Discrete Optimization
The examination timetabling problem at Universiti Malaysia Pahang: Comparison of a constructive heuristic with an existing software solution

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Abstract

This paper presents a real-world, capacitated examination timetabling problem from Universiti Malaysia Pahang (UMP), Malaysia. The problem has constraints which have not been modelled before, these being the distance between examination rooms and splitting exams across several rooms. These constraints provide additional challenges in defining a suitable model and in developing a constructive heuristic. One of the contributions of this paper is to formally define this real-world problem. A further contribution is the constructive heuristic that is able to produce good quality solutions for the problem, which are superior to the solutions that are produced using the university’s current software. Moreover, our method adheres to all hard constraints which the current systems fails to do.

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,j1…N
r,p1...R
s1…S
t1...T

Parameters
NThe number of examinations
RThe number of examination rooms
SThe number of students
TThe number of available timeslots
SiThe number of registered students in exam i
RtThe number of examination rooms available at timeslot t
BrThe building for room r
frThe total capacity for room r
cijThe 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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