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Management and optimal distribution of large student numbers

机译：大学生人数的管理和优化分配

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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-n-nnrolled 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.
机译：原则上，时间表问题出现在每所学校和大学中。但是，随着学生和课程安排的增加，难度大大增加。从数学的观点来看，这是一个“难题”，因为计算机的运行时间无法通过简单的定律（即通过多项式定律）通过参数数量来估计。这些问题称为“ NP困难”。大学中的时间安排问题有三个重要版本，称为大学时间安排问题，即基于课程的课程时间安排，注册后时间安排和考试时间安排。所有指定的问题对于大学的房间管理，实现可以根据课程学习的课程以及学生和老师的满意度都很重要。这些问题与房间管理和人员成本的优化有关（例如通过统一分配学生）。因此，解决这些问题的方法与优化“实际”成本有关，后者是（德国）大学中越来越重要的经济因素。分为两层的学士和硕士课程提高了德国大学对这些问题的认识：由于新课程众多，已经建立并经时间考验的时间表不再可用。此外，课程的结构更加趋于合理，并且与古典学校的情况有很强的相似性。必修课是必修课，各模块之间的依赖性决定了课程的可行性。在批准新的学习课程时，还将评估这种可行性。自2003年以来，我们一直使用由团队成员实现的算法来解决柏林理工大学基于注册后的课程时间表问题。对于拥有超过2000名电子报名参加的学生的课程来说，组织本身是一个挑战。问题可能包括将这些班级分成几个单独的讲座，将相关的教程安排成小批学生，分配足够的房间，并安排考试。此外，需要进行家庭作业和考试，从而根据学习领域，要遵守非常不同的规则。这尤其适用于数学系，因为它为柏林工业大学提供的所有学习领域提供大多数数学必修课。这些是大学里最大的课程，大多数学生都将参加。因此，自2004年以来一直在开发和使用Moses（学生移动服务）帐户。该基于Web的软件允许学生注册教程，并提供给定日期的首选项列表。一种特殊的算法提供了全局优化的（相对于学生的意愿和可用资源）解决方案，该算法处理所有注册。

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