A New Algorithm for Student-Optimal Matching: A Framework for Management Institution's Admission in India

Abstract

College admission problem is a matching problem with colleges offering seats (admission offer) to students. Each college has its own preference list of students and each student has also its list of preferred colleges. Many stable matching can be achieved. One of these matching is college-optimal, and one is student-optimal. Existing application of centralized matching offers static solution, since features of market places are static. In the context of proposed application for post graduate admission processes at management institutions in India, outside-market exit option by student is allowed till the start of the course, which in turn leads to further confirmation of wait-listed status. Possibility of outside-market exit option makes it difficult to apply deferred acceptance algorithm as one time application. This paper proposes a matching algorithm and a framework which allow outside-market exit option to have less impact on both parties. The matching obtained by existing process is not a stable matching, since it works as deferred acceptance procedure terminated in finite time, approximately 60 days with larger time-window for non-acceptance. The clearing house, of the proposed framework, can obtain stable matching on 8th day only, and remaining time period will be reserved for the settlement due to outside-market exit option.