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

This paper discusses the possibilities of analysis of risk and uncertainty in forward planning in time for implementation of transport requirements by means of “chance-constrained” programming models [1]. The possibilities of using chance-constrained programming models, in place of queuing models, and the solution of such a model for the leasing of tanker fleets. is considered in some detail.

Some problems and models for time-phased transport requirements. Chance constrained programs with normal deviates and linear decision rules

An acceptance region theory for chance-constrained programming

A mathematical simulation analysis of refuse collection and disposal systems is presented. A computer program capable of considering stochastic variations in the system parameters has been written for the daily route method of refuse collection. Initial computations serve to delineate the relationships of the several performance parameters (over-all collection efficiency, length of workday, etc.) to the characteristics of the system (average daily quantity of refuse, daily variability in the quantity of refuse, truck capacity, etc.). Results are presented in a series of nineteen graphs. Useful extensions of this work are briefly considered.

Simulation and Analyses of a Refuse Collection System

Solution theorems in probabilistic programming: a linear programming approach.

Manpower planning for equal employment opportunity (EEO) must ensure a representation of social groups within the organization that matches their representation in the environment surrounding that organization. This paper discusses a multi-level system of goal programming models with embedded Markoff processes—a master model for evaluating corporate goals and a “coherence” model for local personnel management decisions. Both models have unique state-of-the-art features such as dual goal sets, the incorporation of flexibility options, the use of “bridge positions” and the use of piece-wise linear goal functionals in a capacitated distribution model format. A brief description of each model is given, followed by a discussion of some issues surrounding the process of goal setting and attendant issues of reporting and accountability.

Abraham Charnes

Papers

Some problems and models for time-phased transport requirements. Chance constrained programs with normal deviates and linear decision rules

An acceptance region theory for chance-constrained programming

Simulation and Analyses of a Refuse Collection System

Solution theorems in probabilistic programming: a linear programming approach.

Equal Employment Opportunity Planning and Staffing Models