Teoria do grafos e o problema de fluxos em redes: aplicação ao Salão Internacional de Ensino, Pesquisa e Extensão (SIEPE) realizado na Universidade Federal do Pampa

Abstract

The aim of this work is the study and application of the Graph Theory, an area of discrete mathematics. The methodology presented in this work permits the further development of the qualitative research through a case study, which performs analyses based on mathematical modeling, with the purpose of mapping problems to be solved in an optimized manner. Therefore, the defined case corresponds to analyze and determine which of the ten UNIPAMPA campuses can host the event SIEPE (International Fair of Teaching Institutions of Pampa) would result in a lower cost to the institution in relation to logistics. To perform the study, the following factors were considered: the infrastructure of the campuses of UNIPAMPA, the total number of students in each campus, the number of the registered people in the event from the 7th edition, the transport fleet of UNIPAMPA and the distances between all the campuses. Thus, with the knowledge of Network Flow Problem it was possible to observe that through the Minimum Generating Trees method it was feasible to obtain an appropriate solution to the problem. For this solution, it was realized analysis and implementation of Prim’s and Kruskal’s algorithms in which it was possible to obtain two of the UNIPAMPA campuses which best fit the proposed standards, being possible to find the shortest route for the movement of the students to the event.