We consider a complex university timetabling problem arising in a four-year study program of teacher education where every student has to choose two subjects. Since any combination of two subjects is feasible, the goal of designing a collision-free timetable for every student seems to be unreachable. However, the task becomes more tractable because for most courses several parallel groups are offered, i.e. sectioning of students is possible. Further difficulties arise from the highly individual progress of students who often follow neither the prescribed term of each course nor the prescribed ordering of courses. Under these and other conditions an optimized timetable should be determined and adjusted to the estimated student numbers and their past achievements. After moving main lectures into a regular time grid with minimal changes concerning the previously existing plan, the task of finding a timetable for all lectures with parallel groups is modeled as an integer linear program (ILP). Later, students with their actual demands are allocated a non-overlapping set of courses that is relevant and feasible for their individual study situation. This part can be handled by an assignment-type model followed by a round-robin allocation of remaining capacities.
E et al. (2022) studied this question.