Minimax and maximin formulations of cross-efficiency in DEA

Lim, Sungmook

doi:10.1016/j.cie.2011.11.010

Cited by 75 publications

(27 citation statements)

References 6 publications

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“…Their model cannot only guarantee the maximum self-assessment efficiency of DMU under evaluation, but also reduces the differences in the weighted inputs and weighted outputs during the evaluation process. Lim (2012) proposed aggressive and benevolent formulations of cross efficiency in DEA where a minimax or a maximin type secondary objective is incorporated. These formulations determine the optimal weights that maximize the efficiency score of a particular DMU under evaluation and subsequently minimize (or maximize) the cross efficiency of the best (or worst) peer DMU.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

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

2015

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“…Using the secondary goal models is the main method to solve this question. Up to now, there are many secondary goal models proposed by many scholars such as aggressive and benevolent models proposed by Doyle and Green [9], the neutral model by Wang (2010), the weight-balanced model by Wu et al [15], the maximin model by Lim [16], and the satisfaction degree model by Wu et al [17]. The aggressive and benevolent models proposed by Doyle and Green [9] are two classical ways among the many models.…”

Section: Introductionmentioning

confidence: 99%

A Revised Model of the Neutral DEA Model and Its Extension

Liu

Wang

Chang

2017

Mathematical Problems in Engineering

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The neutral data envelopment analysis (DEA) model is an alternative way to determine the weights in DEA cross-efficiency evaluation, while avoiding the difficulty in making a choice between the aggressive and benevolent formulations. However, the weights determined by the neutral model merely make the efficiency of part output bigger than other sets of weights. The neutral model is not able to make the efficiency of each output of the DMU biggest among the favorable weights. This neutral model is not purely "neutral" and not most favorable to the DMU. We proposed a revised model for the neutral model. Based on the idea that the DMU should choose a set of weights to maximize its own efficiency, this paper proposes a new cross-efficiency model. The weights determined by the two models are neutral, neither aggressive nor benevolent.

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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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Minimax and maximin formulations of cross-efficiency in DEA

Cited by 75 publications

References 6 publications

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

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

A Revised Model of the Neutral DEA Model and Its Extension

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

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