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2007 | Buch

General Discussion Kapitel lesen Erstes Kapitel lesen

Data Envelopment Analysis

A Comprehensive Text with Models, Applications, References and DEA-Solver Software

verfasst von: William W. Cooper, Lawrence M. Seiford, Kaoru Tone

Verlag: Springer US

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References, And DEA-Solver Software, 2nd Edition is designed to provide a systematic introduction to DEA and its uses as a multifaceted tool for evaluating problems in a variety of contexts. Each chapter accompanies its developments with simple numerical examples and discussions of actual applications. Emphasis is placed on the use as well as an understanding of DEA and the topics in this book have been selected and treated accordingly. The first nine chapters cover the basic principles of DEA and the final seven chapters are more advanced treatment of DEA. These final chapters were completely revised into new chapters, reflecting recent developments that greatly extend the power and scope of DEA and lead to new directions for research and DEA uses. Together with the first ten chapters of the basic principles, they will provide students and researchers with a solid understanding of the methodology, its uses and its potential.

Inhaltsverzeichnis

Frontmatter
1. General Discussion
William W. Cooper, Lawrence M. Seiford, Kaoru Tone
2. The Basic CCR Model
William W. Cooper, Lawrence M. Seiford, Kaoru Tone
3. The CCR Model and Production Correspondence
Abstract
In this chapter we described the CCR model in some detail in both its input-oriented and output-oriented versions.
1.
We also relaxed assumptions of a positive data set to semipositivity.
 
2.
We defined the production possibility set based on the constant returns-to-scale assumption and developed the CCR model under this assumption.
 
3.
The dual problem of the original CCR model was introduced as (DLP o) in (3.6)–(3.9) and the existence of input excesses and output shortfalls clarified by solving this model. (To avoid confusion and to align our terminology with the DEA literature, we referred to the dual as the “envelopment model” and the primal (LP o) introduced in Chapter 2 as the “multiplier model.”)
 
4.
In Definition 3.2 we identified a DMU as CCR-efficient if and only if it is (i) radial-efficient and (ii) has zero-slack in the sense of Definition 3.1. Hence a DMU is CCR-efficient if and only if it has no input excesses and no output shortfalls.
 
5.
Improvement of inefficient DMUs was discussed and formulae were given for effecting the improvements needed to achieve full CCR efficiency in the form of the CCR-projections given in (3.22) and (3.23).
 
6.
Detailed computational procedures for the CCR model were presented in Section 3.6 and an optimal multiplier values (v, u) were obtained as the simplex multipliers for an optimal tableau obtained from the simplex method of linear programming.
 
William W. Cooper, Lawrence M. Seiford, Kaoru Tone
4. Alternative Dea Models
William W. Cooper, Lawrence M. Seiford, Kaoru Tone
5. Returns to Scale
William W. Cooper, Lawrence M. Seiford, Kaoru Tone
6. Models with Restricted Multipliers
Abstract
In this chapter, we introduced the assurance region and cone-ratio methods for combining subjective and expert evaluations with the more objective methods of DEA.
1.
Usually expressed in the form of lower and upper bounds, the assurance region method puts constraints on the ratio of input (output) weights or multiplier values. This helps to get rid of zero weights which frequently appear in solution to DEA models. The thus evaluated efficiency score generally drops from its initial (unconstrained) value. Careful choice of the lower and upper bounds is recommended.
 
2.
Not covered in this chapter is the topic of “linked constraints” in which conditions on input and output multipliers are linked. See Problem 6.3.
 
3.
The cone-ratio method confines the feasible region of virtual multipliers v, u, to a convex cone generated by admissible directions. Formulated as a “cone ratio envelopment” this method can be regarded as a generalization of the assurance region approach.
 
4.
Example applications were used to illustrate uses of both of the “assurance region” and “cone ratio envelopment” approaches.
 
