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

Data envelopment analysis (DEA) - Thirty years on

In this Chapter, we imagine a decision maker (or a group of experts) trying to establish or examine fair procedures to combine opinions about alternatives related to different points of view.

Multiple criteria decision making

Since the original Data Envelopment Analysis (DEA) study by Charnes et al. [Measuring the efficiency of decision-making units. European Journal of Operational Research 1978;2(6):429–44], there has been rapid and continuous growth in the field. As a result, a considerable amount of published research has appeared, with a significant portion focused on DEA applications of efficiency and productivity in both public and private sector activities. While several bibliographic collections have been reported, a comprehensive listing and analysis of DEA research covering its first 30 years of history is not available. This paper thus presents an extensive, if not nearly complete, listing of DEA research covering theoretical developments as well as “real-world” applications from inception to the year 2007. A listing of the most utilized/relevant journals, a keyword analysis, and selected statistics are presented.

Evaluation of research in efficiency and productivity:a survey and analysis of the first 30 years of scholarly literature in DEA

General Discussion.- The Basic CCR Model.- The CCR Model and Production Correspondence.- Alternative Dea Models.- Returns To Scale.- Models with Restricted Multipliers.- Discretionary, non-Discretionary and Categorical Variables.- Allocation Models.- Data Variations.- Super-Efficiency Models.

Introduction to Data Envelopment Analysis and Its Uses: With DEA-Solver Software and References

Data Envelopment Analysis (DEA) is a nonparametric approach to evaluating the relative efficiency of decision making units (DMUs) that use multiple inputs to produce multiple outputs An assumption underlying DEA is that all the data assume the form of specific numerical values In some applications, however, the data may be imprecise For instance, some of the data may be known only within specified bounds, while other data may be known only in terms of ordinal relations DEA with imprecise data or, more compactly, the Imprecise Data Envelopment Analysis (IDEA) method developed in this paper permits mixtures of imprecisely- and exactly-known data, which the IDEA models transform into ordinary linear programming forms This is carried even further in the present paper to comprehend the now extensively employed Assurance Region (AR) concepts in which bounds are placed on the variables rather than the data We refer to this approach as AR-IDEA, because it replaces conditions on the variables with transformations of the data and thus also aligns the developments we describe in this paper with what are known as cone-ratio envelopments in DEA As a result, one unified approach, referred to as the AR-IDEA model, is achieved which includes not only imprecise data capabilities but also assurance region and cone-ratio envelopment concepts

Idea and Ar-Idea: Models for Dealing with Imprecise Data in Dea

Data Envelopment Analysis (DEA) models, as ordinarily employed, assume that the data for all inputs and outputs are known exactly. In some applications, however, a number of factors may involve imprecise data, which take forms such as ordinal rankings and knowledge only of bounds. Here we provide an example involving a Korean mobile telecommunication company. The Imprecise Data Envelopment Analysis (IDEA) method we use permits us to deal not only with imprecise data and exact data but also with weight restrictions as in the (now) widely used "Assurance Region" (AR) and "cone-ratio envelopment" approaches to DEA. We also show how to transform AR bounds on thevariables, obtained from managerial assessments, for instance, intodata adjustments. This involves an extended IDEA model, which we refer to as AR-IDEA. All these uses are illustrated by an example application directed to evaluate efficiencies of branch offices of a telecommunication company in Korea.

An Illustrative Application of Idea Imprecise Data Envelopment Analysis to a Korean Mobile Telecommunication Company

This paper is concerned with the use of incomplete information on both multicriteria alternative value scores and importance weights in evaluating decision alternatives under certainty. Two decision concepts-dominance and potential optimality (PO)-are employed to determine outperforming alternatives or acts. Given incomplete weights and exact value scores, it is known that the set of nondominated acts implies the set of potentially optimal acts. We here rediscover this set inclusive relation in a different and computationally efficient manner that develops a mixed-integer programming approach to dominance. When both value scores and weights are incomplete, we show that the set inclusive relation between dominance and PO may or may not hold. This is a result of how we define PO. Two different definitions of PO-weak PO and strong PO-are made in the sense that an act is weak potentially optimal when there exists at least one exact vector of value scores in the given incomplete value scores which render this act potentially optimal. An act is strong potentially optimal when this act is potentially optimal for all possible value scores. Less formally, this means that under the given incomplete information, weak PO stands for sometimes good while strong PO stands for always good, so we can thus say that the latter outperforms than the former. As a result, we show that the set of nondominated acts implies the set of strong potentially optimal acts. No certain set inclusive relationship exists between nondominated acts and weak potentially optimal acts. We also present computational aspects of establishing dominance, weak and strong PO, which include transformations of nonlinear problems into linear programming problems.

Mathematical programming models for characterizing dominance and potential optimality when multicriteria alternative values and weights are simultaneously incomplete

Comparing methods for multiattribute decision making with ordinal weights

IDEA (Imprecise Data Envelopment Analysis) extends DEA so it can simultaneously treat exact and imprecise data where the latter are known only to obey ordinal relations or to lie within prescribed bounds. AR-IDEA extends this further to include AR (Assurance Region) and the like approaches to constraints on the variables. In order to provide one unified approach, a further extension also includes cone-ratio envelopment approaches to simultaneous transformations of the data and constraints on the variables. The present paper removes a limitation of IDEA and AR-IDEA which requires access to actually attained maximum values in the data. This is accomplished by introducing a dummy variable that supplies needed normalizations on maximal values and this is done in a way that continues to provide linear programming equivalents to the original problems. This dummy variable can be regarded as a new DMU (Decision Making Unit), referred to as a CMD (Column Maximum DMU).

Kyung Sam Park

Papers

Idea and Ar-Idea: Models for Dealing with Imprecise Data in Dea

An Illustrative Application of Idea Imprecise Data Envelopment Analysis to a Korean Mobile Telecommunication Company

Mathematical programming models for characterizing dominance and potential optimality when multicriteria alternative values and weights are simultaneously incomplete

Comparing methods for multiattribute decision making with ordinal weights

IDEA (Imprecise Data Envelopment Analysis) with CMDs (Column Maximum decision making units)