Problem definition: Treating many blood-related diseases requires transplantation of genetically compatible hematopoietic stem cells (HSCs) extracted from the bone marrow (BM) of live donors or the umbilical cord blood (CB) of babies. To facilitate the search for HSCs, institutions known as BM registries collect the details of potential donors and CB banks store units of CB. This paper focuses on the problem of joint optimization of the capacity of these two institutions. Academic/practical relevance: With more than 10 million genetic variants, limited inventory relative to this variety, and random replenishment, BM registry and CB bank compositions are random, interdependent, and change nondeterministically over time. Furthermore, BM and CB differ in their supply, costs, genetic matching criteria, and influences on medical outcomes, giving rise to important tradeoffs such that neither is preferred exclusively to the other. Jointly determining the optimal capacity of both sources is therefore both technically challenging and has immediate policy implications. Methodology: We develop a simulation-based approach to estimate the temporal variation in matching probabilities before incorporating the associated regression parameters into a mathematical model closely matching the research context. Results are contrasted against a simplified mathematical model, highlighting the importance of the dynamic setup. Results: Inventories of 17.5 million registered BM donors and 335,000 CB units are estimated as optimal for the U.S. population under reasonable assumptions. Expanding capacity to these levels would satisfy 33% of the currently unmet demand, increasing the transplantation rate to 98.7% and delivering $770 million of extra social surplus annually. Managerial implications: Rigorous policy analyses are imperative for designing evidence-based, cost-effective policies that deliver societal benefits. To this end, we provide quantitative evidence in support of calls for further expansion of the national BM registry and CB banks in the United States. We also propose annual recruitment targets for BM donors and CB units tomaintain the two institutions at their suggested levels.