A proposal for the laboratory assignment problem of students and its mathematical properties

In many universities, students are assigned to laboratories (i.e., professors) to conduct their graduation study. Since both sides of students and laboratories have their preferences, the situation resembles the stable marriage problem. But it is different in that more than one student is usually assigned to a laboratory, and only partial information about preferences is made explicit (from the consideration that the number of students is large). In this paper, we propose a scheme that contains a rational method to determine capacities of laboratories, and a modified Gale–Shapley algorithm to compute an assignment of students with a desirable stability property. Computational experiment indicates that this can be a realistic method for use in universities and other organizations.