A mixed-integer mathematical modeling approach to exam timetabling

This paper explores mathematical programming models for an exam timetabling problem related to Kuwait University (KU). In particular, we consider two subproblems: (a) the ExamTimetabling Problem (ETP), which is concerned with assigning exams to designated exam-periods and classrooms, and (b) the Proctor Assignment Problem (PAP), which deals with the assignment of proctors to exams. While this exam timetabling problem is ubiquitous in many academic institutions worldwide, idiosyncrasies of the problem related to gender-based policies and having multiple exam centers at KU require novel models. A mixed-integer exam timetabling programming model (ETM) is developed for ETP, which takes into account restrictions related to exam-period conflicts, facility and human resources, and commuting and traffic considerations. Assuming that exam-periods are specified for all exams as determined by ETM, another mixed-integer programming model is formulated for PAP, denoted by PAM, which incorporates the proctors' preferences for specific days and exam-periods. Computational results are reported and analyzed for solving ETM and PAM directly using the CPLEX Optimization Software (version 9.0), and for implementing a specialized sequential LP-based heuristic for solving PAM. The results obtained significantly improve upon those derived via the existing manual approach implemented at KU, in terms of eliminating conflicts as well as from the overall efficiency and equity points of view.