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 examination of the efficiency of the marketing distribution channel and organizational structure for insurance companies is presented from a framework that views the insurer as a financial intermediary rather than as a "production entity" which produces "value added" through loss payments. Within this financial intermediary approach, solvency can be a primary concern for regulators of insurance companies, claims-paying ability can be a primary concern for policyholders, and return on investment can be a primary concern for investors. These three variables (solvency, financial return, and claims-paying ability) are considered as outputs of the insurance firm. The financial intermediary approach acknowledges that interests potentially conflict, and the strategic decision makers for the firm must balance one concern versus another when managing the insurance company. Accordingly, we investigate the efficiency of insurance companies using data envelopment analysis (DEA) having as insurer output an appropriately selected (for the firm under investigation) combination of solvency, claims-paying ability, and return on investment as outputs. These efficiency evaluations are further examined to study stock versus mutual form of organizational structure and agency versus direct marketing arrangements, which are examined separately and in combination. Comparisons with the "value-added" or "production" approach to insurer efficiency are presented. A new DEA approach and interpretation is also presented.

https://papers.ssrn.com/sol3/Delivery.cfm?abstractid=782996

Financial Intermediary Versus Production Approach to Efficiency of Marketing Distribution Systems and Organizational Structure of Insurance Companies

Uses of modeling in science and society

Evaluations of publicly announced investment strategies of open-end mutual funds were secured from a questionnaire sent to brokers and editors of financial newsletters. Ex Ante evaluations secured in this manner are compared with ex post performance over the period 1984-1988 and rated via data from Morningstar, Inc., and Business Week on mutual fund Performances over this same period. The present study is designed so that separations can be effected between risk and return evaluations and Performance over all pertinent ex ante and ex post pairings. Ex ante evaluations of risk and return are found to be positively correlated—as posited in the finance, decision theory and economics literatures—but their ex post pairings are negatively related. Somewhat surprisingly, ex ante to ex post evaluations of risk are positively correlated while ex ante to ex post evaluations of return are negatively correlated. The source of the ex ante to ex post negative relations is therefore in the return rather than the risk evaluations. This casts additional light on the Bowman Paradox (and related topics) which have been extensively studied in the Strategic management literature. It also adds to these paradoxes and suggests programs for further research in a manner that is discussed in the addendum to this paper.

A Study Of Evaluations Of Mutual Fund Investment Strategies

The February 2002 issue of Omega contains an article by M.N. Nickel and M.C. Rodriguez which reviews and evaluates research dealing with what is called the “Bowman Paradox” in the literature of strategic management. Using accounting reports from business firms this paradox arises from the persistent showing that risk and return are negatively related—i.e., high risk is associated with low return and low risk is associated with high return. The present commentary describes an article in a literature not covered by Nickel and Rodriguez which (a) extends the Bowman Paradox to mutual fund reports based on market data and (b) resolves the outstanding problems noted by Nickel and Rodriguez as needing further research.

Commentary on “a review of research on the negative accounting relationship between risk and return: Bowman's paradox by M.N. Nickel and M.C. Rodriguez”

: A new algorithm for multi-attribute assignment models is presented. Built around the concept of a biased quadratic objective, it proceeds via a sequence of related assignments. Optional stopping is applied when an approximation to the optimum assignment is identified. A second part of the paper deals with manpower planning and organization designs which interact dynamically. A spectral analysis approach is utilized to obtain estimates of career patterns and aspirations in terms of observed and potential transition problems. Goal programming approaches are utilized in both parts of this paper. This is done not only to relate them to each other but also to relate these developments to prior modeling efforts which the authors have undertaken in related areas of manpower planning. (Author)

William W. Cooper

Papers

Financial Intermediary Versus Production Approach to Efficiency of Marketing Distribution Systems and Organizational Structure of Insurance Companies

Uses of modeling in science and society

A Study Of Evaluations Of Mutual Fund Investment Strategies

Commentary on “a review of research on the negative accounting relationship between risk and return: Bowman's paradox by M.N. Nickel and M.C. Rodriguez”

An Algorithm for Multi-Attribute Assignment Models and Spectral Analyses for Dynamic Organization Designs