A graph-based MIP formulation of the International Timetabling Competition 2019

The International Timetabling Competition 2019 (ITC 2019) posed a university timetabling problem involving assigning classes to times and rooms for an entire semester while assigning students to required classes. We propose a new mixed integer programming (MIP) formulation of the problem. The MIP formulation takes advantage of different graph structures in conflict graphs to construct a strong formulation of the constraints. In addition, we introduce a reduction algorithm that removes redundancies from the input data. We show that the reduction algorithm, combined with the graph-based MIP formulation, outperforms the MIP formulated by Holm et al. (A MIP formulation of the International Timetabling Competition 2019 problem, 2020) and thus becomes the new state-of-the-art MIP formulation for the ITC 2019. This paper reports the graph-based MIP formulation, which we used during the ITC 2019, and discusses additional approaches that one can use to strengthen the MIP.