Disruptions in timetables: a case study at Universidade de Lisboa

Solving university course timetabling problems is a large and complex task. Moreover, every new academic term, a new timetable is likely to be scheduled due to disruptions (e.g., changes in teacher-lecture allocation). Nevertheless, the university infrastructure, the overall curricular plans, and the number of students/teachers is still very similar in consecutive terms. For this reason, a timetable does not need to be always scheduled from scratch since it can produce a completely different solution from the previous one, thus creating undesirable changes for many actors. This paper addresses the Minimal Perturbation Problem (MPP) in university course timetabling. Given a set of disruptions that make a timetable no longer feasible, a solution to the MPP is the closest new feasible timetable with respect to the original timetable. We propose and analyze two different integer programming models to encode the MPP. To validate the proposed models, disruptions are randomly generated based on the probability distributions learned from the history of timetables over the last five years in the Instituto Superior Técnico (IST) the engineering school from Universidade de Lisboa. Overall, our models, combined with an incremental approach, are shown to be able to efficiently solve all problem instances.