A mathematical formulation for constructing feasible solutions for the Post Enrollment Course Timetabling Problem

The scheduling community has long been interested in educational timetabling. Particularly in academia, since timetabling dictates the day to day operation of Universities, great effort has been exercised to produce high quality schedules. Typically, timetabling problems are NP-Hard and several approaches have been tried in order to generate schedules that satisfy all stakeholders. A number of timetabling competitions have been organized through the last two decades focusing on problems stemming from educational operations. In this paper we use data from two such competitions, ITC2002 and ITC2007 about the post enrollment course timetabling problem. We propose a mathematical model that captures the problem in its entirety and we use it in order to construct feasible solutions initially, and then explore the prospect of optimization. We employ a pre-process stage that attempts to reduce the size of the model and then use an open source solver, that produces solutions in reasonable time for most of the cases. We also propose a simple decomposition of the problem in a day by day basis that can improve the initial feasible solutions.