An Introduction to Timetabling: Constraints, Parameters and Objective Functions Una introducción a la programación de horarios: restricciones, parámetros y funciones objetivo

Abstract

Timetabling in educational institutions is a combinatorial optimization problem whose objective is to assign courses, instructors, classrooms, and time slots in a coordinated manner while satisfying a set of constraints. This article introduces the mathematical modeling of such a problem, distinguishing between hard and soft constraints, and formalizing the definition of sets, parameters, and objective functions that structure the model. Three illustrative examples are presented to demonstrate how variations in the weights assigned to preferences and penalties, together with the punctual reassignment of events, directly affect the objective function value. These examples show that balancing criteria and implementing minor adjustments in the allocations can significantly improve the quality of the generated timetables. This work provides a didactic introduction and a starting point for future research aimed at addressing the academic timetabling problem.