【作者】 王芳；

【导师】 汤鹏志；

【作者基本信息】 华东交通大学 ， 运筹学与控制论， 2010， 硕士

【摘要】 数据包络分析（Data Envelopment Analysis,简称DEA）,自1978年由A.Charnes和W.W.Cooper等学者提出至今已有32年的历史。它是一个新的交叉领域,涵盖了数学、数理经济学、运筹学和管理科学。它是以同类决策单元“相对效率评价”概念为基础、以单输入单输出评价有效性向多输入多输出迈进为目标创建的一种效率评价方法。因为DEA的理论研究价值以及其先天的“经济背景”,所以自1978以来,已有数以千计DEA的研究论文、工作报告等发表。某些运筹学或经济学的重要刊物,如Annals of Operational Research, European Journal of Operational Research, Journal of Productivity Analysis等都出版了DEA研究的特刊。本文在前人研究的基础上,所做的主要工作如下:一、构建M-Bi-GDEA模型综合考虑投入缩小比率以及产出扩大比率,探索了带有锥结构（决策者偏好）的投入产出型DEA模型,然后在此模型上引入时间窗,构建M-Bi-GDEA模型,可以从横向（一个DMU处于不同时段）、纵向（同一时段的不同DMUS）、整体（处于不同时段的不同DMUS）上得出相对效率的变化情况。此模型不仅克服了传统DEA模型的局限性,而且在决策单元相对效率评价和非有效决策单元改进方面能以考虑决策者偏好的投入、产出整体最优来优化各决策单元的投入和产出。二、模型DEA有效与Pareto解的等价性数据包络分析与帕累托最优密切相关。因此,本文在第三章研究了偏好型双目标GDEA多阶段评价模型下的DEA有效与Pareto解的等价性问题。通过严格的证明可知:若DMU j0为DEA有效,则（x₀（t₀）,y₀（t₀））为多目标规划（VP）的Pareto解。三、模型应用到高新技术产业中DEA模型的应用非常广泛,本文将所构建的模型在第四章中应用到了江西省高新技术产业中,通过实例,详细地分析了如何确定指标、时间窗以及决策者的偏好。并在有偏好和无偏好的实证评价分析中特别强调了模型多阶段评价与偏好型评价的优点。数据包络分析作为一种效率评价方法极大地丰富和发展了微观经济中的生产函数理论,它以其独有的优势（避免主观因素等）备受人们的关注,不论在理论研究还是实际应用方面都得到了迅速的发展。但是DEA毕竟是一门刚兴起的交叉学科,它的理论和应用还有待进一步的丰富与完善。更多还原

【Abstract】 Data envelopment analysis （DEA for short）, originally formulated by A. Charnes, Cooper and Rhodes, has more than 20 years of history up to now. It is a new cross-subject that covers mathematics, operational research economics as well as management science. The performance of a DMU depends only on the identified efficient frontier characterized by the DMUs with a unity efficiency score. For its“natural”economic background, so from 1978, there have been thousands of the research thesis and work reports about DEA. Some operational research or the important publication of economics, such as Annals of Operational Research, European Journal of Operational Research, Journal of Productivity Analysis, Journal of Econometric, which all publish the special issue for DEA studies.Fore the foundation of studies, I do of main work as follows:First, set up M-Bi-GDEA modelConsidering the devotion narrows ratio and produces extension ratio, I investigated to the devotion-produced DEA model which having the awl structure （decision maker hobby）, then leads into time window into this model, set up M-Bi-GDEA model, this model can get the variety circumstance of opposite efficiency from horizontal （a DMU is placed in a different time）, lengthways （different DMUS of the same time）, whole （be placed in different DMUS of different time）. This model not only overcame limiting of traditional DEA model, but also, in the aspects of making policy unit opposite efficiency evaluation and not efficiency evaluation, consider decision maker hobby of devotion and produce. Second, the equivalence between the model of DEA and the Pareto solutions Data Envelopment Analysis and Pareto optimality are closely linked. Therefore, this article in Chapter III studies the equivalence between the multi-stage’s pre-bi-objective GDEA model and the Pareto solutions. Through a rigorous proof we can see: If the DEA is efficient, so （x₀（t₀）,y₀（t₀）） is the Pareto solution of multi-objective planning.Third, the model applied to high-tech industriesThe DEA model is widely used, this article constructed a model in the fourth chapter which applied to high-tech industries in Jiangxi Province, through the example, we do a detailed analysis of how to determine the targets, time window, as well as decision-makers preferences. And in the analysis of the preference and not-preference, we do special emphasis on the merits of the multi-stage evaluation and preference-based evaluation.As a method of efficiency evaluation, data envelopment analysis has greatly enriched and developed the micro-economic theory of the production function, which with its unique advantages （to avoid subjective factors, etc.） getting much attention, both in theoretical research or practical applications, it have been developed rapidly. But the DEA, after all, a newly emerging cross-disciplinary, its theory and application remains to be further enriched and improved.更多还原