It is crucial that blood products be available at the right time, and right quantity, lest it might result in the loss of lives. Thus, efficient matching between supply and demand for blood products is significant, however, it is understudied in the setting of a supply chain that involves both a blood center and hospital operations. In most blood supply chains, including that in Canada, blood centers and hospitals make individual decisions, resulting in an inefficient structure of the blood supply chain, which in turn renders supply and demand matching a challenging exercise. In this work, we make the very first attempt to model the interaction between blood centers and hospitals and optimize their operations. Specifically, this paper investigates collection, production, replenishment, issuing, inventory, and wastage decisions under three different blood supply chain channel structures, i.e., the decentralized, centralized, and coordinated structures. We propose a bi-level optimization program to model the decentralized system and use the KKT optimality conditions to solve the bi-level problem. In such a system, hospitals tend to order more than their actual need, resulting in overcollection, overproduction, and consequently a high wastage rate. On the other hand, in a centralized system blood centers and hospitals are coordinated and decisions are made by a central decision maker, which results in higher performance. Recognizing the challenges of implementing a centralized (integrated) system, we design a novel coordination mechanism to motivate hospitals to operate in a centralized system. Analysis of a realistic case study indicates that integration can decrease the mean gap between production and consumption by 69.84 units and total cost by 93.11%; allowing substitution between blood products can decrease the total cost of the blood supply chain by 14.41%; an increase in supply or decrease in demand facilitate coordination mechanism; under inappropriate organizational structure, increase in supply and decrease in demand can be detrimental for the blood supply chain; and offering subsidy beyond a threshold is not beneficial to the blood centers.