William W. Cooper, Lawrence M. Seiford, Kaoru Tone
7. Non-Discretionary and Categorical Variables
Abstract
In this chapter we expanded the ability of DEA to deal with variables that are not under managerial control but nevertheless affect performances in ways that need to be taken into account when effecting evaluations. Non-discretionary and categorical variables represent two of the ways in which conditions beyond managerial control can be taken into account in a DEA analysis. Uses of upper or lower bounds constitute yet another approach and, of course, these approaches can be combined in a variety of ways. Finally, uses of Wilcoxon-Mann-Whitney statistics were introduced for testing results in a nonparametric manner when ranking can be employed.
Illustrative examples were supplied along with algorithms that can be used either separately or with the computer code DEA-Solver. We also showed how to extend DEA in order to deal with production possibility sets (there may be more than one) that are not convex. Finally we provided examples to show how new results can be secured when DEA is applied to such sets to test the efficiency of organization forms (and other types of activities) in ways that were not otherwise available.
William W. Cooper, Lawrence M. Seiford, Kaoru Tone
8. Allocation Models
William W. Cooper, Lawrence M. Seiford, Kaoru Tone
9. Data Variations
William W. Cooper, Lawrence M. Seiford, Kaoru Tone
10. Super-Efficiency Models
Abstract
This chapter introduced the concept of super-efficiency and presented two types of approach for measuring super-efficiency: radial and non-radial. Super-efficiency measures are widely utilized in DEA applications for many purposes, e.g., ranking efficient DMUs, evaluating the Malmquist productivity index and comparing performances of two groups (the bilateral comparisons model in Chapter 7).
William W. Cooper, Lawrence M. Seiford, Kaoru Tone
11. Efficiency Change over Time
Abstract
In this chapter, we introduced two methods for measuring efficiency change over time: “window analysis” and “Malmquist index” using non-parametric DEA models.
William W. Cooper, Lawrence M. Seiford, Kaoru Tone
12. Scale Elasticity and Congestion
William W. Cooper, Lawrence M. Seiford, Kaoru Tone
13. Undesirable Outputs Models
William W. Cooper, Lawrence M. Seiford, Kaoru Tone
14. Economies of Scope and Capacity Utilization
Abstract
In this chapter, we have covered two subjects; economies of scope and capacity utilization.
1.
Economies of scope concerns the problem whether any significant difference in efficiency exists between specialized and diversified firms. The specialized firms produce different (specialized) products, whereas the diversified firms produce all of the concerned products. We extended this model to comparisons of two business models where both models utilize common inputs for producing common outputs but their business styles are different.
 
2.
Capacity utilization deals with the situation where some input values are fixed and cannot be easily altered while some are flexibly alterable. Thus, we divided inputs into fixed and variable inputs, and studied the effect on efficiency caused by the variable inputs according to whether relaxation of variable inputs improves the efficiency of DMU under evaluation. We analyzed two aspects of capacity utilization; (1) technical and (2) price-based.
 
3.
Example applications were presented to illustrate uses of both these approaches.
 
William W. Cooper, Lawrence M. Seiford, Kaoru Tone
15. A Dea Game
Abstract
In this chapter we have introduced a consensus-making method in a multiple criteria environment using a combination of DEA and cooperative game theory. It is demonstrated that both DEA max and min games have the same Shapley value.
Problems like the one exemplified in this chapter are usually solved by means of (among others)
  • conventional custom
  • a single criterion decision or
  • a fixed weights rule.
These approaches are not always “rational.”
The proposed scheme has diverse applications in areas, such as,
  • cost or burden sharing in international organizations, e.g., United Nations, NATO, UNESCO and so forth,
  • research grant allocation to applicants by a foundation, and
  • resource distribution for R&D.
These problems are multifaceted and should be solved in a cooperative frame-work. The DEA game proposed in this chapter can be a promising method for solving these important problems and will open a new dimension to cooperative game theory.
William W. Cooper, Lawrence M. Seiford, Kaoru Tone
16. Multi-Stage Use of Parametric and Non-Parametric Models
Abstract
Observed data for use in DEA may suffer from non-controllable environmental effects and statistical noise. Hence, detaching these external effects from data and uncovering the true managerial efficiency are crucial for evaluating DMUs’ performance. In this chapter, we have covered these subjects and demonstrated a case study dealing with Japanese banking using a three-stage approach.
William W. Cooper, Lawrence M. Seiford, Kaoru Tone
Backmatter
Metadaten
Titel
Data Envelopment Analysis
verfasst von
William W. Cooper
Lawrence M. Seiford
Kaoru Tone
Copyright-Jahr
2007
Verlag
Springer US
Electronic ISBN
978-0-387-45283-8
Print ISBN
978-0-387-45281-4
DOI
https://doi.org/10.1007/978-0-387-45283-8

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