A multi-objective mixed integer linear programming model for thesis defence scheduling

Abstract

In this paper, we address the thesis defence scheduling problem, a critical academic scheduling management process, which has been overshadowed in the literature by its counterparts, course timetabling and exam scheduling. Specifically, we address the single defence assignment type of thesis defence scheduling problems, where each committee is assigned to a single defence, scheduled for a specific day, hour and room. We formulate a multi-objective mixed-integer linear programming model, which aims to be applicable to a broader set of cases than other single defence assignment models present in the literature, which have a focus on the characteristics of their universities. For such a purpose, we introduce a different decision variable, propose constraint formulations that are not regulation and policy specific, and cover and offer new takes on the more common objectives seen in the literature. We also include new objective functions based on our experience with the problem at our university and by applying knowledge from other academic scheduling problems. We also propose a two-stage solution approach. The first stage is employed to find the number of schedulable defences, enabling the optimisation of instances with unschedulable defences. The second stage is an implementation of the augmented ϵ-constraint method, which allows for the search of a set of different and non-dominated solutions while skipping redundant iterations. The methodology is tested for case-studies from our university, significantly outperforming the solutions found by human schedulers. A novel instance generator for thesis scheduling problems is presented. Its main benefit is the generation of the availability of committee members and rooms in availability and unavailability blocks, resembling their real-world counterparts. A set of 96 randomly generated instances of varying sizes is solved and analysed regarding their relative computational performance, the number of schedulable defences and the distribution of the considered types of iterations. The proposed method can find the optimal number of schedulable defences and present non-dominated solutions within the set time limits for every tested instance.