DAE 分析方法介绍
1978年由著名的运筹学家A.Charnes,W.W.Cooper和 E.Rhodes首先提出了一个被称为数据包络分析（Data Envelopment Analysis，简称DEA）的方法，去评价部门间的相对有效性（因此被称为DEA有效）．他们的第一个模型被命名为CCR模型．从生产函数角度看，这一模型是用来研究具有多个输入、特别是具有多个输出的“生产部门”同时为“规模有效”与“技术有效”的十分理想且卓有成效的方法.1984年 R.D.Banker,A.Charnes和W.W.Cooper给出了一个被称为BCC的模型.1985年Charnes,Cooper和 B.Golany, L.Seiford, J.Stutz给出了另一个模型（称为CCGSS模型），这两个模型是用来研究生产部门的间的“技术有效”性的．1986年Charnes，Cooper 和魏权龄为了进一步地估计“有效生产前沿面”，利用Charnes, Cooper和K.Kortanek于1962年首先提出的半无限规划理论，研究了具有无穷多个决策单元的情况，给出了一个新的数据包络模型——CCW模型．1987年Charnes, Cooper，魏权龄和黄志民又得到了称为锥比率的数据包络模型——CCWH模型．这一模型可以用来处理具有过多的输入及输出的情况，而且锥的选取可以体现决策者的“偏好”．灵活的应用这一模型，可以将CCR模型中确定出的DEA有效决策单元进行分类或排队等等．这些模型以及新的模型正在被不断地进行完善和进一步发展．
DEA is commonly used to evaluate the efficiency of a number of producers. A typical statistical approach is characterized as a central tendency approach and it evaluates producers relative to an average producer. In contrast, DEA is an extreme point method and compares each producer with only the "best" producers. By the way, in the DEA literature, a producer is usually referred to as a decision making unit or DMU. Extreme point methods are not always the right tool for a problem but are appropriate in certain cases. (See Strengths and Limitations of DEA.)
A fundamental assumption behind an extreme point method is that if a given producer, A, is capable of producing Y(A) units of output with X(A) inputs, then other producers should also be able to do the same if they were to operate efficiently. Similarly, if producer B is capable of producing Y(B) units of output with X(B) inputs, then other producers should also be capable of the same production schedule. Producers A, B, and others can then be combined to form a composite producer with composite inputs and composite outputs. Since this composite producer does not necessarily exist, it is sometimes called a virtual producer.
The heart of the analysis lies in finding the "best" virtual producer for each real producer. If the virtual producer is better than the original producer by either making more output with the same input or making the same output with less input then the original producer is inefficient. Some of the subtleties of DEA are introduced in the various ways that producers A and B can be scaled up or down and combined.#p#分页标题#e#
The procedure of finding the best virtual producer can be formulated as a linear program. Analyzing the efficiency of n producers is then a set of n linear programming problems. The following formulation is one of the standard forms for DEA. lambda is a vector describing the percentages of other producers used to construct the virtual producer. lambda X and lambda Y and are the input and output vectors for the analyzed producer. Therefore X and Y describe the virtual inputs and outputs respectively. The value of theta is the producer's efficiency.
