Variations on the theme of slacks-based measure of efficiency in DEA
Variations on the theme of slacks-based measure of efficiency in DEA
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DOI：
10.1016/j.ejor.2009.01.027
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发表时间：
2010-02
期刊：
影响因子：
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通讯作者：
K. Tone
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文献类型：
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作者：
K. Tone
在数据包络分析中，通常有两种方案来衡量决策单元的效率：径向和非径向。径向模型假定投入/产出成比例变化，通常不直接将剩余的缺口归因于效率低下。另一方面，非径向模型单独和独立地处理每个投入/产出的松弛，并将它们集成到一个效率度量中，称为基于松弛的度量(SBM)。在本文中，我们指出了SBM模型的不足，并提出了SBM模型的四种变体。原始的SBM模型参考一个范围内最远的边界点来评估决策单元的效率。这导致了目标DMU的最难得分，并且投影可能到达有效前沿上的远程点，这可能不适合作为参考。为了克服这一缺陷，我们首先研究了生产可能性集的前沿(刻面)结构。然后，我们提出了变体I，它通过与SBM发现的相同边界上的最近点来评估每个DMU。然而，评估决策单元还有其他潜在的方面。因此，我们提出了变体II，它从各个方面对每个决策单元进行评估。然后，我们使用聚类方法将决策单元分类为几个组，并在每个簇中应用变体II。这一变体III以更少的努力给出了更合理的效率分数。最后，我们提出了一种减少刻面枚举负担的随机搜索方法(变种IV)。结果是近似的，但在实际应用中是实用的。
In DEA, there are typically two schemes for measuring efficiency of DMUs; radial and non-radial. Radial models assume proportional change of inputs/outputs and usually remaining slacks are not directly accounted for inefficiency. On the other hand, non-radial models deal with slacks of each input/output individually and independently, and integrate them into an efficiency measure, called slacks-based measure (SBM). In this paper, we point out shortcomings of the SBM and propose four variants of the SBM model. The original SBM model evaluates efficiency of DMUs referring to the furthest frontier point within a range. This results in the hardest score for the objective DMU and the projection may go to a remote point on the efficient frontier which may be inappropriate as the reference. In an effort to overcome this shortcoming, we first investigate frontier (facet) structure of the production possibility set. Then we propose Variation I that evaluates each DMU by the nearest point on the same frontier as the SBM found. However, there exist other potential facets for evaluating DMUs. Therefore we propose Variation II that evaluates each DMU from all facets. We then employ clustering methods to classify DMUs into several groups, and apply Variation II within each cluster. This Variation III gives more reasonable efficiency scores with less effort. Lastly we propose a random search method (Variation IV) for reducing the burden of enumeration of facets. The results are approximate but practical in usage.