Bipartite matching in the case of indifferent order relations and matching aspirations

A matching-aspiration-based methodology is developed to solving the bipartite matching problem in the case of indifferent order relations. The bipartite matching problem with indifferent order relations and matching aspirations is firstly given. Then, the indifferent order relations are translated into the indifferent Borda number matrix. Based on the indifferent Borda number matrixes, matching aspiration matrix and matching matrix, a bipartite matching model under the conditions of one-to-one bipartite matching is developed. Then the bipartite matching model is translated into a single-objective bipartite matching model by using the linear weighted methodology. The bipartite matching scheme can be got by solving the matching model. In the end, a position-staff matching example is presented to illustrate the application of the presented methodology.