Mathematical programming models and algorithms for a class-faculty assignment problem

This paper presents mathematical programming models for assigning faculty members to classes including, among typical academic class scheduling issues, certain specialized central policies at Kuwait University. The time-slots for classes are initially assumed to be given and an integer programming model (CFAM) is constructed to solve the resulting problem, which aims to minimize the individual and collective dissatisfaction of faculty members in a fair fashion, where dissatisfaction is measured by a function of the assignment of faculty members to time-slots and specific classes. In order to enhance the quality of results obtained in practice, the model is modified (ECFAM) so that the time-slots for the classes can be changed, however, with restrictions related to efficient facility utilization and permitting an administratively regulated maximum number of changes. Gender-based modeling considerations are also introduced in order to maintain desirable class offering patterns. Computational results are presented based on solving the models directly by the CPLEX-MIP (version 7.5) package and also using a specialized LP-based heuristic. The faculty schedules generated via the proposed approach based on a number of case studies related to the Department of Mathematics and Computer Science at Kuwait University reveal that this approach yields improved schedules in terms of fairness and enhanced satisfaction levels among faculty members.