next up previous contents
Next: Methods Up: Graph Coloring and Previous: Graph Coloring

Course Scheduling

The scheduling of courses at a university is a practical example of the timetabling problem. In this example, the resources involved, which may be required by no more than one course at any particular time, are instructors, classrooms, and students. This problem can be addressed from different angles. For example, one could assume that a particular set of courses will be offered during a term by particular instructors, and first assign them times and rooms, and then allow students to register only for courses whose times do not conflict. A second approach would be to decide which courses would be offered, allow students to register for them, and then assign times and rooms to each course, so that the number of students who have course conflicts is minimized. Here we will briefly look at the problem from the first of these two points of view. The restrictions involved in creating a schedule of courses from this point of view may be divided into two categories, ``hard'' and ``soft'' constraints.

Hard constraints are those which must be satisfied in order to have a legitimate or legal schedule. For example, courses may only be offered during a fixed set of days and times during the week, and each course must meet a particular number of hours per week. No instructor may be scheduled to teach two courses during the same time slot. Similarly, courses which enroll the same set of students, such as a physics lecture course and the accompanying laboratory course, may not be scheduled in the same time slot, since there is an overlap of students in the two classes. Each of these hard constraints deals with time-related, or temporal, issues.

In addition to temporal constraints, there are other hard constraints which deal with meeting space assigned to each course. These spatial constraints arise from the fact that a fixed number of rooms exist on a given campus, and any courses held during the same time slot may not be held in the same room. In addition, since rooms have a fixed size, course size must not exceed the capacity of the room it is assigned. Furthermore, each room is of a particular type, such as auditorium, laboratory, or seminar room. Similarly, each course requires one of these types of rooms, so room type must be a consideration in the assignment of rooms.

Soft constraints associated with creating a course schedule are requests that should be fulfilled, if possible. However, if soft constraints are not fulfilled, the schedule is still considered legal provided that all hard constraints have been satisfied. For example, an instructor may request a particular time slot free during the week, or may want a lecture hall in the same building as his or her office. All instructors may prefer that, if they teach two courses in contiguous time slots, the courses are not in different buildings. These types of constraints are reasonable, but it may not be possible to fulfill each of these in addition to all of the hard constraints.



next up previous contents
Next: Methods Up: Graph Coloring and Previous: Graph Coloring



HPF demo web account
Mon Nov 18 19:45:42 EST 1996