针对基于序值偏好信息的一对多双边匹配问题,提出了一种决策方法.首先对一对多双边匹配问题进行了描述,其次阐述了一对多双边匹配中稳定匹配的相关概念;进一步地,为了获得匹配结果,将一对多双边匹配问题转化为一对一双边匹配问题,进而在稳定匹配条件下,以每方主体序值之和最小为目标,构建了多目标优化模型;然后使用基于隶属函数的加权和方法将多目标优化模型转换为单目标优化模型,通过模型求解获得最优匹配结果.最后,通过一个算例说明了提出方法的实用性和有效性.
A decision method is proposed to solve the one-to-many two-sided matching problem,in which the ordinal number information is given by two-sided agents.Firstly,the description of one-to-many two-sided matching problem is given.Then,the related concept on stable matching in one-to-many two-sided matching is introduced.Furthermore,to obtain the matching result,one-to-many two-sided matching problem is converted into one-to-one two-sided matching problem.In order to minimize the sum of ordinal numbers of two-sided agents,a multi-objective optimization model is developed under the stable matching condition.The weighted sums method based on membership functions is used to convert the multi-objective optimization model into a single objective optimization model,and the optimal matching result can be obtained by solving the model.Finally,an example is given to illustrate the practicality and effectiveness of the proposed method.