Integer programming for the generalized high school timetabling problem

Recently the XHSTT format for (High) School Timetabling was introduced, which provides a uniform way of modeling problem instances and corresponding solutions. The format supports a big variety of constraints, and currently 38 real-life instances from 11 di erent countries are available. Thereby the XHSTT format serves as a common ground for researchers within this area. This paper describes the rst exact method capable of handling an arbitrary instance of the XHSTT format. The method is based on a Mixed-Integer linear Programming (MIP) model, which is solved in two steps with a commercial generalpurpose MIP solver. Computational results show that our approach is able to nd previously unknown optimal solutions for 2 instances of XHSTT, and proves optimality of 4 known solutions. For the instances not solved to optimality, new non-trivial lower bounds were found in 11 cases, and new best-known solutions were found in 9 cases. Furthermore the approach is shown to be competitive with the nalist of Round 2 of the International Timetabling Competition 2011.