带权重约束的DEA超效率评价模型及其应用研究

DEA Super Efficiency Evaluation Model with Weight Constraints and Its Application

针对产学研协同创新项目的相对效率比较问题,数据包络分析(DEA)法是比较有效的数量分析方法。但DEA法所构建的优化模型中,由于约束条件没有充分考虑评价指标体系内部指标之间客观存在的内在权重大小信息,从而导致模型过分强调了评价单元的投入产出特征差异,甚至出现了原本非常重要的指标其权重却为0的不合理现象。本文提出DEMATEL法和数据包络分析法有机结合的思想,将运用DEMATEL法获得的指标之间内在的权重大小信息,纳入DEA法非阿基米德无穷小量ε限制的CCR模型及其超效率模型的约束条件,创新模型的可行域,构建了权重约束型ε-CCR模型和超效率ε-CCR模型。并以美国2014-2015年度国家科学基金会产学研合作研究中心发布的年度报告数据,对美国71个以高校为主导的产学研协同创新中心的相对效率进行了实证分析。实证结果显示,权重约束型超效率ε-CCR模型比没有权重约束的超效率ε-CCR模型更有效,不仅能对多个评价单位进行全排序,而且能克服无权重约束的超效率ε-CCR模型存在的评价结果不合理现象。这些结果有助于进一步推动DEA法的理论创新和应用推广,并能为多投入多产出项目的决策提供新的方法,使实际问题决策更合理更科学。

For a group of evaluation units with multiple inputs and multiple outputs,such as a group of industry-academia collaborative innovation projects to evaluate their relative effectiveness,the Data Envelopment Analysis(DEA)method is an effective and commonly used quantitative analysis method.However,in the optimization model constructed by the DEA method,because the feasible region does not fully consider the objectively important information among the indicators,it leads to the model overemphasizing the differences in the input and output characteristics of the evaluation unit,even led to an unreasonable phenomenon that the weight of a very important indicator is 0.An idea is proposed that combines DEMATEL method and data envelopment analysis method.That is to say,the index weight information obtained by the DEMATEL method is included in the constraints of the non-Archimedean limitlessε-CCR model and its super-efficiency model,and constructed a weight-constrainedε-CCR model and a weight-constrained super-efficiencyε-CCR model.Based on the above model,using the annual report data released by the US-Institute Collaborative Research Center of the National Science Foundation from 2014 to 2015,an empirical analysis of the relative efficiency of 71 university-led I/UCRC programs is conducted.The empirical results show that super-efficiencyε-CCR model with weight constraints is more effective than super-efficiencyε-CCR model without weight constraints,which can not only fully rank evaluation units,but also overcome the irrational evaluation result by super-efficiencyε-CCR model without weight constraints.These results help to further promote the theoretical innovation and application of DEA method,provide new methods for decision-making problems of multi-input and multi-output projects,and improve the scientific decision-making of related departments.