Some insights about the Uncapacitated Examination Timetabling Problem

Abstract

Timetabling problems easily become hard due to their inherent combinatorial structure. In this work we investigate the examination timetabling problem for Universities. We step back and analyze the best known variant of the problem, the Uncapacitated Examination Timetabling Problem (UETP). In the process we unmask some properties of the UETP. Firstly, we detect components that can be used for decomposition of problem instances by running a connected components identification algorithm. This process reveals the presence of more of the so called noise students and noise examinations that can safely be removed from the problem without affecting the essence of the problem. Secondly, we revisit the idea of identifying lower bounds based on penalties that are impossible to avoid. We strengthen those bounds by exploiting the theoretically maximum number of students that could possibly be scheduled in a single period. Thirdly, we propose a novel way of breaking symmetry, based on ordering examinations that share common characteristics. Since examination timetabling is an active research problem, counting several contributions each year, the present work aims to serve as a useful resource, by revealing properties of the UETP that were not identified before.