In this talk we will survey the results of four recent research projects, where we applied integer programming approach for solving matching problems under preferences. The first application is the Hungarian university admission, where the standard Gale-Shapley setting is enriched with the presence of ties, lower quotas, common quotas, and paired applications. The second application is the CEMS business project allocation at Corvinus University with special distributional requirements. Then, we present a general cutoff-based solution concept, motivated by an application of distributing funding for PhD-students under two-sided preferences at a university in Sydney. In the last project we studied a new solution concept for the school choice problem that we tested with computer simulations on an Estonian kindergarten admission dataset.
[1] Ágoston, K. C., Biró, P., Kováts, E., Jankó, Z. (2022). College admissions with ties and common quotas: Integer programming approach. European Journal of Operational Research, 299(2), 722-734.
[2] Ágoston, K. C., Biró, P., Szántó, R. (2018). Stable project allocation under distributional constraints. Operations Research Perspectives, 5, 59-68.
[3] Aziz, H., Baychkov, A., Biró, P. (2022). Cutoff stability under distributional constraints with an application to summer internship matching. Mathematical Programming, 1-23.
[4] Biró, P., Gudmundsson, J. (2021). Complexity of finding Pareto-efficient allocations of highest welfare. European Journal of Operational Research, 291(2), 614-628.