The development of a general algorithmic procedure for university examination timetabling

The problem of scheduling university examinations is becoming difficult for examination officers especially when they have to construct the timetables manually. It is largely due to the increasing number of students and greater freedom in choosing the courses. Examination officers would have to spend a considerable amount of time checking for student conflicts so that no student would have to sit for more than one exam at any one time. There are also other limitations such as the number of examination rooms, the length of the examination period and others. The examination timetabling problem varies between institutions, depending on their particular needs and limited resources. Most of the existing computerised examination timetabling systems found in the literature are developed and used by particular institutions. Therefore, the aim of the research is to produce a general computerised system for timetabling examinations which can be used by most universities. The research is done in two stages; the first stage involves carrying out a survey on the university examination timetabling systems and the second stage is the construction of a university examination timetabler incorporating the common objectives and constraints found in the survey. The survey was carried out to determine the extent to which the computerised examination timetabling procedures are used, to identify the objectives and constraints which are commonly considered when constructing examination timetables and to evaluate the effectiveness of the existing examination timetabling systems in achieving the objectives and satisfying the constraints The construction of the general examination timetabling system is done in two parts. In the first part, a new algorithmic rule is developed to assign exams to the minimum number of sessions without creating conflicts for any student. The rule adopts a clique initialisation strategy as a starting point and a graph colouring approach for assigning the exams. This rule is also quite capable of scheduling exams to the sessions which are as close as to the least number of sessions possible, without having to carry out any backtracking process. The backtracking process can sometimes be time consuming if there are a lot of exams firstly to be scheduled, and secondly clashing with each other. The second part of the work involves minimising the total number of students taking two exams on the same day and scheduling large exams early in the examination period subject to a specified time limit on the overall examination period and a maximum number of students that may be examined in any session. A swapping rule was introduced where exams in one of the sessions in any day with large number of sameday exams are interchanged with exams in other sessions which will reduce the total number of same-day exams. The experimentation showed that if the swapping procedures are repeated three times, the total number of same-day exams will be reduced by 50%. The total number of same-day exams will be reduced even more if some extra sessions can be added to the initial minimum number of sessions. A simple rule was devised to schedule large exams early in the examination period.