A Budgeted Robust Cohort-Transition Model for Enrollment Capacity Planning Under Demographic Decline

Demographic contraction reaches university admissions with a long delay and propagates through enrollment stocks of different durations. We integrate lagged demographic indices, cohort transitions and budgeted robust optimization to plan ramp-constrained incremental educational activity. The formulation uses a lower enrollment envelope for an activity floor and an upper envelope for resource protection while jointly propagating intake uncertainty and retention stress. A public-data case distinguishes four-year direct entry and two-year transfer routes around a 20,073-undergraduate reference. Under stated assumptions, nominal enrollment in 2043 is 12,067 and the lower envelope at uncertainty budget two is 11,357; an 85% activity floor requires 5705 peak incremental full-time equivalents (FTEs). Under the same envelope, deterministic and delayed-start plans produce 1046 and 4474 cumulative FTE-years of shortfall. Because the least-cost plan attains its ramp and capacity limits, operational draws that tighten a binding limit require re-planning; planning with those limits derated by 20% keeps the unchanged schedule feasible in all 1000 draws at 36% higher cost. Convergence checks, structural scenarios and public-record reconstructions support verification, but grade-level predictive validation remains unavailable. The results are conditional planning trade-offs, not validated forecasts or guarantees of participation in new programs.