基于网络流理论的非线性规划评价模型  

An Evaluation Model Based on the Non-linear Programming Method and the Network Flow Theory

作　　者：李永立[1] 吴冲[1] 

机构地区：[1]哈尔滨工业大学管理学院,黑龙江哈尔滨150001

出　　处：《运筹与管理》2013年第4期85-92,共8页Operations Research and Management Science

基　　金：国家自然科学基金(71271070;60979016);高等学校博士点专项基金资助项目(20092302110060);教育部新世纪优秀人才支持项目资助(NCET-08-0171)

摘　　要：针对既有的评价模型缺乏对评价结果保序性的讨论,以及难以有效处理缺失数据的问题,本文建立了一个新的评价模型用以解决以上问题。该模型建立在三个标准的基础上,这三个标准分别为"结果一致性"、"最小偏离性"和"最小差异性",其为模型的建立提供了依据和理论基础;在已建立的非线性规划模型基础上,进行了模型的性质讨论,并将其归结为一类最小凸费用循环流的统一表述,这是解决模型的算法问题和揭示其蕴含的更为深刻的管理学意义的核心;最后,模型被用于一个示例分析和含有缺失数据的大规模数据集的实证分析,这些分析论证了该新模型的有效性。本文的模型提供了新的评价工具,扩展了运筹学和决策科学之间相互运用的案例,具有较好的保序性和处理缺失数据的能力,含有理论和实践的双重意义。To solve the problem of isotonicity in the existing evaluation models and to deal with the widespread phenomenon of data omitting, a new evaluation method is established. The new non-linear programming model is made based on three criterions composed of ＂results consistency＂, ＂minimum deviation＂ and ＂minimum separation＂ which are the theoretical basis of making the model. The presented model is expressed further as a kind of minimum convex cost network flow problem, and the idea is the core of the paper to solve the problem of the model＇ s algorithm and indicate the profound management implication of the new model. Lastly, the model＇ s effectiveness is demonstrated by an example analysis and an empirical analysis based on a large data base with omitting data. In conclusion, the model provides a new toot of evaluation theory, enriches examples using the theory relationship between operations research and decision theory, owns the ability to solve the problems of isotonicity and omitting data, and has the significance in theory and practice.

关 键 词：决策理论 评价模型 网络流 非线性规划 保序性 

分 类 号：C931.1[经济管理—管理学]