Mathematical model of the problem of formation and correction of academic classes at the university

The paper is devoted to the development of a mathematical apparatus that makes it possible to form and adjust the academic schedule in universities. The object of research in this work is the process of scheduling academic classes in higher education institutions. The presence of rather strict restrictions (heavy workload of classrooms, teachers, the presence of several academic buildings, etc.) makes this process very time-consuming. Existing approaches and software tools do not fully meet all the limitations that exist in real practice. This makes the subject of this study relevant and practically significant. The subject of the research is models and methods of formalizing the task of forming and adjusting the schedule. The aim is to develop a mathematical model that makes it possible to describe an aggregated objective function and a set of soft and hard constraints both for the task of forming a schedule and for correcting it. The paper analyzes the specifics of the task of scheduling for educational institutions, suggests limitations that occur in real universities, and formulates criteria that allow teachers to take into account their preferences, as well as take into account the nuances of the educational process. As a result, a mathematical model is proposed that takes into account the hierarchical structure of educational units, a joint description of the tasks of forming and adjusting the schedule, as well as the use of a system of private quality criteria. The model provides the opportunity to formalize both hard and soft constraints, as well as minimize deviations from the original schedule when it is adjusted.