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.

Complexity and computability of solutions to linear programming systems

Abstract: Through key examples and constructs, exact and approximate, complexity, computability, and solution of linear programming systems are reexamined in the light of Khachian's new notion of (approximate) solution. Algorithms, basic theorems, and alternate representations are reviewed. It is shown that the Klee-Minty example hasnever been exponential for (exact) adjacent extreme point algorithms and that the Balinski-Gomory (exact) algorithm continues to be polynomial in cases where (approximate) ellipsoidal “centered-cutoff” algorithms (Levin, Shor, Khachian, Gacs-Lovasz) are exponential. By “model approximation,” both the Klee-Minty and the new J. Clausen examples are shown to be trivial (explicitly solvable) interval programming problems. A new notion of computable (approximate) solution is proposed together with ana priori regularization for linear programming systems. New polyhedral “constraint contraction” algorithms are proposed for approximate solution and the relevance of interval programming for good starts or exact solution is brought forth. It is concluded from all this that the “imposed problem ignorance” of past complexity research is deleterious to research progress on “computability” or “efficiency of computation.”

A discrete probability chance-constrained capital budgeting model.

Abstract: : Aspects of the duality theory for semi-infinite programming are extended to fields with properties of non-Archimedean order. Emphasis is on nonstandard semi-infinite programming problems in Hilbert's Field. The ideas of regularization are generalized to include powers of the relative infinites in terms of the indeterminates. (Author)

Extended Pincus Theorems and Convergence of Simulated Annealing

Abstract: Pincus’ 1968 formula for the (unique) global minimum of a continuous function on a compact set in E n is extended to finite multiple optima and to discrete and special variants. The impact of these on associated ergodic irreducible aperiodic Markov chain computation (Pincus 1970)—currently called ‘simulated annealing’—is exemplified and assessed leading to grave concern about what current simulated annealing processes may converge to, instead of optima.

Some Uses of Model Prototypes in an Operations Research Study

Abstract: Management planning problems are often so huge and unwieldy that it is necessary to attack them with a variety of devices. One strategy involves the use of model types and prototypes. This is the topic which will be discussed in this paper in the context of a long-range oil field development problem, one which has aspects that are common to many attempts at longrange facilities planning. The emphasis will be on concepts. however, rather than the details of the actual problem and even these concepts will be dealt with in broad fashion. Further de-

On weakly balanced games and duality theory

Abstract: : The notion of a 'weakly balanced game' under very general conditions involving no topology whatever is defined. The work of Schmeidler is extended by establishing duality results for a pair of (possibly) infinite dimensional linear programming problems arising from a generalized game. A necessary and sufficient condition is given in order that a separating hyperplane argument can be employed to prove the existence of a candidate core member for a weakly balanced game. This candidate is shown to be in the core if and only if the game is balanced. No use is made of topological ideas, but conditions are given under which the core member takes on values in a bounded set. The Charnes-Kortanek M-operator is used to characterize the redundancy of certain coalition values in restriction core membership.

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.