Balancing equity and efficiency in kidney allocation: An online adaptive stochastic bi-objective approach

Kidney allocation presents a persistent trade-off between medical urgency (equity) and post-transplant survival (efficiency). This paper introduces an intelligent decision-support system that integrates stochastic optimization and game-theoretic reasoning to balance these competing objectives under uncertainty. We formulate a bi-objective stochastic model that compares pre-transplant mortality risk and expected post-transplant survival while enforcing regional chance constraints to limit graft-failure rates. To identify a fair and actionable policy, the framework applies the Nash Bargaining Solution to select a balanced compromise on the Pareto frontier. The resulting weights are then incorporated into an online adaptive two-stage stochastic program, enabling real-time allocation of newly available kidneys based on historical performance and predicted future capacity. Using national US waiting list data, the proposed system increases monthly deceased-donor transplants by 4.5%, reduces graft-failure probability by 6.22%, and raises average expected survival by 22.95%, while improving access for high-urgency candidates by 15%. These results demonstrate how combining optimization and adaptive learning principles can yield an intelligent, equitable, and efficient decision-support system for organ transplantation.