In the determination of weight sets to compute cross-efficiency ratios in DEA

Lam, Kim Fung

doi:10.1057/jors.2008.138

Cited by 44 publications

(29 citation statements)

References 24 publications

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“…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. In addition to the well-known aggressive (minimal) and benevolent (maximal) formulations, other secondary-goal techniques are proposed and investigated [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Since it is possible that these two different formulations produce two different ranking results, decision makers may need to make a choice between these two formulations.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

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

Liu

2016

Entropy

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“…Their model can significantly reduce the number of zero weights for both inputs and outputs in the cross efficiency evaluation. For non-uniqueness of the optimal weights in DEA, Lam (2010) proposed a mixed-integer linear programming formulation based on linear discriminant analysis and the super efficiency method. Wang et al (2011a) proposed four neutral DEA models for cross efficiency evaluation from the perspective of multiple criteria decision analysis (MADA), which are built using the ideal DMU and anti-ideal DMU.…”

Section: Introductionmentioning

confidence: 99%

“…The problem of multiple optimal solutions in DEA, Lam (2010) proposed a mixed-integer linear programming formulation based on linear discriminant analysis and the super efficiency method. In this paper, we modify this model and introduce a new model to choose suitable weight sets to be used in cross efficiency evaluation.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we modify this model and introduce a new model to choose suitable weight sets to be used in cross efficiency evaluation. Lam (2010) used a h constant to separate efficient and inefficient DMUs. In the Lam (2010) model, h constant is determined from the super efficiency model.…”

Section: Introductionmentioning

confidence: 99%

“…In the Lam (2010) model, h constant is determined from the super efficiency model. As h is considered as a variable in our proposed model, it is not necessary to use the super efficiency model to determine h. Lam (2010) used three data scenario to illustrate his model. We used these data scenarios.…”

Section: Introductionmentioning

confidence: 99%

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A modification of a mixed integer linear programming (MILP) model to avoid the computational complexity

2015

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Having multiple optimal solutions to weights affects to a great extent the consistency of operations related to weights. The cross efficiency method is the most frequently studied topic in data envelopment analysis (DEA) literature. Originally, the cross efficiency method included the efficiency evaluations that were obtained for a decision making unit (DMU) by the classical DEA for the reuse of optimal weights in other DMUs. As the optimal weights in classical DEA solutions usually have multiple solutions, this reduces the usefulness of the cross evaluation. Lam (J Oper Res Soc 61:134-143, 2010) proposed a mixed-integer linear programming (MILP) formulation based on linear discriminant analysis and super efficiency method to choose suitable weight sets to be used in cross efficiency evaluation. In this study, Lam's MILP model has been modified to reduce the steps during the solution process. The model also becomes a linear programming model after the modification to make it easier to use and to reduce the computational complexity. Numerical examples indicate that the proposed weight determination model both reduces the steps and minimizes computational complexity. Furthermore, it has similar performance with Lam's MILP model for the cross efficiency evaluation.

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Using Induced Ordered Weighted Averaging (IOWA) Operators for Aggregation in Cross-Efficiency Evaluations

León

Ramon

Ruiz

et al. 2014

Int. J. Intell. Syst.

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This paper proposes an enhancement of the cross‐efficiency evaluation through the aggregation of cross‐efficiencies by using a particular type of induced ordered weighted averaging (IOWA) operator. The use of a weighted average of cross‐efficiencies for the calculation of the cross‐efficiency scores, instead of the usual arithmetic mean, allows us to introduce some flexibility into the analysis. In particular, the main purpose of the approach we present is to provide aggregation weights that reflect the decision maker (DM) preferences regarding the relative importance that should be attached to the cross‐efficiencies provided by the different decision‐making units. To do it, an ordering is to be induced in the rows of the matrix of cross‐efficiencies, so the IOWA operator weights can be attached accordingly to the elements in each of the columns. The DM can thus incorporate his/her preferences by means of the choice of the variable that induces such ordering, and he/she may also adjust the importance to be attached to the most preferred cross‐efficiencies with the level of orness that is used when the aggregation weights are obtained.

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In the determination of weight sets to compute cross-efficiency ratios in DEA

Cited by 44 publications

References 24 publications

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

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

A modification of a mixed integer linear programming (MILP) model to avoid the computational complexity

Using Induced Ordered Weighted Averaging (IOWA) Operators for Aggregation in Cross-Efficiency Evaluations

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