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 comment on “models, modelling and modellers: an application to risk analysis” by B. Wahlström European Journal of Operational Research 75 (1994) 477–487

Quantitative planning and control: Essays in honor of William Wager Cooper on the occasion of his 65th birthday

: The paper discusses manpower planning systems for a large Naval laboratory which are being developed from an integrated point of view. This includes the implementation results of a goal programming model with embedded Markov processes to assist in the evaluation of staffing plans. A description is given of the methods used to bring together manpower and budgetary information through the integration of technical program, financial, and personnel data. Included are the verification of initial results of model application and a discussion of other analyses which are being used in addition to the models. (Author)

Integrated Manpower and Program Planning Models for Laboratory Management.

Presidential address about the background leading to TIMS formation. Delivered before the first national meeting of the Institute of Management Sciences, Oct. 21--22, 1954. Parts of the address are omitted.

Presidential Address to TIMS

This paper covers some of the past accomplishments of DEA and its future prospects. It starts with the engineering-science definitions of efficiency and uses the duality theory of linear programming to show how, in DEA, they can be related to the Pareto-Koopmens definitions used in welfare economics. Some of the models that have now been developed for implementing these concepts are then described and properties of these models are examined for weaknesses and strengths along with different measures of distance that may be used to determine their optimal values. Relations between the models are also demonstrated en route to delineating paths for future developments. These include extensions to different objectives such as satisfactory vs. full (or strong) efficiency. They also include extensions from efficiency to effectiveness evaluations of performances as well as extensions to evaluate social-economic performances of countries and other entities where inputs and outputs give way to other categories in which increases and decreases are located in the numerator or denominator of the ratio (=engineering-science) definition of efficiency in a manner analogous to the way output (in the numerator) and input (in the denominator) are usually positioned in the fractional programming form of DEA. Beginnings in each of these extensions are cited and the role of applications in bringing further possibilities to the fore is highlighted.

William W. Cooper

Papers

A comment on “models, modelling and modellers: an application to risk analysis” by B. Wahlström European Journal of Operational Research 75 (1994) 477–487

Quantitative planning and control: Essays in honor of William Wager Cooper on the occasion of his 65th birthday

Integrated Manpower and Program Planning Models for Laboratory Management.

Presidential Address to TIMS

DEA: Past Accomplishments and Future Prospects