Finding robust timetables for project presentations of student teams

This article describes a methodology developed to find robust solutions to a novel timetabling problem encountered during a course. The problem requires grouping student teams according to diversity/homogeneity criteria and assigning the groups to time--slots for presenting their project results. In this article, we develop a mixed integer programming (MIP) formulation of the problem and then solve it with CPLEX. Rather than simply using the optimal solution reported by CPLEX, we obtain a set of solutions provided by the {\em solution pool} feature of CPLEX. We then map these solutions to a network, in which each solution is a node and an edge represents the distance between a pair of solutions (as measured by the number of teams assigned to a different time slot in those solutions). Using a scenario--based exact robustness measure, we test a set of metrics to determine which ones can be used to heuristically rank the solutions in terms of their robustness measure. Using seven semesters' worth of actual data, we analyze performances of the solution approach and the metrics. The results show that by using CPLEX's solution pool feature, analysts can quickly obtain a set of Pareto--optimal solutions (with objective function value and the robustness measure as the two criteria). Furthermore, two of the heuristic metrics have strong rank correlation with the robustness measure (mostly above 0.80) making them quite suitable for use in the development of new heuristic search algorithms that can improve the solution pool beyond that given by CPLEX