Research On Several Methods For Two-sided Satisfied Matching Based On Preference Orders

Two-sided matching problem based on preference orders is a problem with extensive practical backgrounds in reality, such as marriage matching, students and schools matching in college admission, persons and positions matching in human resource management and so on. The main purpose of traditional theories and methods of two-sided matching problem based on preference orders is to obtain stable matching results, but less to consider the satisfaction degree of agents on both sides and discuss deeply the factors that affect the satisfaction degree of agents on both sides, such as psychological reaction and other factors. Therefore, it still needs to research further the two-sided matching problem based on preference orders. The related concepts of two-sided satisfied matching need to be defined, the research framework of two-sided satisfied matching needs to be provided, and the targeted methods for two-sided satisfied matching based on preference orders need to be present. All those studies are of great important theoretic and practical significance.The purpose of this thesis is to make a deep theoretical analysis and methodological research on two-sided satisfied matching problem based on preference orders. A series of research works are conducted as follows.First, the analysis on the related concepts of two-sided satisfied matching based on preference orders is provided. Specifically, it mainly concludes the following three aspects, i.e.,1) The related concepts of two-sided satisfied matching are defined; 2) The stability of two-sided satisfied matching results and the psychological behaviors characteristics of agents on both sides are analyzed and discussed; 3) The two-sided satisfied matching problems based on preference orders considering a variety of situations are refined and defined, including two-sided satisfied matching problem based on preference orders, stable two-sided satisfied matching problem based on preference orders, two-sided satisfied matching problem considering agents’ behavior based on preference orders and so on.Second, the methods for the two-sided satisfied matching problem based on preference orders is provided. Specifically, it mainly concludes the following three aspects, i.e.,1) the research framework of two-sided satisfied matching problem based on preference orders is provided; 2) The method for one to one two-sided satisfied matching problem based on preference orders is proposed. In this method, two-sided satisfied matching problem is firstly transformed into weight matching problem, and then the one to one two-sided satisfied matching results can be obtained by solving the weight matching problem; 3) The method for one to many two-sided satisfied matching problem based on preference orders is proposed. In this method, the satisfaction degrees of agents on both sides is firstly obtained according to preference orders of agents on both sides, and then the one to many two-sided satisfied matching results can be obtained by constructing and solving the bi-objective optimization model.Third, the methods for the stable two-sided satisfied matching problem based on preference orders is provided. Specifically, it mainly concludes the following three aspects, i.e.,1) the research framework of stable two-sided satisfied matching problem based on preference orders is provided; 2) The method for stable one to one two-sided satisfied matching problem based on preference orders is proposed. The matching result obtained by this method is one result in the stable matching set and can achieve the maximum satisfaction for agents on both sides, which can give consideration to both "stable matching" and "satisfied matching"; 3) The method for stable one to many two-sided satisfied matching problem based on preference orders is proposed. Specifically, the one to many two-sided satisfied matching problem is firstly transformed into one to one two-sided satisfied matching problem, and then the stable one to many two-sided satisfied matching results can be obtained.Fourth, the methods for the two-sided satisfied matching problem considering agents’ behavior based on preference orders is provided. Specifically, it mainly concludes the following three aspects, i.e.,1) the research framework of two-sided satisfied matching problem considering agents’ behavior based on preference orders is provided; 2) The method for one to one two-sided satisfied matching problem considering agents’ behavior based on preference orders is proposed. In this method, disappointment theory of behavioral decision theory is introduced into the study of two-sided matching, and the matching results which turn out to the satisfaction of agents on both sides reflect the psychological behavior of agents; 3) The method for stable one to one two-sided satisfied matching problem considering agents’behavior based on preference orders is proposed. In this method, considering the disappointment and elation of agents to possible matching results, the perception utility is used to describe the satisfaction degree of agent to the matching with the opposite agent, and under the linear constraints of stable matching, the stable two-sided satisfied matching results can be obtained by constructing and solving the optimization model.Several proposed methods for the two-sided satisfied matching problem based on preference orders by this thesis can be used to solve many two-sided satisfied matching problems in reality, and also can be extended to solve the decision problems with characteristics of two-sided satisfied matching. The research work in this thesis provides a theoretical guidance framework and methodical framework to the study of two-sided satisfied matching problems in reality.