标题: | 求解大规模资料包络分析问题 Solving Large-scale Data Envelopment Analysis Problems |
作者: | 赖圣咏 Lai, Sheng-Yung 陈文智 Chen, Wen-Chih 工业工程与管理学系 |
关键字: | 资料包络分析;线性规划;计算效率;Data envelopment analysis;linear programming;computational efficiency |
公开日期: | 2011 |
摘要: | 资料包络分析(data envelopment analysis, DEA)以线性规划(linear programming, LP)计算求解各受评单位的相对效率(relative efficiency),一般理论上来说, LP问题的求解是简单的,然而当问题中的资料量相当大的时候,计算求解的负荷和计算时间将非常可观。本论文将提出一个演算法使得大规模DEA问题的求解效率能显着提升,特别的是,本研究提出之演算法能够将求解DEA问题时之个别LP问题的规模控制在一定范围内,例如可要求每单一LP问题使用的资料量在300笔以内。因此单一LP问题规模将大幅减小(例如由10,000笔减至300笔)而使计算效率提升,同时也可做为以试用版 (trial version)或免费版软体(例如AMPL、GAMS)求解任何规模DEA问题的理论基础。 Data envelopment analysis (DEA) is a method, utilizing linear programming (LP), to compute relative efficiencies of all decision making units (DMUs). Solving LP problems is easy in theory. However, in practice, computational loading cannot be ignored for large-scale data. This thesis proposes an algorithm that significantly improves computational effort for solving large-scale DEA problems. Specifically, the proposed algorithm is able to control the size of individual LP problems, e.g. no more than 300 DMUs are used in every LP problem, for computing relative efficiency. As a result, computational efficiency is improved from LP problem size reduction (e.g. from 10,000 to 300 DMUs). This work can also be the theoretical foundation of using trial version or free software (e.g. AMPL and GAMS) to solve DEA problems in any scale. |
URI: | http://140.113.39.130/cdrfb3/record/nctu/#GT079933552 http://hdl.handle.net/11536/50120 |
显示于类别: | Thesis |