A computational study of a cutting plane algorithm for university course timetabling

In this paper, we describe a case-study where a Branch-and-Cut algorithm yields the "optimal" solution of a real-world timetabling problem of University courses (University Course Timetabling problem). The problem is formulated as a Set Packing problem with side constraints. To tighten the initial formulation, we utilize well-known valid inequalities of the Set Packing polytope, namely Clique and Lifted Odd-Hole inequalities. We also analyze the combinatorial properties of the problem to introduce new families of cutting planes that are not valid for the Set Packing polytope, and their separation algorithms. These cutting planes turned out to be very effective to yield the optimal solution of a set of real-world instances with up to 69 courses, 59 teachers, and 15 rooms.