Deployment of AI-Assisted Interventions: Capacity Constraints and Noisy Compliance

AI tools increasingly guide targeted interventions in healthcare, education, and recruiting. Algorithms score individuals, trigger outreach to those above a threshold (e.g., high-risk or high-value), and encourage them to request service; then providers deliver service to those who request. Standard practice sets the threshold and selects the algorithm to maximize predictive accuracy, assuming that better predictions yield better outcomes. We show that this approach is suboptimal when limited service capacity and probabilistic behavioral responses influence who receives service. In such settings, the optimal score threshold must balance two effects: ensuring all capacity is filled (utilization) and ensuring high-value individuals are served despite competition between requests (cannibalization). We characterize the optimal threshold and prove that policies based solely on predictive accuracy are generally suboptimal. Further, because optimal thresholds vary with service capacity, algorithm selection metrics like AUC, which weight all thresholds equally, are misaligned with operational performance. We introduce a new metric--Operational AUC (OpAUC)--and show it leads to optimal algorithm selection. Finally, we conduct a case study on sepsis early warning data and illustrate the magnitude of improvement that can be achieved from improved threshold and algorithm selection.