Efficiency and Cross-efficiency in DEA: Derivations, Meanings and Uses

Doyle, John R.; Green, Rodney

doi:10.1057/jors.1994.84

Cited by 1,018 publications

(283 citation statements)

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“…In 1985, Charnes et al [2], counted the number of times that an efficient DMU play the role of benchmark unit for others, and used this norm to rank these units. In 1986, Sexton et al [3] developed the cross-evaluation Matrix and this approach was extended by Doyle and Green [4], both of which are referred to as the cross efficiency ranking methods. Andersen and Petersen [5] modify the CCR model to allow for a ranking of the efficient units.…”

Section: Introductionmentioning

confidence: 99%

A note on ranking efficient DMUs based on a single virtual inefficient DMU in DEA

Balf¹

2017

Data Envelopment Analysis and Decision Science

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In this paper we give a comment on paper by Shetty and Pakkala [U. Shetty, T.P.M. Pakkala, (2010), Ranking efficient DMUs based on single virtual inefficient DMU in DEA. OPSEARCH, 47 (1):50-72]. They proposed an approach to rank the efficient decision making units based on a virtual DMU in the constant return to scale DEA model. The input and output levels of this virtual DMU are the average of input and outputs of all DMUs. We obtain another method for select virtual DMU as negative ideal DMU. Our approach doesn't need to existence at least an inefficient DMU in the set DMUs. In addition, it can be used in constant and variable return to scale DEA models. This brief comment provides an alternative approach for their work.

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Section: Introductionmentioning

confidence: 99%

A note on ranking efficient DMUs based on a single virtual inefficient DMU in DEA

Balf¹

2017

Data Envelopment Analysis and Decision Science

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“…As an extension of DEA, cross-efficiency evaluation is to provide a ranking for CCR-efficient units [2,3]. The purpose of this method is to employ DEA to do peer-evaluation, rather than to have it perform in a self-evaluation mode.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, cross-efficiency scores obtained from the original DEA methodology are generally not unique [3]. It may be possible to improve a DMU's (cross-efficiency) performance rating, but generally only by worsening the ratings of others [14].…”

Section: Introductionmentioning

confidence: 99%

“…It may be possible to improve a DMU's (cross-efficiency) performance rating, but generally only by worsening the ratings of others [14]. In this regard, the methods of Sexton et al [2] and Doyle and Green [3] use a secondary-goal methodology to deal with the multiple DEA solutions. They develop aggressive (minimal) and benevolent (maximal) formulations to identify optimal weights that not only maximize the efficiency of a particular DMU under evaluation, but also minimize the average efficiency of other DMUs.…”

Section: Introductionmentioning

confidence: 99%

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Ranking DMUs by Comparing DEA Cross-Efficiency Intervals Using Entropy Measures

Liu

2016

Entropy

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Cross-efficiency evaluation, an extension of data envelopment analysis (DEA), can eliminate unrealistic weighing schemes and provide a ranking for decision making units (DMUs). In the literature, the determination of input and output weights uniquely receives more attentions. However, the problem of choosing the aggressive (minimal) or benevolent (maximal) formulation for decision-making might still remain. In this paper, we develop a procedure to perform cross-efficiency evaluation without the need to make any specific choice of DEA weights. The proposed procedure takes into account the aggressive and benevolent formulations at the same time, and the choice of DEA weights can then be avoided. Consequently, a number of cross-efficiency intervals is obtained for each DMU. The entropy, which is based on information theory, is an effective tool to measure the uncertainty. We then utilize the entropy to construct a numerical index for DMUs with cross-efficiency intervals. A mathematical program is proposed to find the optimal entropy values of DMUs for comparison. With the derived entropy value, we can rank DMUs accordingly. Two examples are illustrated to show the effectiveness of the idea proposed in this paper.

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“…This is primarily due to the fact that the composite DMU that dominates the inefficient DMU does not exist in the same sector. To overcome these problems researchers have utilized performance-based clustering methods for identifying more appropriate benchmarks (Doyle & Green, 1994;Talluri & Sarkis, 1997). These methods cluster inherently similar DMUs into groups, and the best performer in each cluster serves as a benchmark for other DMUs in that cluster.…”

mentioning

confidence: 99%

Benchmarking and Ranking of Quoted Manufacturing Companies in Nigeria: A Data Envelopment Analysis Approach

Osamwonyi¹,

Imafidon²

2015

International Journal of Financial Research

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The objective of this study is to identify quoted manufacturing companies in Nigeria that can be used as benchmark for less efficient companies. To achieve this objective, the study adopted the output orientated DEA model with total asset, shareholder's equity, cost of goods sold and operating expenses as input variables, while the output variables are sales/turnover, net profit, return on asset, and return on equity. The output orientated DEAP Version 2.1 package with variable return to scale assumption [multi-stage DEA approach] was employed. The analysis revealed the inefficient quoted manufacturing companies that should emulate the efficient ones in terms of input-output mix. The result indicates that twenty-seven companies can be used for benchmarking. The study recommends possible merger of the inefficient companies with efficient ones in the same sector in order to strengthen them and enhance their contributions to development of Nigeria.

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Efficiency and Cross-efficiency in DEA: Derivations, Meanings and Uses

Cited by 1,018 publications

References 11 publications

A note on ranking efficient DMUs based on a single virtual inefficient DMU in DEA

A note on ranking efficient DMUs based on a single virtual inefficient DMU in DEA

Ranking DMUs by Comparing DEA Cross-Efficiency Intervals Using Entropy Measures

Benchmarking and Ranking of Quoted Manufacturing Companies in Nigeria: A Data Envelopment Analysis Approach

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