A Fluid Model for One-Sided Bipartite Matching Queues with Match-Dependent Rewards

When allocating scarce resources such as organs or public housing units, the policy maker needs to carefully balance two conflicting objectives: maximizing the reward from matching and minimizing inequity across different types of candidates. We consider an implementable class of policies that ranks the candidates by the sum of their waiting score and matching score. Similar policies had been proposed for allocating deceased-donor kidneys to patients on the transplant waitlist. This article provides a modeling framework to characterize the waitlist system under this type of ranking policy. This framework allows the policy maker to predict and compare the allocation outcome under different ranking policies. When the efficiency and fairness measurements take certain forms, we derive a closed-form scoring formula that optimizes the outcome of the system in the long run.