Initial Results on Fairness in Examination Timetabling

Examination timetabling problems have attracted many researchers during the last couple of decades, and especially since the work of Carter [2], and Carter, Laporte and Lee [3]. The problems are NP-complete and challenging, and so have nurtured different approaches and techniques; for a recent survey see [9]. In standard formulations the quality of a solution, from the student perspective, is given by an objective function which is a simple weighted sum of penalties for the timetable of each student. For example, in the classic Toronto benchmarks [3], the penalty per student is designed to reflect the natural desire of students that their exams do not take place too close together in time. Hence, minimising the objective is intended to maximise the average student satisfaction with the personal spread of examinations; however, it does not do anything to ensure equality between students. Students may consider the assessments to be unfair if some students have well spread out exams (small penalty) whilst others have many exams close together (large penalty). We believe that it is reasonable that overall student satisfaction could also be improved by increasing the fairness of treatment between students. In this paper, we make preliminary investigations of how to increase such fairness. For general background, the common sense definitions of fairness in political science and political economics are discussed in [6] which defines fairness as an allocation where “no person in the economy prefers anyone else’s consumption bundle over his own.” In general resource allocation, there are two well-accepted and common notions of fairness criteria: max-min fairness and proportional fairness. Max-min fairness allows to say an allocation is fairer than another allocation but does not measure how much fairer [10], whilst Proportional fairness is quantitative measure of fairness (see [1] for details). Fairness has been studied before in combinatorial optimisation problems; for