Consider a simplified scheduling problem for a new postgraduate course as follows. All students of a new postgraduate course will take exactly the same n modules. Each module has two lectures, and each lecture requires a 1 hour time slot. We need to schedule these lectures to non-clashing time slots and lecture theatres. The University has m lecture theatres, and lectures can be booked between 9:00 and 18:00, Monday to Friday. The size of the cohort is not large, because this is the first time that this course is provided. So, any lecture theatre has enough capacity for the cohort. As some of the students live far, we would like to reduce the number of days that students need to come to the University. However, the availability of time slots and lecture theatres is limited, due to other courses that have already been scheduled. So, only a smaller subset of the total number of lecture theatres and time slots is available.
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