Two-sided Matching under the Conditions of Strict Order Relations and Threshold Orders

A matching approach is proposed for solving the two-sided matching problem, where the preferences given by the two-sided agents are in the format of strict order relations and threshold orders. The two-sided matching problem under the conditions of strict order relations and threshold orders is firstly described. The related concepts of the twosided matching are also introduced. In order to solve the considered two-sided matching problem, the strict order relations are converted into the Borda number matrix, and the threshold orders are transformed into the threshold Borda numbers. According to the Borda number matrix and the threshold Borda numbers of each side, the two Borda number cut matrix can be established, and then the two normalized Borda number cut matrixes can be set up. According to the two normalized Borda number cut matrixes, the synthetical normalized Borda number cut matrix can be established. Based on the synthetical normalized Borda number cut matrix, a matching model considering the twosided matching constraint conditions can be developed. The matching alternative can be obtained by solving the matching model. Finally, a matching example between positions and staffs is given to illustrate the use of the proposed approach.