Mathematical programming formulations for the examinations timetable problem: The case of the University of Dar es Salaam

The Examinations Timetabling Problem (ETP) is the problem of assigning courses to be examined and candidates to time periods and examination rooms while satisfying a set of constraints. Every University has a different set of constraints and structure of examinations. Thus there is no general ETP model for all Universities around the world. ETP is NP-Hard and therefore no optimal algorithm is known for this problem which can solve a general problem within reasonable time. However, exact methods can be used to provide a benchmark for the heuristic methods. There is no general model for University Timetabling Problems because the problem feature differs from one University to another. In this paper we focus in the formulation of the ETP for the University of Dar es Salaam. We formulate, test and compare three Integer Programming models. It is concluded that, although exact methods cannot give a solution to a real-size problem, these models give a good benchmark for testing the performance of other approaches. This paper also gives a direction for better exact models for the University of Dar es Salaam's ETP.