AZuR – how should university courses be assigned to time slots and rooms so that there are no conflicts?
AZuR – Time Tabling and Room Assignment for University CoursesProject Leader: Prof. Dr. Jörg Rambau
Prof. Dr.-Ing. Stefan Jablonski
Contact: Prof. Dr. Jörg Rambau
Project start: 2010/03/01 Project end: 2013/08/31
One important aspects of the quality of a study program at a university is the whether or not it can actually be studied. In particular, all courses that should be taken in the same semester should not overlap in time. Otherwise, for the students a conflict arises which course to skip. So, the question comes up how all courses of a university can be assigned a time slot and a room so that for no study program there are conflicts. The task involves besides optimization techniques a lot of data that usually is not readily available in appropriate formats. In order to join forces in optimization and data bases/information systems, the Lehrstuhl Wirtschaftsmathematik (Prof. Dr. Jörg Rambau) cooperates in this project with the Lehrstuhl Angewandte Informatik IV (Prof. Dr. Stefan Jablonski).
Contribution to the Mission of MODUS
The mission of MODUS is followed two-fold in this project. First of all, a model of what the presence requirements of a study program are is needed. This can partly be extracted from the by-laws, partly expert knowledge has to be formalized in a logically sound data base structure. Based on this information, an optimization model is needed to actually compute good suggestions for time slot and room assignments. The assignment itself can be formalized in two principally different ways: One possiblity is to use binary variables to indicate whether or not course c should be assigned to time slot t and room r (compact model). Another possiblity is to enumerate possible weekly schedules for the students of a particular program and indicate each such weekly schedules with its own binary variable (extended model). Then, methods from mixed-integer linear programming (MILP) are used to compute solutions in reasonable time. These suggestions can then be visualized inside the information system used to collect the data.
The project team has succeeded in producing a software tool to compute assignments that drastically reduced the number of conflicts at the University of Bayreuth. Because of the introduction of the CampusOnline system, the stand-alone information tool has not been put to practice. However, the core optimization methods are successfully used on a regular basis in the Fakulät für Mathematik, Physik und Informatik to minimize conflicts.