Publication Date


Document Type


Committee Members

Caroline Cao (Committee Member), Subhashini Ganapathy (Committee Member), Nan Kong (Committee Member), Pratik Parikh (Committee Member), Xinhui Zhang (Advisor)

Degree Name

Doctor of Philosophy (PhD)


Enrollment Management and Financial Aid. Enrollment management is the term that is often used to describe the synergistic approaches to influence the enrollment of higher education institutions, and consists of activities such as student college choice, transition to college, retention, and graduation. Of all the factors, financial aid, institution rank, and tuition are the three most important ones that affect students' choice processes and matriculation decisions; as such, with the continuous increase of tuition over the years, financial aid serves as a marketing tool and plays an important role in attracting students. In the United States, in the 2012-2013 academic year, there were a total of 20.4 million students enrolled in degree-granting institutions and more than eighty percent of them received financial. The Optimal Scholarship Allocation Problem: The widespread use of financial aid leads to an important problem yet to be solved in the literature, i.e., how to optimally allocate the limited financial aid to students with various social and economic backgrounds so as to achieve enrollment goals. Though financial aid can be of various forms, merit-based scholarships are the primary part of the allocation process. This problem, referred to as the optimal scholarship allocation problem, has puzzled the enrollment management teams at many higher institutions and is the focus of this thesis. Solution Approach: This thesis proposes a series of predictive and optimization models to solve the optimal financial aid allocation problems. The methodology consists of three sequential phases: 1) predictive models to find the responses (enrollment and graduation probabilities and years of study) to various levels of scholarship for students with various socioeconomic backgrounds; 2) optimization models to find the maximum revenue for given budget based on the response discovered to the various levels of scholarships; and 3) data mining models to discover patterns and transform results from the optimization model to simple and effective policies. Phase I: Predictive Models. A series of predictive models have been investigated to esti- mate the responses from students to various levels of scholarship awards. These responses can be classified into two categories: the first category includes enrollment and graduation decisions and the second one is the number of years of study once a student enrolls in the institution. In the first category, because of the binary nature of the responses (enroll or not enroll), logistic regression based models have been adopted to predict the probability of enrollment and the probability of graduation given that student enrolls. In the second category, regression analysis are adopted. Phase II: Optimization Models. An optimization model is designed to allocate financial aid to applicants with an objective to maximize the revenue, which is composed of net tuition, i.e., tuition minus scholarship, over the years of study, plus the state share of instruction once the student graduates. The constraints to be observed include the total budget limitations and a fairness constraint. For a merit-based scholarship, the fairness constraint stipulates that a student with better academic performance must be assigned to an equal or higher level of scholarships than that of students with a lower academic performance. The inclusion of the fairness constraint has dramatically increased the size of the model, and to reduce computational burden, the concept of a minimum dominance set is developed. This has reduced the size of the model by orders of magnitude and enabled the efficient solution of the resulting mathematical model. Phase III: Policies Analysis Models. Regression analysis is developed to discover patterns in the optimization results, in the form of the amount of scholarship awarded for each student, and translate them into si...

Page Count


Department or Program

Ph.D. in Engineering

Year Degree Awarded


Included in

Engineering Commons