Exam timetabling with allowable conflicts within a time window

The exam timetabling problem is considered an NP-complete problem and its complexity depends on the different constraints and policies set by an institution's administration. The goal of this work is to facilitate exam timetabling for Masdar Institute (MI), which is a graduate level institution. Besides the renowned constraint on conflicts for students, MI's timetabling case includes the incorporation of venues’ limited capacities, special instructor requests, and the number of exams scheduled for one student within a preset window of days. To the best knowledge of the authors, the latter constraint is new to the literature. Moreover, it increases the problem's complexity since it requires cross-validation on both student and course levels. This contrasts with conventional exam timetabling which only deals with checks on a course level. We introduce an integer programming (IP) formulation that captures all the studied constraints. The proposed formulation can solve small problems using commercial software; however, this formulation's performance deteriorates as the problem size increases. Therefore, the paper proposes heuristics to solve medium and large sized problems in a timely manner. This study employs graph coloring algorithms that include a new approach, within the steps of the proposed exam timetabling heuristics. Four real-case studies from MI are solved to illustrate the feasibility and competitiveness of the proposed heuristic. Finally, a computational study is presented to benchmark the proposed heuristics against the IP formulation. The results show that the proposed heuristics are capable of obtaining optimal and near-optimal solutions in smaller computational time.