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

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 model for measuring the efficiency of Decision Making Units =DMU's is presented, along with related methods of implementation and interpretation. The term DMU is intended to emphasize an orientation toward managed entities in the public and/or not-for-profit sectors. The proposed approach is applicable to the multiple outputs and designated inputs which are common for such DMU's. A priori weights, or imputations of a market-price-value character are not required.

A mathematical programming model applied to observational data provides a new way of obtaining empirical estimates of extrernal relations-such as the production functions and/or efficient production possibility surfaces that are a cornerstone of modern economics. The resulting extremal relations are used to envelop the observations in order to obtain the efficiency measures that form a focus of the present paper.

An illustrative application utilizes data from Program Follow Through =PFT. A large scale social experiment in public school education, it was designed to test the advantages of PFT relative to designated NFT =Non-Follow Through counterparts in various parts of the U.S. It is possible that the resulting observations are contaminated with inefficiencies due to the way DMU's were managed en route to assessing whether PFT as a program is superior to its NFT alternative. A further mathematical programming development is therefore undertaken to distinguish between "management efficiency" and "program efficiency." This is done via procedures referred to as Data Envelopment Analysis =DEA in which one first obtains boundaries or envelopes from the data for PFT and NFT, respectively. These boundaries provide a basis for estimating the relative efficiency of the DMU's operating under these programs. These DMU's are then adjusted up to their program boundaries, after which a new inter-program envelope is obtained for evaluating the PFT and NFT programs with the estimated managerial inefficiencies eliminated.

The claimed superiority of PFT fails to be validated in this illustrative application. Our DEA approach, however, suggests the additional possibility of new approaches obtained from PFT-NFT combinations which may be superior to either of them alone. Validating such possibilities cannot be done only by statistical or other modelings. It requires recourse to field studies, including audits e.g., of a U.S. General Accounting Office variety and therefore ways in which the results of a DEA approach may be used to guide such further studies or audits are also indicated.

Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through

Efficiency decomposition in two-stage data envelopment analysis: an application to non-life insurance companies in taiwan

Short communication: measuring efficiency of decision making units

: A method called Data Envelopment Analysis (DEA) is used to decompose the efficiency of Decision Making Units (DMU's) into two parts: (1) a component resulting from managerial decisions and (2) a component resulting from constraints (called programs) under which management operates. The DEA approach accomplishes this by enveloping the input-output observations with extremal relations developed in terms of a specified nonlinear programming model (and/or its linear programming equivalent). Differences between the observations and the progam specific envelopes -- called alpha-envelopes--are imputed to managerial inefficiencies. An inter-program envelope is then constructed from 2 or more such alpha-envelopes and used to identify 'program' inefficiencies, which are the inefficiencies that remain after the previously determined managerial inefficiencies have been eliminated. Numerical illustrations accompanied by suggested tests of a probabilistic/information theoretic character are provided by means of recenty released data from 'Program Follow Through.' Designed as a study of possible ways of reenforcing or extending Program Head Start - an ongoing pre-school program for disadvantaged children -- the Program Follow Through experiment provides data on agreed upon inputs and outputs for both PFT (Program Follow Through) and matched NFT (Not Follow Through) participants in various parts of the U.S.

A Data Envelopment Analysis Approach to Evaluation of the Program Follow through Experiment in U.S. Public School Education.

: A series of linear programming models are used to clarify and extend a measure of efficiency The duals to these models are shown to yield estimates of production coefficients from the same empirical data and computations that yield the measures of efficiency The nature of the resulting production functions and ways in which they differ from more customary ones are discussed en route to synthesizing the associated cost functions and other such (economic) relations Methods for adjusting observations are suggested for economic inferences and policy applications Multiple output-multiple input extensions are effected via a new definition of efficiency which involves a nonlinear model for determining the optimal input and output weights from observational data The theory of fractional programming is used to secure ordinary linear programming models from which the weights and efficiency measures may also be obtained

W W Cooper

Papers

Short communication: measuring efficiency of decision making units

A Data Envelopment Analysis Approach to Evaluation of the Program Follow through Experiment in U.S. Public School Education.

Measuring the Efficiency of Decision Making Units with Some New Production Functions and Estimation Methods.