基于二层规划的数据包络分析方法及应用研究

With the standardization of internal processes, the departmental division of enterprise and their links are becoming much clearer which make hierarchy more obvious. When the hierarchy increases, the difficulty of managing enterprise also increases. So the feedback is needed to control the enterprise. Then how to assess the efficiency of these types of enterprises, including efficiencies of the enterprise level and departmental level, and further optimize the operation of the enterprise by these efficiencies are becoming meaningful. By introducing the basic concepts of bilevel programming and using the theory of data envelopment analysis, this project is planned to evaluate and improve the efficiency of the above systems as follows. First of all, we explore and describe the nature, characteristics and operational mechanism of the dual variables. According to the basic theory of bilevel programming, some evaluation models with theirs solving algorithms are established. Secondly, due to the fact that it is not easy to improve the efficiency of the decision-making system with dual variables, the project intends to analyze it by adopting Monte Carlo simulation methods. Finally, these methods will be used to evaluate the efficiency of the reverse supply chain system, solve the problem of bank's fixed cost sharing and analyze the allocation of resources of research institutions. These studies will extend and complete the theory of data envelopment analysis. Also they expand the scope of application of data envelopment analysis.

随着业务流程的规范化，企业部门的划分和联系越来越清晰，层次性愈加明显。层次的增加会加大管理者在整体上驾驭企业的难度，这时，反馈变得尤为重要。如何对有反馈的、层次性明显的企业的效率进行合理的评价，包括企业层面的效率评价和部门层面的效率评价，并通过这些评价来进一步优化企业的运作变得很有意义。 本项目拟引入二层规划的基本理念，运用数据包络分析方法对上述系统的效率评价和改进问题进行深入研究。首先，通过探讨和刻画双性变量的性质、特征及运作机制，根据二层规划的基本理论，给出决策系统的效率评价模型以及相应的求解算法。其次，含有双性变量的决策系统通常不容易进行效率改进操作，本项目拟采用蒙特卡罗模拟的方法对此进行分析。研究成果将为逆向供应链系统的效率评价、银行的固定成本分摊、科研机构的资源分配等问题提供管理决策支持。这些研究在一定程度上丰富和完善了DEA理论体系，拓展了DEA方法的应用范围。

多阶段系统的效率评价是近几年数据包络分析领域的研究热点。本项目以两阶段序贯系统为研究对象，基于二层规划的基本理念，运用数据包络分析方法研究其效率评价和改进问题。首先对无反馈的两阶段序贯系统进行了研究，利用二层规划的思想，并充分考虑到两个依存的子系统之间的重要性，分别构建了规模报酬不变约束下的基于二层规划的效率评价包络模型。这些模型可以帮助决策者获得对子系统效率的总体认识，也能够帮助决策者站在整个系统的角度对其效率进行改进。接着引入反馈变量，把无反馈的两阶段序贯系统推向有反馈的系统。同样，利用二层规划的思想建模，提出启发式算法，并得到了近似全局最优解。从决策单元的管理者、决策单元本身、决策单元的子系统等角度讨论了反馈变量的特征和作用，深化了对反馈变量的理解。进一步认识到反馈变量可以作为资源配置问题的切入点，这在科研机构的科研经费配置的应用研究中得到了体现。然后在系统规模报酬和系统结构两个方向进行扩展，很自然地把这些模型扩展到可变规模报酬、递增规模报酬和递减规模报酬等情形，以及扩展到有“共享投入”和“后继阶段有额外投入”等结构的情形。最后是模型的应用研究，完成了决策单元生产率变动分析和技术变革分析，研究了大学的科研经费配置和逆向供应链的效率测度等问题。