The process of enrolling and completing the courses needed to earn an undergraduate degree involves complex interactions between individual students and institutional policies and procedures, especially because student and institutional priorities do not always align. Traditional social and behavioral statistical methods are ineffective for modeling these interactions. Simulation and algorithm-based modeling approaches have been underutilized in higher education, but their adaptability can accommodate the complexity of the degree attainment process. The purpose of this research was to design, develop, validate, and apply a multi-method Course Enrollment Simulation Model (CESM), which mirrored the process of college students enrolling in courses required for a specific undergraduate degree program. Simulated output from the model included graduation outcomes, like six-year graduation rates and average terms for students to obtain the degree, which are metrics commonly tracked by institutions of higher education. As proof of concept, data from a Fall 2015 student cohort and graduation requirements for an undergraduate computer science program at a large public university were used to create and test the CESM. The model integrated elements of discrete event simulation, agent-based modeling, and microsimulation methods into one architecture. Monte Carlo experiments were used to assess the validity of the model, which was more accurate than comparable inferential statistics. Finally, the CESM was used to evaluate summer enrollment policy options intended to improve graduation outcomes in a computer science program, finding that the effectiveness of the proposed policies depended on student factors as well as course requirements of the degree program. This dissertation is formatted as a collection of three studies, each organized into a publishable manuscript.