I admit I was not specific enough. To serve as a real help, I would have come up with a concrete methodology to formulate your problem as an ILP, which I missed to do. The problem is that I am not familiar enough with timetabling and currently, I do not have time to do the essential research. Hopefully, some other monks will do it...:-) By all means, I pretty much recommend you to take the time and look into linear programming. You will be surprized, how generic problem solving technique it gives to your disposal and might very well open up a completely new way of thinking about optimization.

The only thing that I could find, which could get you started is this paper, or better to say, Section 2 of the paper... It gives the basic notation (which might look like a bit bloated for the first sight, and yes, for the second too), but once you get the point, it is much simpler than you might have expected.