A MIP Formulation of the International Timetabling Competition 2019 Problem

This report considers the problem presented in the International Timetabling Competition 2019 (ITC2019). The ITC2019 problem description presents a generalized model for the University Course Timetabling problem combined with an XML data format. The generalized model aims to include most of the aspects that universities worldwide might consider when constructing a timetable. The model has been simplied to some extent, but the complexity of the problem remains. To understand the origin of the data, the data format, and to get a more in-depth description of the generalized model, it is encouraged to read the ITC2019 problem description (Muller et al., 2018).

When considering an operational research problem like the ITC2019, it can be benecial to describe the problem with a mathematical model. It is an excellent way to check if the problem formulation has been wholly understood. It also provides some idea of the problem's complexity. Additionally, if a commercial solver can solve the mathematical model, no further work needs to be done. Moreover, a mathematical model can serve as a basis for developing matheuristics and can also validate solutions from other solution methods, i.e., metaheuristics.

In this report, the ITC2019 problem is described using a linear Mixed Integer Programming (MIP) model. The MIP model has been veried by comparing objective penalties and feasibility of solutions with the validator provided for the ITC2019 (www.itc2019.org/validator).