# Student Sectioning Solver.

Student sectioning is often considered as a subproblem of course timetabling. Once a timetable has been developed, the object is to assign students to classes (i.e., individual sections of a course) in order to minimize conflicts while respecting individual student course requests and preferences along with various other constraints.
Before and during the construction of the timetable course demands are collected from students. During this preregistration process, each student can indicate the list of requested courses together with his or her preferences. These preferences contain course priorities (order of courses based on their importance for the student), alternative course requests (each course request can have one or more alternative courses), free time requests, wait-list preferences (if a student cannot be enrolled into the course, e.g., because of the space available, should he or she be assigned to the appropriate wait-list for the course), and additional schedule distribution preferences.

## Initial Sectioning

During the construction of the course timetable, course demands of already pre-registered students are considered. Since many students are anticipated to register later in the process, projected course demands are considered as well. These are deducted from the last-like semester enrollments, e.g., Fall 2006 course enrollments are used to predict Fall 2007 course demands. Minimization of potential student conflicts is one of the optimization criteria of the timetabling solver. Two classes are conflicting, i.e., they cannot be attended by the same students, if they are overlapping in time or if they are back-to-back (the second class starts just after the first ends) being placed in rooms that are too far apart.
Before the course timetabling solver is started, an initial sectioning of students into classes is processed. This sectioning is based on Carters (Carter 2001) homogeneous sectioning and is intended to minimize future student conflicts. However, it is still possible to improve on the number of student conflicts in the solution. This is accomplished by moving students between alternative classes of the same course during or after the search for a timetabling solution.

## Batch Sectioning

After the course timetable for the whole university is constructed, batch student sectioning process is executed. In this process, all pre-registered students are assigned to specific sections (classes) of courses in order to minimize conflicts as well as optimize preferences provided by students. Additional constraints deducted from the course structure as well as various reservations, that can be put on courses or particular classes, are respected. Students that were not able to get a requested course (or any of the provided alternatives) are enrolled to the appropriate waitlists.
The batch student sectioning is also using the projected student demands to compute the expected number of students in each class for the following online phase, however, pre-registered students take precedence before projected student demands. This means that a pre-registered student cannot be bumped out a requested course because of a projected student, but he or she may end up with a class which does not prevent projected students to take the course as well. Based on the computed solution, pre-registered students are assigned to classes and wait-lists and the projected students demands are used to identify space in each section that is to be reserved for students that are not yet registered. This information is then used in the online sectioning phase in order to direct already registered students from sections that are expected to be taken by the future students.

## Online Sectioning

After the first student schedule is created, till the begining of the semester, students can make changes in their schedules using the online interface. During this phase, existing students are allowed to remove themself from the requested courses or request additional courses and a new sectioning solution is provided to them in realtime. They can also change their class enrollments if there are other classes of the course that are available or wait-list themselves on classes that are not available. Wait-lists are automatically processed as the space frees on courses and classes. Some changes in the course timetable might occur as well, potentiality causing some re-sectioning of existing students. New students are using the same interface as existing students. They start with the course demands first, based on which they are sectioned to courses in real-time, and then they can continue as existing students.
As students submit schedule requests, each course is ranked in priority order. During realtime sectioning of a student, the search employs a backtracking process considering possible assignments beginning with those classes associated with the students highest priority course. As it evaluates each possible assignment, it compares available space with the space expected to be taken by the future students for each class. This difference between available space and the expected need for each class is used to direct students away from class assignments that would result in excess demand, however, in no case is an eligible student blocked from scheduling a course offering as a result of expected future demand. As students are assigned to specific classes during the sectioning process, the expected demand for each class is adjusted to reflect the assignment.