求解大型資料包絡分析問題之建模語言軟體程式庫

Abstract

本研究開發一套以建模語言(modeling language)為基礎的開放原始碼(open source)軟體程式庫(package)用以求解大型資料包絡分析(data envelopment analysis, DEA)問題。資料包絡分析法是一種以線性規劃(linear programming, LP)衡量組織相對績效的工具，在實證應用上需使用各種計算軟體求解。我們開發的工具能讓使用者享有建模語言相對於其它工具所帶來的彈性和親和性，降低學習時間和技術門檻；特別的是不受問題規模限制，能節省求解的成本與時間。

Data envelopment analysis (DEA) determines the relative performance of an organization by comparing to its peers, and can consider multiple inputs/outputs simultaneously without prespecified weights. Implementing DEA requires formulating and solving many linear programs (LPs), and can becomes obstacles to empirical researchers from different application domains. This thesis develops a computational tool for DEA computation, it is based on an algebraic modeling languages for mathematical programming that is easy to learn and flexible for variant models and analyses. While taking the advantage of flexibility and powerful solvers from a modeling language, this package can solve larger-scale DEA problems without limitation on constraints and variables, and with better computational performance.