A column generation mathematical programming approach for a class-faculty assignment problem with preferences

This paper presents a column generation approach for assigning faculty members to sections of offered classes (class-sections) in a case study related to Kuwait University. For a given class, the total number of class-sections to be offered is known; however, the distribution of these class-sections into available time-slots is determined via a mixed-integer programming model that takes into consideration faculty members’ aggregate preferences for specific offered classes and the time-slots of the corresponding sections, as well as other restrictions imposed by the Office of the Registrar. Subsequently, upon fixing the time-slot assignments of the class-sections, another mixed-integer programming model is formulated and solved to select weekly schedules for faculty members, while considering their preferences for specific classes and time-slots. In this latter model, each variable corresponds to a feasible schedule of a faculty member, and by exploiting its special structure, we demonstrate that its continuous relaxation can be solved very efficiently via a column generation method in order to heuristically derive a good quality feasible solution. Computational results are provided for a number of test instances, including 10 real cases pertaining to the Department of Mathematics at Kuwait University.