A Study on Overall Efficiency Measure in Data Envelopment Analysis

在本研究中，我提出了一种基于松弛的数据包络分析(DEA)中的效率度量(SBM)。这一措施考虑到了效率径向措施如CCR和BCC措施中没有涉及的投入过剩和产出不足。这一度量(SBM)被定义为两项的比率，一项涉及产出不足，另一项涉及投入过剩。证明了SBM不大于COR度量。可以对SBM进行修改，以适应输入导向和输出导向。这些改进使得SBM与传统的效率测量方法的比较变得容易。然后，我观察了SBM的两面性，发现它最大化了虚拟利润。因此，可以从经济学的角度对SBM进行解释。因此，关于投入和产出的价格信息可以以类似于保证域法和锥比模型的方式被纳入。此外，我还研究了低效分解为混合低效、技术低效和纯技术低效等主题。这些结果将拓展数据包络分析的应用领域。

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.