Before revision:  We also present an extension to three-sided markets with quotas , where each student conducts several projects, and each project is supervised by one advisor and one co-advisor. As it is often the case in practice that the same student should not do more than one project with the same advisor or co-advisor, we modify our PhD algorithm for this setting by adapting the two-sided Gale--Shapley algorithm to many-to-many two-sided markets, in which the same pair can match at most once. We also generalize the three-sided market to an n-sided market consisting of n-1 two-sided markets. We extend the PhD algorithm to this multi-sided setting to compute ]  a stable matching in polynomial time, and we discuss its extension to arbitrary quotas.
After revision:  We also present an extension to three-sided markets with quotas and show how they can model supply chain networks. Finally, we show how our algorithm outperforms the baseline given by ] a stable matching in polynomial time, and we discuss its extension to arbitrary quotas.