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

A non-linear congestion network model for planning internal movement in the Hajj

The successful management of urban systems is becoming increasingly a matter of successful information about the urban area and its environment. Using information as a basis for developing a structure for, and outlining the flows in, an urban area, this paper develops a dual hierarchy of information requirements and management activities. Each level of the hierarchy is discussed in terms of the emergent problems and requirements that are likely to confront management scientists and urban administrators in the future. As the information requirements of urban areas become more complex and as the components of the urban system become more highly interrelated, developments in information technology can be expected to have a direct impact on the activities of urban area administrators. This development is illustrated here through the presentation of a selected number of possible impacts of information technology developments upon the information and management hierarchies of urban systems.

Information Requirements for Urban Systems: A View into the Possible Future?

: This paper contains an application of chance-constrained programming to a problem in financial planning. In particular the problem is one of planning for liquidity in a savings and loan association first discussed by Charnes and Thore. The optimal rules for this problem are found and compared with the optimal linear rules given by Charnes and Thore. The discontinuous nature of the optimal rules is discussed from economic and control theory viewpoints.

http://www.dtic.mil/dtic/tr/fulltext/u2/625050.pdf

Application of chance-constrained programming to solution of the so- called 'savings and loan association' type of problem

An Introduction to Linear Programming.

: The paper deals with an n-period E model of chance-constrained programming in which each period j = 1,...,n generates exactly one new constraint. It is shown that there are cases in which the problem can be reduced to one of solving n rather simple one-variable nonlinear programming problems. The results of this paper are illustrated by means of an example giving the solution of a two-period problem of planning for liquidity in a savings and loan association.

Abraham Charnes

Papers

A non-linear congestion network model for planning internal movement in the Hajj

Information Requirements for Urban Systems: A View into the Possible Future?

Application of chance-constrained programming to solution of the so- called 'savings and loan association' type of problem

An Introduction to Linear Programming.

Optimal decision rules for the triangular e model of chance-constrained programming