Management of blood component preparation

In transfusion medicine, the process of preparing or separating blood components from the whole blood is essential because the indication for the use of unfractionated whole blood almost does not exist nowadays. Since blood is uneasily-collected and easily-perished, a blood center or a hospital blood bank might as well aggressively manage the volume of each blood component, so as to decrease any waste. We assume that the process of blood component preparation can be underlaid by a so-called blood component tree, where each vertex representing a blood component with a certain value is derived from its parent vertex. Initially given a certain amount of the root blood component in a blood component tree (noticing that the amount of every other blood component is zero initially), the blood component preparation problem is concerned with finding the assignment of amount of each blood component such that the total value is maximized while satisfying the demand limit of every blood component. In this paper, we propose a linear time algorithm (in the size of vertices) for efficiently coping with the concerned problem, which also can be modeled as a linear program. Some theoretical analyses are included in this paper.