Modelo de programação linear inteira para o problema de alocação de salas de uma universidade federal

Abstract

The present study is conducted at the Federal University of Catalão on the common classroom assignment problem that educational institutions are used to face. The objective is to improve the semester assignment of disciplines from the undergraduate courses to the classrooms available in the teaching buildings, optimizing the resources of time and administrative staff necessary for this task. From literature studies and considering the requirements imposed by the university, an integer linear programming model is proposed to solve the university's problem. The proposed model is evaluated in terms of solution quality and computing time. It was implemented in a high-level programming language and tested on 75 instances generated from two real university cases. In this way, two instances correspond to classroom assignment requests for the 2023's first and second semesters. For such instances, the integer linear programming model obtained optimal solutions with 99.63% of the disciplines assigned to the available classrooms in the first semester and 100% of the disciplines assigned in the second semester, improving the results presented by the university staff. Before the proposal of the mathematical optimization model, this problem was solved manually by the administrative staff, taking about one week to have the first feasible assignment of disciplines. Therefore, with the proposal of the model, this thesis contributes to the administrative staff, reducing the time to carry out such a task and optimizing the personnel resources used by the university.