A column generation approach for examination timetabling

In examination timetabling we have to assign the exams of a given set of courses to time slots, such that conflicting exams are assigned to different time slots. We study the problem that occurs at our department. The characteristics of this problem are as follows. The exams have to take place in 5 days, and per day there are 2 time slots. Teachers can express their preferences for the time slots. The exams preferably take place in the small rooms, but there are some bigger rooms available as well; since these big rooms are used by other departments as well, using these is not encouraged. Finally, we try to avoid students having two exams on one day as much as possible. Many authors have presented a number of approaches for solving a myriad of variants of the examination timetabling problem, but remarkably enough column generation seems to have been ignored. We apply column generation to solve several variants of our problem. The pricing problem boils down to a complicated weighted independent set problem, which we solve by a branch-and-bound algorithm. In this way we find very good solutions in a matter of seconds. We further indicate situations in which column generation is applicable. 1980 Mathematics Subject Classification (Revision 1991): 90B35.