Management and optimal distribution of large student numbers

In principle, timetabling problems appear at every school and university. However, the degree of difficulty increases dramatically with an increasing number of students and courses for which the scheduling shall be carried out. From the mathematical point of view this is a “hard” problem, since the runtime on a computer cannot be estimated by a simple law (i.e. by a polynomial law) by the number of parameters. These kinds of problems are called “NP hard”. There are three important versions of the timetabling problem at universities, known as the university timetabling problem, i.e. curriculum-based course timetabling, post-enrollment timetabling and examination timetabling. All specified problems are important for room management at universities, for the realization of courses that can be studied according to curricula, and for the satisfaction of students and teachers. These problems are related to the optimization of room management and personnel costs (e.g. by a uniform distribution of students). Thus, the solution to these problems is related to the optimization of “real” costs, a more and more important economic factor at (German) universities. Introduction of the two-tiered Bachelor and Master courses has raised awareness for these problems at German universities: due to the multitude of new courses the timetables which have been established and stood the test of time cannot be used any longer. Moreover classes tend to be more structured and have strong similarities to classical school situations; attendance is compulsory and dependencies between modules determine the feasibility of the curricula. This feasibility is also evaluated while accrediting new study courses. Since 2003, we have been using using an algorithm that has been realized by members of our team for the solution of the post-enrollment-based course timetabling problem at the Technische Universität Berlin. For classes with more than 2000 e- - nrolled students, organization by itself is a challenge; problems may include splitting of those classes into several separate lectures, arranging the associated tutorials into small groups of students, allocating adequate rooms, and scheduling examinations. Moreover, homework and exams need to be administered, whereby, depending on the field of study, very different rules are to be obeyed. This especially pertains to the Department of Mathematics because it offers most of the compulsory classes in mathematics for all fields of study held at Technische Universität Berlin. These are the biggest classes at the university and are to be attended by the majority of students. Thus, the Moses (Mobile Services for Students)-Account has been being developed and used since 2004. This web-based software allows students to enroll in tutorials with a list of preferences for given dates. A special algorithm, providing a globally optimized (with respect to the students´ wishes and resources available) solution, processes all registrations.