Efficient solutions for a university timetabling problem through integer programming

Integer programming has always been an alternative for formulating combinatorial problems such as the university timetabling problem. However, the effort required for modeling complicated operational rules, as well as the computational difficulties that result from the size of real problems have discouraged researchers and made them turn their interest to other approaches. In this paper, a two-stage relaxation procedure that solves efficiently the integer programming formulation of a university timetabling problem is presented. The relaxation is performed in the first stage and concerns the constraints that warrantee consecutiveness in multi-period sessions of certain courses. These constraints, which are computationally heavier than the others, are recovered during the second stage and a number of sub-problems, one for each day of the week, are solved for local optima. Comparing to a solution approach that solves the problem in a single stage, computation time is reduced significantly without any loss in quality for the resulting timetables. The new solution approach gives a chance for further improvements in the final timetables, as well as for certain degree of interaction with the users during the construction of the timetables.