Optimal blood issuing by comprehensive matching

Mass-scale red blood cell genotyping of donors and transfusion recipients increases the availability of extended antigen matched red blood cell units. Therefore, a new mathematical framework is developed that can be applied for general blood groups (i.e., beyond the ABO, RhD blood groups). It determines which red blood cell units should be issued from inventory, such that requests from hospitals can be satisfied with antigen compatible red blood cell units, shortages for future requests are avoided, and outdating is prevented. The optimization model consists of two steps: a binary vector representation for general blood groups and the formulation of the inventory allocation problem as a minimum cost flow problem. The potential practical performance of the optimization model is evaluated by iterative simulations, based on historical data on supply and demand of red blood cell units in the Netherlands. When including the fourteen clinically most relevant antigens, more than 90% of all requests can be satisfied with antigen identical red blood cell units. Shortages and outdating can be kept restricted and could even be reduced to virtually zero, when only the ABO, RhD blood groups are considered.