MISTA 2013
Building university course timetables with minimized resulting student
flows
A case study at the Hogeschool-Universiteit Brussel
Jeroen Beliën • Annelien Mercy
1
Introduction
The growing student numbers at colleges and universities have resulted into an enlarged
complexity in terms of planning and organization. One of the tasks that becomes increasingly
complex is the development of course timetables. Course timetables have to satisfy various
requirements of different stakeholders including non-overlap of courses, free hours, lecturers’
preferences, student preferences, etc. Furthermore, the course timetable can have a huge
impact on queues in stair halls and elevators, particularly for universities or colleges with
many students that follow courses in a single building. The congestion problems in stair halls
and elevators are caused by traveling students that all have to switch rooms at the same time
between two consecutive lectures. Clearly, student flows can be controlled and monitored via
the course timetables. For example, if the schedules are arranged so that consecutive lessons
take place in rooms situated on the same floor (or on a floor as close as possible), there will be
far fewer queues at the elevators and in the stairwells. Thus, next to the various constraints and
preferences of different stakeholders, the resulting student flows should also be taken into
account when building the course timetable.
Despite the large complexity in building course timetables, in many educational institutes
course timetables are still developed manually, which requires a lot of time and creativity of
the planners. It is nearly impossible for human planners to solve the enormous puzzle taking
into account the constraints and preferences of all stakeholders, let alone to incorporate the
resulting student flows. This paper therefore presents an automated approach to develop course
timetables based on a two-stage integer programming (IP) approach. In the first stage, lectures
are assigned to timeslots taking into account the various constraints and maximizing the
Jeroen Beliën
Center for Informatics, Modeling and Simulation, Hogeschool-Universiteit Brussel,
Warmoesberg 26, B-1000 Brussel, Belgium
Center for Operations Management, KULeuven, Naamsestraat 69, B-3000 Leuven, Belgium
E-mail: jeroen.belien@hubrussel.be
Annelien Mercy
Nationale Delcrederedienst
E-mail: annelien_mercy@hotmail.com
stakeholders’ preferences, while the second stage allocates each lecture-timeslot combination
to a room with the objective of minimizing the resulting student flows.
This research was motivated by the course timetabling problem at the Faculty of
Economics and Management at the Hogeschool-Universiteit Brussel (HUB). In recent years,
the HUB has gone through a process of campus consolidation in which several buildings at
different locations in Brussels have been sold and the lectures of all economic programs have
been concentrated at a single location in the center of Brussels. As a result, over 8000 students
daily follow classes in a single building, which inevitably causes major problems in terms of
congestion at the elevators and the stairwells during lecture transitions.
Since many HUB students travel to Brussels by train, avoiding free hours in the course
timetable is of key importance. Unfortunately, incorporating free hours through hard or soft
constraints in the IP models turned out to be computationally intractable for the HUB problem
size. Therefore, we introduce the concept of masks. A mask is defined for each student group
and is a set of timeslots during which the lectures that are taken by the corresponding student
group need to be scheduled. Each mask contains exactly as many timeslots as the weekly
number of lectures that are taken by the corresponding student group. The masks determine
how many lectures (not which ones) will be scheduled consecutively and how many lectures
have free hours in between.
2
Literature review
The university course timetabling problem (UCTP) can be defined as the construction of
a weekly timetable in which all operational rules and requirements of the academic institution
are met and as many wishes as possible of the staff and students are satisfied [7]. Various
solution techniques have been proposed for automating the development of course timetables
[6]. Overviews are given in [4], [5], [13], [3], [11], [9] and [10].
In the past, due to computational difficulties the use of mathematical programming for
solving UCTPs has been limited to small size instances. However, thanks to strong advances in
computer software and hardware, and in IP formulations, mathematical programming
approaches for timetabling problems have become more popular ([7], [15]). Examples of IP
formulations for UCTPs can be found in [8], [7], and [14]. One advantage of mathematical
programming approaches is the ease of incorporating additional soft constraints [5].
To the best of our knowledge, the studies in [1], [2] and [12] are the only ones that, to a
limited extent, incorporate student flows. In [1] and [2] students and faculty members are
adequately spread over all the available timeslots by constraints that impose an upper bound on
the number of students that follow classes (take exams) during each timeslot in order to reduce
parking problems and traffic congestions. [12] formulates a soft constraint specifying that
students must follow consecutive lectures as much as possible in the same room in order to
avoid traveling students. Hence, they do not model student flows that depend on the distance
(e.g., in terms of number of floors) between the rooms of consecutive lectures.
3
Two-stage integer programming approach
Our two-stage approach aims at building the course timetable for one semester. Both
stages involve the solution of an IP model. The first stage assigns lectures to timeslots and
rooms taking into account lecture preferences, room (capacity) restrictions, free hours, work
regulations, event-clash constraints, etc. The goal of this first stage IP model is to minimize
weighted violations of lecturers being scheduled during timeslots for which they prefer not to
be scheduled. The second stage changes the room assignment of the lecture-timeslots from the
first stage with the objective of minimizing the resulting student flows. In the second stage the
lecture-timeslot combinations that result from stage 1 are assigned to a new room with the aim
of minimizing the resulting student flows. The stage 2 objective function minimizes the
number of students that have to use the elevator (or stairways) for at least two floors between
two consecutive lectures. We realize that this definition of student flows is somewhat
arbitrarily. Therefore, alternative definitions of student flows have been studied as well.
4
Results
The course scheduling problem at the HUB involves 396 lectures, 436 student groups,
171 lecturers and 56 rooms (including 9 pc rooms). Only 31 lectures require a pc room. Both
IP models were solved using IBM-ILOG CPLEX Optimization Studio 12.3 on a pc with a 2
GHz Intel® Core™ 2 Duo processor and 2 Gb RAM. The two-stage approach only requires
six minutes of CPU time. To evaluate the quality of the solutions the results are compared with
the manually developed (and used) course timetable for the second semester of the academic
year 2011-2012. The results listed in Table 1 indicate that the automated two-stage approach
outperforms the manual scheduling with respect to both the lecturers’ preferences and the
student flows.
Table 1: Comparison between the two-stage approach and the
manual approach (based on 365 of the 396 lectures)
Penalty cost lecturer
preferences
Student
flows
Two-stage
approach
425
282
Manual
535
3,731
Table 2 compares the results of the manual and the two-stage model for alternative
definitions of student flows. The first column of Table 2 repeats the results of the basic case.
The second column shows that, when also incoming student flows at 08:30 and 13:30 are
incorporated, the automated two-stage approach still succeeds in finding a course timetable
with considerably reduced student flows compared to the manual approach. The results listed
in the third column indicate that the automated two-stage approach even finds a solution of
zero student flow when student flows between rooms that differ less than three floors are
neglected.
Table 2: Comparison between the two-stage approach and the manual approach for alternative
definitions of student flows (based on 365 of the 396 lectures)
Student flows only
between
consecutive classes.
Student flows between
consecutive classes and incoming
flows at 08:30 and at 13:30.
Student flows only
between consecutive
classes.
Rooms are
separated by at least
two floors.
Rooms are separated by at least
two floors.
Rooms are separated
by at least three
floors.
Two-stage
approach
282
4,181
0
Manual
3,731
6,870
1,991
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