DAE 分析方法介紹
1978年由著名的運籌學家A.Charnes,W.W.Cooper和 E.Rhodes首先提出了一個被稱為數據包絡分析（Data Envelopment Analysis，簡稱DEA）的方法，去評價部門間的相對有效性（因此被稱為DEA有效）．他們的第一個模型被命名為CCR模型．從生產函數角度看，這一模型是用來研究具有多個輸入、特別是具有多個輸出的“生產部門”同時為“規模有效”與“技術有效”的十分理想且卓有成效的方法.1984年 R.D.Banker,A.Charnes和W.W.Cooper給出了一個被稱為BCC的模型.1985年Charnes,Cooper和 B.Golany, L.Seiford, J.Stutz給出了另一個模型（稱為CCGSS模型），這兩個模型是用來研究生產部門的間的“技術有效”性的．1986年Charnes，Cooper 和魏權齡為了進一步地估計“有效生產前沿面”，利用Charnes, Cooper和K.Kortanek于1962年首先提出的半無限規劃理論，研究了具有無窮多個決策單元的情況，給出了一個新的數據包絡模型——CCW模型．1987年Charnes, Cooper，魏權齡和黃志民又得到了稱為錐比率的數據包絡模型——CCWH模型．這一模型可以用來處理具有過多的輸入及輸出的情況，而且錐的選取可以體現決策者的“偏好”．靈活的應用這一模型，可以將CCR模型中確定出的DEA有效決策單元進行分類或排隊等等．這些模型以及新的模型正在被不斷地進行完善和進一步發展．
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#分頁標題#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.
