不确定条件下的网络DEA模型及其应用研究

Conventional DEA models evaluate the efficiencies of decision making units from the whole perspective, which can not characterize the performance of decision making units when internal structures are known. Thus, many network DEA models are developed in recent years when internal structures are considered. However, these network DEA models assume all indexes to be deterministic and crisp, which is not in accord with facts. In our project, stochastic and fuzzy theories will be used for characterizing the data uncertainty. Graph and game theories are utilized to describe the internal structures and organizational mechanisms in decision making units, respectively. A whole string new network DEA models will be developed under uncertainty, including stochastic and fuzzy network DEA models. The new concepts of "efficient" under uncertainty, the algorithms for computing the efficiencies of the whole system and its components will be studied together with their relationships. Methods for improving the overall efficiency and optimizing the resource allocation will be developed based on the above research work. Network DEA software will be developed and used for efficiency evaluation and optimization in many areas, such as logistics, finance, education, energy, national defense, etc., which can provide decision makers with usefule suggestions for performance management. Our project will consummate the theory of performance evaluation and optimization, enhance the wide applications of DEA approach, which is of great theoretical importance and practical values.

经典的DEA模型从系统层面评价决策单元的效率，没有探究内部结构特征对整体效率的影响，为此很多学者提出了多种网络DEA模型。然而现有的网络DEA模型普遍假设所有指标都是确定且精确可测的，这与实际情况不符。本项目根据不确定性的两种表现形式，在现有网络DEA模型的基础上，通过引入随机理论和模糊理论来描述实际获取到的数据的不确定性，利用图论、博弈论等来刻画系统内部结构及运作模式，构建若干不确定条件下的网络DEA模型，主要包括随机网络DEA模型和模糊网络DEA模型，研究不确定条件下有效性的定义、系统和子系统效率计算方法及其关联关系，提出相应的效率改进和资源优化配置方法，开发图形化的网络DEA分析软件，并将其应用于物流、金融、教育、能源、国防等领域的效率评价与优化问题，为实际绩效管理提供决策参考。本项目对于完善现有的绩效评价与优化理论，促进数据包络分析在各个领域的实际应用具有重要的理论和实际意义。

现有的网络DEA模型普遍假设所有输入输出数据都是确定且精确可测的，然而实际情况并非如此。本项目根据不确定性的两种表现形式，通过引入随机理论和模糊理论来描述实际获取到的数据的不确定性，利用图论、博弈论等来刻画系统内部结构及运作模式，构建不确定条件下的串行、并行和网络系统随机DEA模型和模糊DEA模型，研究不确定条件下有效性的定义、系统和子系统效率计算方法及其关系，提出相应的效率改进和资源优化配置方法，并将其应用于金融、能源、国防等领域的效率评价与优化问题，为实际绩效管理提供决策参考。本项目对于完善现有的评价与优化理论，促进数据包络分析的实际应用具有重要的意义。