Kidney paired donation is a living-donor transplantation scheme allowing patients with end- stage renal disease to get a compatible donor when their own is not a match. Compatibilities among donors and patients can be modelled in a digraph, whose vertex set represents a donor with or without a paired patient and an arc depicts compatibility between donors and patients. Kidney allocation in this context consists of finding a matching, i.e., a set of vertex-disjoint cycles and chains. Despite the broad attention that kidney paired donation has received, we address several gaps in the literature relating to large problem size, robust allocation, and simulation to verify performance over time.