A pricing scheme for a human embryo storage service as a source for a secondary market

A large reservoir of frozen human embryos is a negative outcome of their cryostorage for in vitro fertilization treatments. The existence of unused stored embryos, referred to herein as "remaining embryos", places the service provider (usually a hospital) in a fragile situation. This is especially the case when the issue of discarding unused embryos arises or when unexpected failures associated with preserving the inventory occur. Moreover, the absence of intrinsic incentives for couples to donate embryos to the secondary market, as well as the increased operational costs for maintaining a viable storage service over time, further challenge this unique service. The present paper develops an optimization model that determines a charging scheme for the couples using the storage service and a payment scheme for couples who agree to provide their remaining embryos as a source for the secondary market. Couples who do not agree to receive payment for their remaining embryos are charged for discarding them (referred to herein as the "discarding payment"). While this model includes rewards and motivates couples to provide embryos for the secondary market, it also reduces the remaining inventory, thereby responding to the two key problems of embryo storage. The analytically developed model is used to derive optimal solution algorithms. A numerical example and a sensitivity analysis of the key parameters are presented.