We study a two-stage admission and assignment problem under uncertainty arising in university admission systems. In the first stage, applicants are admitted to an initial two-year program. In the second stage, admitted applicants are assigned to degree programs through an articulation mechanism subject to capacity constraints. Uncertainty stems from the academic performance of admitted applicants within the initial program, as this exit ranking determines the sequence in which students are processed by the articulation mechanism. Admission decisions must therefore be robust to all possible exit orders, giving rise to a robust stable matching problem.
We introduce a notion of robust compatibility for sets of admitted applicants and establish some of its properties. Building on a standard integer programming formulation of stable matching, we derive an adversarial formulation that determines whether a given admission set remains compatible under worst-case realizations of the exit order. This adversarial model underpins a sequential admission algorithm that incrementally constructs a robustly compatible set of applicants. Computational experiments on real admission data from three consecutive cohorts show that computational effort is highly unevenly distributed across iterations. In particular, certifying acceptance decisions is substantially more expensive than certifying rejections, with overall running time dominated by a small number of late iterations in highly congested regimes. We also address how the algorithm has been applied in practice and highlight the benefits in first-year retention rate driven by the proposed mechanism.