Discrete OptimizationThe examination timetabling problem at Universiti Malaysia Pahang: Comparison of a constructive heuristic with an existing software solution
Introduction
Examination timetabling problems can be categorised as either un-capacitated or capacitated. In the un-capacitated examination timetabling problem, room capacities are not considered, whilst in the capacitated problem the room capacities are treated as a hard constraint, in addition to the other commonly used hard constraints, e.g. a clash-free timetable (Pillay and Banzhaf, 2009, Abdullah, 2006). Most of the research in the literature has investigated the un-capacitated examination timetabling problem, concentrating on the algorithm and algorithmic performance in terms of producing solutions effectively and quickly (see Burke and Petrovic, 2002, Qu et al., 2009). In enabling comparisons to be made among the research community, a benchmark dataset proposed by Carter et al. (1996b) is often used. Although un-capacitated benchmark datasets are popular, McCollum, 2007, Carter and Laporte, 1996a believe that, researchers are not dealing with all aspects of the problem. That is, they are only working on a simplified version of the examination problems. Qu et al. (2009), in their survey paper, reveal that most research only addresses a few common hard constraints. For example, no exams with common students assigned simultaneously, the size of exams need to be below room capacity etc. Commonly used soft constraints include spreading conflicting exams as evenly as possible, or not in x consecutive timeslots or days.
The capacitated problem more closely reflects the real-world problem as it includes a room capacity constraint. However, the capacitated problem has received less attention from the research community. This is probably due to the lack of benchmark datasets. In addition, the capacitated problem is much harder to solve; see Burke et al.’s (1996a) survey paper where 73% of the universities agree that accommodating exams is a difficult problem. Capacitated problems also require more comprehensive data as they have to include the room capacity as well as the other data also required for the less complex problem (e.g. student and exam list). This extra information can be difficult to collect (McCollum, 2007).
This paper presents a capacitated examination problem drawn from a real world example from Universiti Malaysia Pahang (UMP). This dataset has several new constraints in addition to those commonly used. In Section 2, we describe the examination timetabling problem and present related work. A description of the UMP examination timetabling problem, including the constraints, is discussed in Section 3. A formal model of the problem is presented in Section 4. In Section 5, we describe the experimental setup for our proposed constructive heuristic. In Section 6, a comparison between the solutions achieved with the current method employed by Universiti Malaysia Pahang (which is produced using a proprietary system), and our method, is presented in order to evaluate the effectiveness of the proposed methodology. In Sections 7 Statement of contribution, 8 Conclusion and future work we summarise the contribution and present our conclusions.
Section snippets
The examination timetabling problem
The university timetabling problem can be divided into two categories: course timetabling (de Werra, 1985, van den Broek et al., 2009) and exam timetabling (Burke et al., 2007). This paper concentrates on examination timetabling. The construction of an examination timetable is a challenging task and is quite often time consuming. The examination timetabling problem is concerned with assigning exams to a specific, or limited, number of timeslots and also assigning rooms so as to satisfy a given
Universiti Malaysia Pahang (UMP): Examination timetabling problem
The Universiti Malaysia Pahang (UMP), formerly known as Kolej Univerisiti Kejuruteraan dan Teknologi Malaysia (KUKTEM), was established in 2002 and is located in Pahang, Malaysia. In 2007, UMP consisted of five faculties with a total of 3550 students. The number of students is growing rapidly as new faculties are being introduced along with an increase in the programs offered. Currently, a total of 17 programs are offered by these faculties. UMP is currently situated in a temporary campus,
Problem formulation
In this section, we present the formal model of the UMP examination timetabling problem as discussed in Section 3.Indices i,j 1…N r,p 1...R s 1…S t 1...T Parameters N The number of examinations R The number of examination rooms S The number of students T The number of available timeslots Si The number of registered students in exam i Rt The number of examination rooms available at timeslot t Br The building for room r fr The total capacity for room r cij The conflict matrix where each element (cij, i, j ∈ {1…N}) is the
Experimental setup
In this section we present our proposed constructive heuristic, along with other algorithmic details to aid reproducibility. The dataset is taken from Universiti Malaysia Pahang (UMP) for semester 1, 2007. The total number of examination papers is 252, across the 17 programs offered by 5 faculties. However, due to the combined exams requirement, the dataset has been pre-processed and the combined exams are given a new examination code and treated as one large exam. This results in a total of
Results
In this section, we compare the examination timetable generated by the proprietary software and the result from our proposed algorithm, shown in Fig. 4.
Statement of contribution
This paper has provided a study of a real-world examination timetabling problem from UMP. In particular, we have investigated the scheduling of exams in a capacitated environment with the aim of minimising the spreading, distance and splitting cost. One of the contributions of this paper is the collection of the necessary requirements (constraints) which has never before been properly documented at UMP. This data collection was carried out with the help and assistance of UMP employees. Studying
Conclusion and future work
It is recognised that a gap exists between theory and practice in examination timetabling. Different institutions have different requirements and it is difficult to produce a common solution methodology. In this paper we have introduced a new examination dataset and two new constraints. A constructive heuristic has been used to generate solutions that produce better solutions when compared to the proprietary software that is used by UMP. For future work, we plan to schedule the invigilators and
Acknowledgements
The examination dataset has been provided by the Academic Management Office, UMP and the research has been supported by the Public Services Department of Malaysia (JPA) and the Universiti Malaysia Pahang (UMP).
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