数据包络分析SBM超效率模型无可行解问题的两阶段求解法

数据包络分析是一种得到广泛应用的基于线性规划的非参数技术效率分析方法,其超效率模型是将被评价DMU从参照集中排除从而使求解得出的效率值可能大于1.超效率模型在文献中用于对有效的DMU进行排序、探测异常值、敏感性和稳定性分析、分析生产率变化的Malmquist模型、二人博弈模型等.超效率模型存在的一个缺陷是在规模收益可变的假设下会出现无可行解的问题.提出了一种基于两阶段求解的SBM超效率模型,并保持了与传统SBM超效率模型的兼容性:在传统的投入(产出)导向SBM超效率模型有可行解时,两阶段法获得的结果与之相同;在传统的投入(产出)导向SBM超效率模型无可行解时,两阶段超效率模型可以得出最接近投入(产出)导向定义的可行解.算例采用实际数据对方法进行了验证.

A Two-Stage Approach to Overcoming the Infeasibility of SBM Super-Efficiency Model in Data Envelopment Analysis

Data envelopment analysis is a linear programming methodology for evaluating the relative technical efficiency for a set of peer decision making units.The super-efficiency model is identical to the standard model,except that the unit under evaluation is excluded from the reference set.The super-efficiency model has been used in ranking efficient units,identifying outliers,sensitivity and stability analysis,measuring productivity changes,and solving twoplayer games.However,under the assumption of variable returns to scale,the super-efficiency model may be infeasible for some efficient DMUs.We develop a 2-stage approach to overcoming this infeasibility issues,while keeping the compatibility with the traditional-oriented models. The newly developed model is illustrated with a real world dataset.