A Study on Overall Efficiency Measure in Data Envelopment Analysis

在本研究中，笔者提出了一种基于松弛的数据包络分析效率度量（SBM）。该措施考虑了投入过剩和产出不足，而这些都不涉及效率的径向措施，例如CCR和BCC措施。该测度（SBM）被定义为两项之比，一项与输出不足有关，另一项与输入过剩有关，并证明了SBM不大于COR测度。可以对SBM进行修改，以适应投入导向和产出导向。这些修改使SBM与传统的效率测量方法进行比较变得容易。然后我观察了SBM的两面性，发现它使虚拟利润最大化。因此，SBM可以用经济学的术语来解释。因此，关于投入和产出的价格信息可以以与保证区域方法和锥比模型类似的方式纳入。此外，我还研究了低效率分解为混合、技术性和纯技术性低效率等主题。这些结果将拓展DEA的应用领域。

In this study, I proposed a slacks-based measure of efficiency (SBM) in Data Envelopment Analysis (DEA). This measure takes account of input excesses and output shortfalls that are not involved in the radial measures of efficiency e.g. the CCR and the BCC measures. This measure (SBM) is defined as a ratio of two terms, one concerning with the output shortfalls, and the other with the input excesses, It was proved that SBM is not greater than the COR measure. SBM can be modified to cope with input-orientation as well as output-orientation. These modifications make easy the comparisons of SBM with the traditional measures of efficiencies. I then observed the dual side of SBM and found that it maximizes a virtual profit. As a consequence, SBM can be interpreted in terms of economics. Hence, price information on inputs and outputs can be incorporated in a similar way as the assurance region method and the cone-ratio model. Furthermore, I studied on the subjects such as decomposition of inefficiency into mix, technical and pure technical inefficiencies. These results will expand the application areas of DEA.