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

An extension to the theory of linear programming over generalized networks is presented which replaces the generalized Kirchoff node conditions by chance constraints. The extension is motivated by a class of problems in sanitary and chemical engineering in which the nonzero entries in the generalized incidence matrix may be random variables. Duality relations are established for appropriate pairs of such chance-constrained programming problems by showing that their deterministic equivalents consist of a deterministic generalized network problem and its dual. It is also shown how these duality relations may be exploited in order to obtain actual solutions to chance-constrained generalized network problems.

Chance-Constrained Generalized Networks

A variety of objectives and constraints are presented for use by a regulatory agency in pricing public services and evaluating capacities under conditions where the demands are random variables with probability distributions that depend on prices in different parts of the system. The models studied include a maximization of the joint probability of achieving at least specified levels of consumers' surpluses in these interacting markets, as well as models that constrain the choices of prices and services to ensure that these surpluses are satisfied to at least specified levels of probability, while observing expected fair return constraints for the producers. Chance constrained programming formulations and reductions to deterministic equivalents are developed to use for evaluating levels of service, etc. Some new “coefficients conditions” establishing concavity for quadratic forms are stated and proved in the Appendix to this paper. This also establishes convexity for the deterministic equivalents develope...

Regulatory Models for Pricing and Evaluation of Transport Services

In place of classical utility conceptions, policy discussions for intergenerational transfers of income involve the balancing of several desirable social goals: maintaining or improving the standard of living of (i) the working popuuion, (ii) the retired population, and (iii) maintaining a stable intergenerational transfer system. The new method of goal focusing achieves both the trade-off analyses of utility function methods at Pareto-efficient points and due accounting for the effects of multiple objectives. A goal-focusing approach is herein developed for the detailed quantitative analysis of intergenerational income transfers of a national social security system.

A goal-focusing approach to analysis of intergenerational transfers of income

The authors deal with a certain specialization of their theory of duality on the case where the objective function is simple continuously differentiable and convex on the set $K$ of the admissible solutions and the constraint functions defining $K$ are continuously differentiable and concave. Further, a way is shown how to generalize the account to the case where the constraint functions of the problem are simple piecewise differentiable and concave. The obtained conditions can be considered as a generalization of Kuhn-Tucher's theorem.

/pdf/semi-infinite-programming-differentiability-and-geometric-4ovpx49nab.pdf

Semi-infinite programming, differentiability and geometric programming: part ii

The basic DEA models discussed in the previous chapter are associated with the way the returns-to-scale, the geometry of the envelopment surface, and the efficient projections are identified This array of choices provides considerable flexibility, which can be further increased by incorporating refinements or extensions to the basic theory These valuable additions to the methodology of DEA allow one to fine tune an analysis to reflect managerial or organization factors, sharpen efficiency estimates, and/or overcome inconsistencies

Abraham Charnes

Papers

Chance-Constrained Generalized Networks

Regulatory Models for Pricing and Evaluation of Transport Services

A goal-focusing approach to analysis of intergenerational transfers of income

Semi-infinite programming, differentiability and geometric programming: part ii

Extensions to DEA Models