Derivatives Tree Problem

• Main Authors: Chun-Cheng Lin, 林春成
• Other Authors: 游張松
• Format: Others
• Language: en_US
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/02331571987307036773

碩士 === 國立臺灣大學 === 商學研究所 === 95 === In this paper, we investigate the derivatives tree problem as well as design a linear time algorithm for solving it. In a derivatives tree, each vertex representing a derivative with a certain value is derived from its parent vertex. Initially given certain amount of the root derivative in a derivatives tree (noticing that the amount of every other derivative is zero initially), the derivatives tree problem is concerned with finding the assignment of amount of each derivative such that the total value is maximized while satisfying the demand limit of every derivative. In practice, the problem has application to the decision-making of blood component preparation in transfusion medicine. Although the derivatives tree problem can be solved by linear programming which is proposed in this paper, one should notice that the linear programming may not be an efficient approach. As a consequence, in this paper, we propose a linear time algorithm (in the size of vertices) for efficiently coping with the derivatives tree problem. Some theoretical analysis is also included in this paper.