Ranking decision-making units using common weights in DEA

Ramezani-Tarkhorani, Somayeh; Khodabakhshi, Mohammad; Mehrabian, S; Nuri-Bahmani, F.

doi:10.1016/j.apm.2013.08.029

Cited by 31 publications

(27 citation statements)

References 8 publications

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“…(1) Ramazani-Tarkhorani et al [30] obtained a common set of weights (CSW) to create the best efficiency score of a group composed of efficient units in DEA. Development of their method for ranking of efficient candidates in voting systems may also produce interesting results.…”

Section: Resultsmentioning

confidence: 99%

Data envelopment analysis approach for discriminating efficient candidates in voting systems by considering the priority of voters

Ebrahimnejad

Bagherzadeh²

2015

HJMS

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There are different ways to allow the voters to express their preferences on a set of candidates. In the traditional voting systems, it is assumed that the votes of all voters have the same importance and there is no preference between them. In this paper, a new approach is proposed to express the preference of voters on a set of candidates. In the proposed approach voters are classified into several categories with different importance levels in which the vote of a higher category may have a greater importance than that of the lower category. Then two models are introduced to measure the best preference scores of the target candidate from the virtual best candidate and the virtual worst candidate point of view. After that, two obtained preference scores are aggregated together in order to obtain an overall ranking. Finally, two numerical examples are provided for illustration the applications of the proposed approach.

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Section: Resultsmentioning

confidence: 99%

Data envelopment analysis approach for discriminating efficient candidates in voting systems by considering the priority of voters

Ebrahimnejad

Bagherzadeh²

2015

HJMS

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“…Olympic Games [20,21] are presented in Table 3. We use this example to compare the proposed method with Azizi and Wang's method [21] and Ramezani-Tarkhorani et al 's method [22].…”

Section: The Input and Output Data Of The Athens 2004 Summermentioning

confidence: 99%

A Multiobjective Programming Method for Ranking All Units Based on Compensatory DEA Model

Cheng

Zhang

Cai

et al. 2014

Mathematical Problems in Engineering

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In order to rank all decision making units (DMUs) on the same basis, this paper proposes a multiobjective programming (MOP) model based on a compensatory data envelopment analysis (DEA) model to derive a common set of weights that can be used for the full ranking of all DMUs. We first revisit a compensatory DEA model for ranking all units, point out the existing problem for solving the model, and present an improved algorithm for which an approximate global optimal solution of the model can be obtained by solving a sequence of linear programming. Then, we applied the key idea of the compensatory DEA model to develop the MOP model in which the objectives are to simultaneously maximize all common weights under constraints that the sum of efficiency values of all DMUs is equal to unity and the sum of all common weights is also equal to unity. In order to solve the MOP model, we transform it into a single objective programming (SOP) model using a fuzzy programming method and solve the SOP model using the proposed approximation algorithm. To illustrate the ranking method using the proposed method, two numerical examples are solved.

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“…Ramon et al [12,13] extended their research on the cross-efficiency evaluation into the common weights DEA method based on the idea of reducing differences between profiles of weights. Some other techniques have also been introduced into the DEA method for determining common weights, such as goral programming [14], regression analysis [15], robust optimization [16] and so on [17][18][19][20]. Applications of the common weights DEA models can be found in economy evaluation [21], technology selection [22], resource allocation [23], and so on.…”

Section: Introductionmentioning

confidence: 99%

Determining Common Weights in Data Envelopment Analysis with Shannon’s Entropy

2014

Entropy

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Data Envelopment Analysis (DEA) is a non-parametric method for evaluating the efficiency of Decision Making Units (DMUs) with multiple inputs and outputs. In the traditional DEA models, the DMU is allowed to use its most favorable multiplier weights to maximize its efficiency. There is usually more than one efficient DMU which cannot be further discriminated. Evaluating DMUs with different multiplier weights would also be somewhat irrational in practice. The common weights DEA model is an effective method for solving these problems. In this paper, we propose a methodology combining the common weights DEA with Shannon's entropy. In our methodology, we propose a modified weight restricted DEA model for calculating non-zero optimal weights. Then these non-zero optimal weights would be aggregated to be the common weights using Shannon's entropy. Compared with the traditional models, our proposed method is more powerful in discriminating DMUs, especially when the inputs and outputs are numerous. Our proposed method also keeps in accordance with the basic DEA method considering the evaluation of the most efficient and inefficient DMUs. Numerical examples are provided to examine the validity and effectiveness of our proposed methodology.

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Ranking decision-making units using common weights in DEA

Cited by 31 publications

References 8 publications

Data envelopment analysis approach for discriminating efficient candidates in voting systems by considering the priority of voters

Data envelopment analysis approach for discriminating efficient candidates in voting systems by considering the priority of voters

A Multiobjective Programming Method for Ranking All Units Based on Compensatory DEA Model

Determining Common Weights in Data Envelopment Analysis with Shannon’s Entropy

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