A. Charnes

Measuring the efficiency of decision making units

Abstract A nonlinear (nonconvex) programming model provides a new definition of efficiency for use in evaluating activities of not-for-profit entities participating in public programs. A scalar measure of the efficiency of each participating unit is thereby provided, along with methods for objectively determining weights by reference to the observational data for the multiple outputs and multiple inputs that characterize such programs. Equivalences are established to ordinary linear programming models for effecting computations. The duals to these linear programming models provide a new way for estimating extremal relations from observational data. Connections between engineering and economic approaches to efficiency are delineated along with new interpretations and ways of using them in evaluating and controlling managerial behavior in public programs.

FOUNDATIONS OF DATA ENVELOPMENT ANALYSIS FOR PARETO-KOOPMANS EFFICIENT EMPIRICAL PRODUCTION FUNCTIONS

The construction and analysis of Pareto-efficient frontier production functions by a new Data Envelopment Analysis method is presented in the context of new theoretical characterizations of the inherent structure and capabilities of such empirical production functions. Contrasts and connections with other developments, including solutions of some remaining problems, are made re aspects such as informatics, economies of scale, isotonicity and non-concavity, discretionary and non-discretionary inputs, piecewise linearity, partial derivatives and Cobb-Douglas properties of the functions. Non-Archimedean constructs are nor required.

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

Abstract Polyhedral Cone-Ratio Data Envelopment Analysis Models generalizing the CCR Ratio Model are developed for situations with a finite number of DMUs and employing polyhedral cones of virtual multipliers. They provide improved definitions of efficiency over CCR models whose input-output data and/or numbers of DMUs are inadequate to capture aspects or restrictions which should be involved. The focus here is on the sum form for cones which easily provides for capturing exogenous expert opinion as well as mathematical reduction to the old form with its very powerful software. Transformation from the usual intersection form to it and vice versa is explicitly given. Thereby the advantages of either or both are available. The theory is illustrated with two-dimensional examples and by real banking examples for motivation.

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

Abstract : 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.

Cone ratio data envelopment analysis and multi-objective programming

A new ‘cone ratio’ data envelopment analysis (DEA) model that substantially generalizes the Charnes-Cooper-Rhodes (CCR) model and the Charnes-Cooper-Thrall approach characterizing its efficiency classes is developed and studied. It allows for infinitely many decision-making units (DM Us) and arbitrary closed convex cones for the virtual multipliers as well as the cone of positivily of the vectors involved. Generalizations of linear programming and polar cone equalizations arc the analytical vehicles employed.

A Structure for Classifying and Characterizing Efficiency and Inefficiency in Data Envelopment Analysis

DEA (Data Envelopment Analysis) attempts to identify sources and estimate amounts of inefficiencies contained in the outputs and inputs generated by managed entities called DMUs (Decision Making Units). Explicit formulation of underlying functional relations with specified parametric forms relating inputs to outputs is not required. An overall (scalar) measure of efficiency is obtained for each DMU from the observed magnitudes of its multiple inputs and outputs without requiring use of a priori weights or relative value assumptions and, in addition, sources and amounts of inefficiency are estimated for each input and each output for every DMU. Earlier theory is extended so that DEA can deal with zero inputs and outputs and zero virtual multipliers (shadow prices). This is accomplished by partitioning DMUs into six classes via primal and dual representation theorems by means of which restrictions to positive observed values for all inputs and outputs are eliminated along with positivity conditions imposed on the variables which are usually accomplished by recourse to nonarchimedian concepts. Three of the six classes are scale inefficient and two of the three scale efficient classes are also technically (zero waste) efficient.

A multiplicative model for efficiency analysis

Abstract This paper develops theory and algorithms for a “multiplicative” Data Envelopment Analysis (DEA) model employing virtual outputs and inputs as does the CCR ratio method for efficiency analysis. The frontier production function results here are of piecewise log-linear rather than piecewise linear form.

Using data envelopment analysis to evaluate efficiency in the economic performance of Chinese cities

Abstract This paper studies the use of DEA (data envelopment analysis) as a tool for possible use in evaluating and planning the economic performance of Chinas cities (28 in all) which play a critical role in the governments program of economic development. DEA promises advantages which include the absence of any need for the assignment of weights on an a priori basis (to reflect the supposed relative importance of various outputs or inputs) when evaluating technical efficiency. It is also unnecessary to explicitly specify underlying functions that are intended to prescribe the analytical form of the relations between inputs and outputs. Finally, as is illustrated in the paper, DEA can be used to identify sources, and estimate amounts of inefficiencies in each citys performance as well as to identify returns-to-scale possibilities in ways that seem well-suited to the mixture of centralized and decentralized planning and performance that China is currently trying to use.

Sensitivity and Stability Analysis in DEA

Abstract : Sensitivity analyses may be regarded as a mathematical programming counterpart of significance testing in statistics since each is concerned with examining allowable ranges of variation in the data. In statistical analysis, this may take the form of examining ranges of possible chi sq values obtained from the data relative to a fitted function from and hypothesized class of statistical distributions. In linear programming, it may take the form of ascertaining ranges within which data may be varied without requiring a change in the set of vectors that constitute an optimum basis. Additional keywords: Reprints.

Chance Constraints and Normal Deviates

Abstract Linear programming as a problem in optimizing a linear functional subject to linear inequality constraints is first discussed along with possible uses of the resulting duality relations. Various approaches to dealing with such problems when parts of the data are subject to error are briefly reviewed. Chance constrained programming refers to the class of such cases in which contraint violations are admissible up to pre- assigned probability levels. This topic is elaborated in the context of a ship-chartering problem in which independent normally distributed deviates from the (known) average demands may occur in any of the periods to be considered. Certain additional assumptions (including the use of a specified class of linear decision rules) make it possible to effect reductions first to a nonlinear (mathematical) programming and then to a linear programming problem. The use of the resulting duality relations for evaluating risk and quality levels of planned performance are then briefly examined.