The measurement of returns to scale under a simultaneous occurrence of multiple solutions in a reference set and a supporting hyperplane
The measurement of returns to scale under a simultaneous occurrence of multiple solutions in a reference set and a supporting hyperplane
复制标题
DOI：
10.1016/j.ejor.2006.05.042
复制
发表时间：
2007-09
期刊：
影响因子：
--
通讯作者：
T. Sueyoshi;Kazuyuki Sekitani
中科院分区：
文献类型：
--
作者：
T. Sueyoshi;Kazuyuki Sekitani
本研究从理论上探讨了DEA（数据包络分析）中可能出现多种解的情况下RTS（尺度回报）的测量。本研究将多解的出现分为I型和II型。类型 I 是参考集中出现多个解。类型 II 是在传递参考集的支持超平面上出现多个解。 I 型和 II 型在 DEA 研究人员中都是众所周知的，但之前的研究尚未充分探索 RTS 测量中同时出现的 I 型和 II 型。这两种多解对DEA测量中的RTS程度有影响。 RTS的这种定量问题是从第一类和第二类问题的角度来考察的。为了解决这些困难，提出了一种新的线性规划方法来识别由参考集组成的所有高效 DMU（决策单元），即使参考集上出现多个解决方案。基于研究结果，我们可以确定RTS测量中何时出现Type I和/或Type II的多个解决方案以及如何处理这些困难。我们的研究结果使得衡量I型和II型同时发生的一定程度的规模经济（RTS）成为可能。
This research theoretically explores the measurement of RTS (Returns to Scale) under a possible occurrence of multiple solutions in DEA (Data Envelopment Analysis). In this study, the occurrence of multiple solutions is classified into Type I and Type II. Type I is an occurrence of multiple solutions in a reference set. Type II is an occurrence of multiple solutions on a supporting hyperplane passing on the reference set. Both Types I and II are very well known among DEA researchers, but previous research has not sufficiently explored a simultaneous occurrence of Type I and Type II in the RTS measurement. The two types of multiple solutions influence a degree of RTS in the DEA measurement. Such a quantitative issue on RTS is examined from the perspective of the Type I and Type II problems. To deal with such difficulties, a new linear programming approach is proposed to identify all efficient DMUs (Decision Making Units) that consist of a reference set, even if multiple solutions occur on the reference set. Based upon the research result, we can identify when multiple solutions of Type I and/or Type II occur on the RTS measurement and how to deal with such difficulties. Our research result makes it possible to measure a degree of scale economies (RTS) under the simultaneous occurrence of Type I and Type II.