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

Models of situations in which individuals are faced with multiple activities among which they must allocate their effort are postulated. Optimal allocations are found for four assumed motivational structures---profit maximization and three involving performance goals in each of the activities. Heuristic approximations to the optimal allocations are developed. Also, the relationships between the various motivation structures are explored.

https://www.jstor.org/stable/info/2627828

Search-Theoretic Models of Organization Control by Budgeted Multiple Goals

: Several important and efficient methods of solution of specific types of linear programming problems have the feature of sometimes providing optimal solutions which are not extreme-point (or basic) solutions, so that important and useful analyses provided by knowledge of the optimal dual evaluators are not available. It is also often desirable to be able to begin with a solution suggested by knowledgeable persons with experience in the field (or other considerations) and to proceed immediately to a basic solution at least as good as the suggested one. In this paper it is shown how part of the technique of proof of the opposite sign theorem can be employed in a simple algorithm to achieve this end. This method is equally valid when maximizing a nonlinear but convex objective function. A tested ALGOL code is provided for executing the algorithm in a manner compatible (as a procedure) with other programs.

/pdf/extreme-point-solutions-in-mathematical-programming-an-454vh304r1.pdf

Extreme point solutions in mathematical programming: an opposite sign algorithm

: DEMON (Decision Mapping via Optimum GO-NO Networks) is a chance-constrained programming model for use in developing a strategy for marketing new products where, inter alia, the pertinent statistical distributions are only partially known and, in fact, may change in response to the strategies employed. The present report depicts DEMON in terms of the decision-and-information networks which are of primary concern for managements confronted with problems in new product marketing. In addition the recursion relations used to establish an optimal marketing plan are discussed in a case history context. (Author)

Demon: a management model for marketing new products.

: The paper extends existing models of inter-temporal bank asset management in the following respects: (a) Bank customers are identified, with requirements that their demands for loan renewals be satisfied. Opportunities are provided for attracting new customers; (b) feedback relationships between loans and deposits are introduced; (c) costs of servicing loans with different degrees of risk are introduced explicitly; (d) future deposits and loan repayments are expressed as jointly dependent random variables; (e) the Federal Reserve Board's liquidity leverage suggestions are replaced by chance-constraints on meeting demands for loans. This leads to a policy of balancing maturities in the bond portfolio. The format of the model is that of chance- constrained programming, with piecewise linear approximations to the non-linear constraints. A 5-period example, with parameterizing on the right hand side, is presented.

Intertemporal bank asset choice with stochastic dependence

Model equivalences may sometimes be used to replace “realistic” but unwieldy initial formulations with simpler counterparts. This can involve sophisticated uses of prototypes, quasi models, etc., or it may involve only simpler ideas of redundancy elimination, removal of extraneous variables, etc. In either case questions can arise concerning the properties of these models when further analyses are to be conducted via parameterizations, duality, etc. These topics are examined in the general context of direct and dual linear programming problems with special reference to boundedness properties of the associated solution sets. It is shown that a bounded solution set in one problem implies an unbounded solution set in the dual problem, unless both are one-point sets. The ideas of projection equivalence are then developed to suggest a possible route for utilizing these one-point solution properties for analyzing or solving linear programming problems. These possibilities might prove useful when, for example, i...

Abraham Charnes

Papers

Search-Theoretic Models of Organization Control by Budgeted Multiple Goals

Extreme point solutions in mathematical programming: an opposite sign algorithm

Demon: a management model for marketing new products.

Intertemporal bank asset choice with stochastic dependence

Some Properties of Redundant Constraints and Extraneous Variables in Direct and Dual Linear Programming Problems