One of the biggest problems in education, particularly in e-learning, is the high dropout rate that occurs in courses, so this paper presents a mathematical optimization model to maximize the completion efficiency of all scheduled courses from the assignment of teachers in each course. This will be achieved using historical data to the teachers in previous courses and observations of courses opening rate in previous years. With this data and the administrative requirements of the institution, a linear programming assignment model will be used to maximize the student completion rate for the entire scheduled period.