Curriculum-based university course timetabling considering individual course of studies

Abstract

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 parallel groups are offered for most courses, i.e. sectioning of students takes place. Difficulties arise from the 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 can be determined by a multi-stage process, adjusted to the estimated student numbers and their past achievements. Some of the features encountered in this planning task were also part of the well-known ITC-2019 timetabling competition, while others constitute new aspects. 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. At a later time, students with their actual demands are allocated a non-overlapping set of courses that is relevant and feasible for their individual study situation. Besides the maximization of allocated courses, a fairness criterion is also invoked at this stage. Since both optimization tasks are prone to infeasibility, we introduce features to resolve this issue in practice.