Modeling and optimization of university timetabling - A case study in integer programming

Abstract

Timetabling is a task that has to be resolved at any school or university. The fact that it is such a common problem and that it is often a large and complex issue makes it an interesting and suitable subject for mathematical optimization. This report presents a model for the problem of scheduling a number of courses given by the department of Mathematical Sciences of the University of Gothenburg and Chalmers University of Technology. It is modeled as an integer programming problem where the constraints take into account the requirements that are necessary for the timetable to be valid and the objective function is chosen in such a way that it reflects the preferences of students and teachers. The model is subsequently solved using AMPL with the solver CPLEX and the results are visualized so that they may provide guidance on areas where the current timetable may be improved. Sensitivity analysis is performed in order to investigate how the solution is affected when various conditions are changed.