduces a non-Archimedean infinitesimal, the algorithm generates a sequence of feasible solutions every cluster point of which is an optimal solution. Computational tests on the problem with up to 196 non-linear variables are presented

On a special class of constrained generalized median problems

Abstract: : By means of elementary properties of the absolute value function, important properties of a special class of 'constrained generalized median' problems (and eventually, the most general class, vide Charnes, Cooper, Thompson) such as existence of solutions, gradient and incremented formulae, linear programming and probabilistic interpretations are obtained for all classes of joint distribution functions for which the problems make sense. Results of A. C. Williams and R. Wets obtained by involved arguments and sophisticated constructs appear, when corrected, as special instances of some of the above results but devoid of the interrelations and interpretations presently adduced.

Semi-infinite relaxation of joint chance constraints in chance-constrained programming Part 1. Zero-order stochastic decision rules†

Abstract: A new class of semi-infinite deterministic (‘determinizations’) dominants and relaxations of joint chance-constraints in chance-constrained programming is developed and specialized to zero-order stochastic decision rule situations. Tight constraint relaxations are obtained where only the partial information of means and variances is known. The tight non-linear semi-infinite relaxations are related to an accessible finite subsystem. When the chance constraints involve linear inequalities, for a large class, the non-linear tight system is proved equivalent to a linear program. Its solutions for the Prekopa-Szantai reservoir construction examples agree well with theirs

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.