Aplicación de cadenas de markov para la proyección de la ocupación de salones en el gimnasio moderno hermann muller de Bogotá

Abstract

This document examines enrollment dynamics between 2017 and 2024, characterizing the evolution of student flows by grade level and the effect of promotion, repetition, and dropout rates. The problem is framed within the need to anticipate classroom overcrowding and ensure that the available infrastructure can meet future demand without compromising academic quality, avoiding both overcrowding and underutilization of resources. Student trajectories are modeled using Markov chains, leveraging their memoryless property to represent the transition between grades and leaving the system. A transition matrix was constructed from historical records, summarizing the probabilities of promotion, repetition, and dropout by grade level. This tool allowed for projecting enrollment over a seven-year horizon under the assumption of constant preschool enrollment. The simulation showed stability in the early grades and a marked increase in the number of 11th-grade students, indicating the possibility of future overcrowding if spaces are not expanded. The analysis of results reveals that the high promotion rates in primary school and the moderate increase in grade repetition in secondary school are consistent with the educational literature. However, the projection predicts an increase in the number of graduating students, which would necessitate expanding classrooms or implementing alternative school schedules. Based on these findings, strategic recommendations are formulated: adjusting classroom capacity per grade level, strengthening the transition from primary to secondary school with pedagogical support, periodically reviewing transition probabilities, and developing retention programs to mitigate dropout rates. In conclusion, the Markov chain model proved to be an effective tool for anticipating saturation scenarios and guiding the management of school infrastructure. The research highlights the importance of combining quantitative analysis with educational policies focused on student retention and well-being, proposing flexible planning that adapts to demographic and socioeconomic variations