University Course Timetabling: Model.
Due to the set of standardized time patterns and administrative rules enforced at the university, it is generally possible to represent all meetings of a class by a single variable. This tying together of meetings considerably simplifies the problem constraints. Most classes have all meetings taught in the same room, by the same instructor, at the same time of day. Only the day of week differs. Moreover, these days and times are mapped together with the help of meeting patterns, e.g., a 2 hours x 3 day per week class can be taught only on Monday, Wednesday, Friday, beginning at 5 possible times
Or, for instance, a 1 hour x 2 day per week class can be taught only on Monday-Wednesday, Wednesday-Friday or Monday-Friday, beginning at 10 possible times
In addition, all valid placements of a course in the timetable have a one-to-one mapping with values in the variable's domain. This domain can be seen as a subset of the Cartesian product of the possible starting times, rooms, etc. for a class represented by these values. Therefore, each value encodes the selected time pattern (some alternatives may occur, e.g., 1.5 hour x 2 day per week may be an alternative to 1 hour x 3 day per week), selected days (e.g., a two meeting course can be taught in Monday-Wednesday, Tuesday-Thursday, Wednesday-Friday), and possible starting times. A value also encodes the instructor and selected meeting room. Each such placement also encodes its preferences (soft constraints), combined from the preference for time, room, building and the room's available equipment. Only placements with valid times and rooms are present in a class's domain. For example, when a computer (classroom equipment) is required, only placements in a room containing a computer are present. Also, only rooms large enough to accommodate all the enrolled students can be present in valid class placements. Similarly, if a time slice is prohibited, no placement containing this time slice is in the class's domain.
As mentioned above, each value, besides encoding a class's placement (time, room, instructor), also contains information about the preference for the given time and room. Room preference is a combination of preferences on the choice of building, room, and classroom equipment. The second group of soft constraints is formed by student requirements. Each student can enrol in several classes, so the aim is to minimize the total number of student conflicts among these classes. Such conflicts occur if the student cannot attend two classes to which he or she has enrolled because these classes have overlapping times. Finally, there are some group constraints (additional relations between two or more classes). These may either be hard (required or prohibited), or soft (preferred), similar to the time and room preferences (from -2 to 2).