Fairness in Academic Course Timetabling

TL;DR

This paper addresses fair course timetabling in universities by proposing formulations based on max-min fairness and Jain's index, introducing new measures for timetable fairness, and evaluating an optimization algorithm to improve fairness with minimal constraint violations.

Contribution

It introduces two novel fairness formulations for course timetabling and develops an optimization algorithm with new measures for assessing timetable fairness.

Findings

Fair solutions can be achieved with minimal increase in soft constraint violations.

Existing solutions are already quite fair according to Jain's index.

New fairness measures impact algorithm performance significantly.

Abstract

We consider the problem of creating fair course timetables in the setting of a university. Our motivation is to improve the overall satisfaction of individuals concerned (students, teachers, etc.) by providing a fair timetable to them. The central idea is that undesirable arrangements in the course timetable, i.e., violations of soft constraints, should be distributed in a fair way among the individuals. We propose two formulations for the fair course timetabling problem that are based on max-min fairness and Jain's fairness index, respectively. Furthermore, we present and experimentally evaluate an optimization algorithm based on simulated annealing for solving max-min fair course timetabling problems. The new contribution is concerned with measuring the energy difference between two timetables, i.e., how much worse a timetable is compared to another timetable with respect to max-min fairness. We introduce three different energy difference measures and evaluate their impact on the overall algorithm performance. The second proposed problem formulation focuses on the tradeoff between fairness and the total amount of soft constraint violations. Our experimental evaluation shows that the known best solutions to the ITC2007 curriculum-based course timetabling instances are quite fair with respect to Jain's fairness index. However, the experiments also show that the fairness can be improved further for only a rather small increase in the total amount of soft constraint violations.