Development of a Solution Model for Timetabling Problems Through a Binary Integer Linear Programming Approach

Abstract

A common situation when each academic period starts in academic institutions is the challenge of assign classrooms for the different courses in each faculty. This article shows an integer binary linear programming model (objective function, constraints and the relationship between decision variables) which, on a daily basis, performs a classroom assignment based on the hourly scheduling and the capacity of each classroom; the model considers two assumptions: (1) the assignment of each subject in a certain time period is already carried out optimally, and (2) the availability of teachers is not a restrictive element of the model. The test and analysis of the proposed model was carried out at the Faculty of Science and Technology of the University of Azuay (Cuenca, Ecuador). The result of the proposed model, which can be solved with any linear programming algorithm, allows an efficient assignment of the different classrooms, considering the constraints mentioned above. It is considered that under the proposed approach the model can be extended considering additional aspects and conditions, however this would increase the complexity which can be managed through a phased approach (fragmented problems).