关于DEA模型的一种有效求解方法

An Efficient Method of Solving the DEA Model

“数据包络分析”（ＤａｔａＥｎｖｅｌｏｐｍｅｎｔＡｎａｌｙｓｉｓ，简称ＤＥＡ）是运筹学的一个新的研究领域．它是研究具有相同类型的部门（或单位）间的相对有效性的十分有用的方法；也是处理一类多目标决策问题理论上非常完备的方法；更是经济理论中估计具有多个输入，特别是具有多个输出的“生产前沿函数”（也称生产前沿面）的有力工具．ＤＥＡ模型经过ＣｈａｒｎｅｓＣｏｏｐｅｒ变换，可以转化为一个等价的线性规划问题，因此求解ＤＥＡ模型可以转化为求解相应的线性规划问题．但是该线性规划问题属于强退化类型，采用传统方法求解比较困难，因此寻找合适的算法对ＤＥＡ方法的推广和应用极为重要．将求解线性规划问题的鞍点算法应用于求解ＤＥＡ模型，该算法通过梯度迭代直接收敛于鞍点，可解退化问题，经过计算机实验证明该方法是十分有效的方法．本文介绍了ＤＥＡ模型，阐述了鞍点算法原理，并给出了求解ＤＥＡ模型的方法和步骤．

Data envelopment analysis is a new operational research field.It is a most useful method to study the relative effectiveness among the departments(or units)belonging to the same category.It is also a very complete theoretical method to solve one category multi objective decision problems.And more important,it is a important tool to estimate production forward function(or called production forward face)with many inputs,especially many outputs.The DEA model is transformed into an equivalent linear programming problem through Charnes Cooper transformation,so solving the DEA model can be transformed into linear programming problem.But this linear programming problem is highly degenerate.So we have difficulty in solving it with traditional method.It is very important to find an efficient algorithm to solving the DEA model for its spreading and applying.Saddle point algorithm for solving linear programming problem is applied to solving the DEA model,that is,directly converges to the saddle point of the problem by the saddle point gradient,which can solve the problem of degenerate.That it is a most effective method proved by many computer experiments.In this paper,author introduces the DEA model and illustrates the principle of the saddle point algorithm,and presents the method and procedures to solve the DEA model.