Lecture and Tutorial Timetabling at a Tunisian University

This paper deals with the Lecture and Tutorial Timetabling Problem at an institution in a Tunisian University. Our objective is to construct a feasible timetable for all lectures and tutorials taken by different groups of each subsection of any section in the institution. For this, we describe the timetabling problem of the institution considered and list all specific hard and soft constraints. We formulate the problem as a zero-one integer linear program in which we define two binary variables corresponding respectively to lectures and tutorials. The quadratic objective function proposed tries to eliminate a real problem of congestion leading to a waste of time and students’ delays. Since the number of constraints is very large, the use of the heuristic procedures is of primary importance. We develop three heuristic procedures: first, we start by assigning all lectures of different student sections having the biggest size in a classroom with the smallest capacity that can fit the students. Second, we complete the output of the first phase by assigning the tutorials for different groups. Lectures and tutorials timetabling problem are correlated and cannot be treated independently if we desire to get a complete solution. The two first heuristics are illustrated with real data of one section at the Faculty of Economics and Management Sciences of Sfax in Tunisia and compared with those manually generated. Since there are several criteria which are preferably satisfied as much as possible, we will formulate the problem as a multiobjective mathematical program, and then we develop later a third heuristic in order to ameliorate the quality of the solution. The different criteria which can be taken into account are: minimize the number of free inter-meetings, maximize the professor preferences, minimize the distance covered by the students between the classrooms and exempt the students as much as possible in the half day. Educational timetabling has been the subject of several papers in various scientific journals and the topic of many theses in different universities. This problem concerns essentially course and exam which are to be scheduled during the academic year. The course timetabling problem consists of scheduling a certain number of courses into a certain number of timeslots spread throughout the week in such away that hard and soft constraints are satisfied. Various techniques have been used to solve Timetabling Problems (see Burke et al. [3], Carter and Laporte [8]). One of the earliest methods used to solve this problem is graph colouring in which vertices represent events and two vertices are connected if