Graduate admission problem with quota and budget constraints

Abstract

In this thesis, we have studied the graduate admission problem with quota and budget constraints as a two sided matching market. We constructed algorithms which are extensions of the Gale - Shapley algorithm and showed that if the algorithms stop then the resulting matchings are core stable (and thus Pareto optimal). However the algorithms may not stop for some problems. Also it is possible that the algorithms do not stop and there is a core stable matching. Also there is no department optimal matching and no student optimal matching under budget constraints. Hence straightforward extensions of the Gale - Shapley algorithm do not work for the graduate admission problem with quota and budget constraints. The presence of budget constraints play an important role in these results.