LINEAR INTEGER MODELING AND MULTICRITERIA FOR THE UNIVERSITY TIMETABLING PROBLEM (MODELAGEM LINEAR-INTEIRA E MULTICRITÉRIO PARA A PROGRAMAÇÃO DE HORÁRIOS EM UNIVERSIDADES)

Valdecy Pereira (valdecy.pereira@gmail.com)
Engenharia de Produção, UFF - Universidade Federal Fluminense
March, 2012
 

Abstract

This work presents an integer linear model for the problem of university course timetabling. The allocation decision can be resolved through one or more criteria, and when more than one criterion is required this work suggests a methodology, which with the help of the AHP method, can allocate professionals with the most desirable profile for the institution. This work also proposes a nonlinear programming model, which reduces the inconsistency, to zero or near zero, through minor adjustments made to the original judgments. The integer linear model was made to generate solutions that meet most of the preferences of the institution taken as the case study, these preferences are: maximize the allocation of teachers with the best profile that servers the institutional needs and minimize costs by joining classes that have in their curriculum disciplines with equivalent subjects. The integer linear model can also find solutions that meet the preferences of teachers' schedules, generating schedules more convenient and comfortable for these professionals. Finally the proposed integer linear model can find feasible solutions even though there are enough teachers to teach the disciplines of the course, this is possible because the model indicates the disciplines that will need new resources. The nonlinear programming model, which reduces the inconsistency, to zero or near zero, is done through minor adjustments made to the original judgments, thus avoiding distortions of the initial perception of decision makers. The adjustments generate solutions that have only discrete values and that fall within the limits of the Saaty scale (1 to 9). If a tolerable level of inconsistency is allowed, the nonlinear model can preserve even more original judgments. The solutions found by the integer linear model with one or more criterion proved to be superior to the solutions found manually.