Optimisation Models for Scheduling Extraordinary University Exams with a Minimum Rest Time Between Consecutive Exams

The scheduling extraordinary exams problem has specific characteristics that make the models for scheduling ordinary exams inapplicable. Some of these characteristics are that exams are only scheduled for subjects requested by students and the impossibility of overlapping exams requested by the same student. This paper proposes an optimisation tool for scheduling extraordinary university exams based on two mixed integer linear programming (MILP) models. The first aims to schedule the most demanded subjects first to leave more correction time for the subjects with more students. It also ensures a minimum rest time between two consecutive exams for all students to improve their academic performance. If all students cannot reach the defined minimum rest time, the model will be unfeasible. In this case, it is possible to decrease the minimum rest time to a lower limit to find a feasible solution. If a feasible solution is not found, a second MILP model is proposed for scheduling exams without considering the requirement for time off between exams but minimising the number of non-compliances with this requirement. These models are applied to the School of Industrial Engineering of the Universitat Politècnica de València (Spain). It is concluded that achieving a schedule that ensures the minimum rest time set by the school for all students is infeasible. Therefore, the second model is solved. The solution shows that the average rest time between two consecutive exams increases considerably compared to the first model, ensuring compliance with the minimum rest time set for 93% of the students.