How to deal with Non-convex Frontiers in Data Envelopment Analysis
How to deal with Non-convex Frontiers in Data Envelopment Analysis
复制标题
数据包络分析中如何处理非凸边界
DOI：
10.1007/s10957-014-0626-3
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发表时间：
2015
影响因子：
1.9
通讯作者：
Miki Tsutsui
中科院分区：
文献类型：
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作者：
Kaoru Tone;Miki Tsutsui
在数据挖掘分析中，经常会遇到固定收益率和可变收益率之间的巨大差异，以及在真实的数据集上经常出现的“凸性生产集综合征”（convexity production set syndrome）。在本文中，我们提出了解决这些问题的方法。首先，我们通过传统的方法来评估所有决策单元的恒定收益规模和可变收益规模分数。我们得到了每个决策单元的规模效率。使用规模效率，我们分解的常数回报规模松弛为每个决策单元的规模无关和规模依赖的部分。在此之后，我们从数据集中消除尺度相关的松弛，从而获得尺度无关的数据集。接下来，我们将决策单元分为几个集群，这取决于规模效率的程度或其他一些预定的特征。我们使用恒定收益规模模型评估同一簇内与规模无关的决策单元的松弛，并获得簇内松弛。通过对尺度相关松弛和簇内松弛求和，我们定义了每个决策单元的总松弛。在此之后，我们评估决策单元的效率得分，并将其投影到有效边界上，这些边界不再保证是凸的，通常是非凸的。最后，我们定义了规模依赖的数据集，我们可以找到每个决策单元的规模弹性。我们将此模型应用于日本大学研究活动的数据集。
In data envelopment analysis, we are often puzzled by the large difference between the constant-returns-scale and variable returns-to-scale scores, and by the convexity production set syndrome in spite of the S-shaped curve, often observed in many real data sets. In this paper, we propose a solution to these problems. Initially, we evaluate the constant-returns-scale and variable returns-to-scale scores for all decision-making units by means of conventional methods. We obtain the scale-efficiency for each decision-making unit. Using the scale-efficiency, we decompose the constant-returns-scale slacks for each decision-making unit into scale-independent and scale-dependent parts. Following this, we eliminate scale-dependent slacks from the data set, and thus obtain a scale-independent data set. Next, we classify decision-making units into several clusters, depending either on the degree of scale-efficiency or on some other predetermined characteristics. We evaluate slacks of scale-independent decision-making units within the same cluster using the constant-returns-scale model, and obtain the in-cluster slacks. By summing the scale-dependent and the in-cluster slacks, we define the total slacks for each decision-making unit. Following this, we evaluate the efficiency score of the decision-making unit and project it onto the efficient frontiers, which are no longer guaranteed to be convex and are usually non-convex. Finally, we define the scale-dependent data set by which we can find the scale elasticity of each decision-making unit. We apply this model to a data set of Japanese universities’ research activities.