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

Polyhedral Cone-Ratio DEA Models with an illustrative application to large commercial banks

: There are four basic questions related to efficiency and capability which are of particular interest to officials in the military services who are interested in better ways of evaluating military capability and efficiency: (1) What level of military capability can the services achieve with available resources? (2) What capability is required, and where are the shortfalls? (3) What resource acquisitions or redistributions are needed to achieve maximum improvement in efficiency and effectiveness? and (4) How can management systems be changed to improve the identification and correction of factors which limit the readiness and efficiency of our military operations? The last question, which differs in its emphasis from the other three, provides an opening to the topics that will be addressed in this report. In particular, reported are results from a study of DEA (Data Envelopment Analysis) as a method for evaluating the efficiency of Air Force Wings--or, more precisely, their maintenance operations--as elements in Numbered Units in the U.S. Air Force.

/pdf/a-developmental-study-of-data-envelopment-analysis-in-41x0cp30fd.pdf

A developmental study of data envelopment analysis in measuring the efficiency of maintenance units in the U.S. air forces

Management Models and Industrial Applications of Linear Programming.

Goal programming and multiple objective optimizations: Part 1

Generalized Efficiency Measures (GEMS) for use in DEA are developed and analyzed in a context of differing models where they might be employed. The additive model of DEA is accorded a central role and developed in association with a new measure of efficiency referred to as RAM (Range Adjusted Measure). The need for separately treating input oriented and output oriented approaches to efficient measurement is eliminated because additive models effect their evaluations by maximizing distance from the efficient frontier (in l1, or weighted l1, measure) and thereby simultaneously maximize outputs and minimize inputs. Contacts with other models and approaches are maintained with theorems and accompanying proofs to ensure the validity of the thus identified relations. New criteria are supplied, both managerial and mathematical, for evaluating proposed measures. The concept of “approximating models” is used to further extend these possibilities. The focus of the paper is on the “physical” aspects of performance involved in “technical” and “mix” inefficiencies. However, an Appendix shows how “overall,” “allocative” and “technical” inefficiencies may be incorporated in additive models.

William W. Cooper

Papers

Polyhedral Cone-Ratio DEA Models with an illustrative application to large commercial banks

A developmental study of data envelopment analysis in measuring the efficiency of maintenance units in the U.S. air forces

Management Models and Industrial Applications of Linear Programming.

Goal programming and multiple objective optimizations: Part 1

RAM: A Range Adjusted Measure of Inefficiency for Use with Additive Models, and Relations to Other Models and Measures in DEA