Strong bounds with cut and column generation for class-teacher timetabling

This work presents an integer programming formulation for a variant of the Class-Teacher Timetabling problem, which considers the satisfaction of teacher preferences and also the proper distribution of lessons throughout the week. The formulation contains a very large number of variables and is enhanced by cuts. Therefore, a cut and column generation algorithm to solve its linear relaxation is provided. The lower bounds obtained are very good, allowing us to prove the optimality of previously known solutions in three formerly open instances.