Socially Optimal Contracting Between a Regional Blood Bank and Hospitals

Motivated by the operational challenges faced by a Regional Blood Bank (RBB) in distributing the blood (and related products) among the hospitals in its service area, we study socially optimal contracting decisions of an RBB serving multiple hospitals. The supply of blood can be uncertain and insufficient to satisfy the total orders from hospitals. In the face of supply uncertainty, hospitals tend to over-order to compensate for a potential supply shortfall. When all hospitals inflate their order quantities, overall allocation of blood suffers and ultimately inflates the total cost of blood, which in turn lightens the wallets of patients. We model the blood bank as a social planner with the objective of minimizing the total cost of shortages and outdates throughout the supply chain. We assume hospitals need some economic incentive to report demand honestly when multiple hospitals compete for limited blood supply. We show that if the blood bank offers a suitable per unit subsidy for every unit of shortage experienced by a hospital, then hospitals would be induced to report demand to the blood bank without inflation. We also investigate whether or not a consignment contract can be consistent with uninflated ordering by hospitals. Finally, we perform a detailed numerical study based on real demand and supply data to investigate the impact of over-ordering by hospitals on shortages and outdates in the supply chain, and the role of the appropriate contracts and allocation policies in obviating the concomitant social costs.