基于满意度的稳定匹配机制建模与优化设计分析——以高校与地方合作机制为例

Modeling and Optimal Design Analysis of Satisfaction-Based Stable Matching Mechanisms—A Case Study of University-Local Government Cooperation

摘要: 合作匹配问题一直是人们社会生活中关注的常见问题，解决合作匹配问题的方法有很多种，稳定匹配就是一种很好的方式，这种方式是指在两个不相交的主体集合对匹配对象给出的偏好信息来给出稳定的匹配方案。对于基于满意度的稳定匹配的高校与地方政府合作机制问题，在合作匹配的概念上增加了稳定匹配作为合作基础，又引入满意度的概念，通过满意度模型的建立，将期望矩阵转化为满意度矩阵，进而得到序值矩阵，由标准满意度函数将序值矩阵转化为标准满意度矩阵，再通过构建优化模型并分析模拟数据表明本文方法的可行性。

Abstract: Cooperative matching problem has always been a common problem in people’s social life. There are many ways to solve cooperative matching problem, and stable matching is a good way. This way is to give a stable matching scheme based on the preference information given by two disjoint subject sets. For the cooperation mechanism between universities and local governments based on stable matching based on satisfaction, stable matching is added to the concept of cooperative matching as the basis for cooperation, and the concept of satisfaction is introduced. Through the establishment of the satisfaction model, the expectation matrix is transformed into the satisfaction matrix, and then the ordinal-valued matrix is transformed into the standard satisfaction matrix by the standard satisfaction function. The feasibility of the proposed method is demonstrated by constructing the optimization model and analyzing the simulation data.