Uncertain Linear Programs: Extended Affinely Adjustable Robust Counterparts

作     者：Chen, Xin Zhang, Yuhan 

作者机构：Univ Illinois Dept Ind & Enterprise Syst Engn Urbana IL 61801 USA 

出 版 物：《OPERATIONS RESEARCH》 (运筹学)

年 卷 期：2009年第57卷第6期

页      面：1469-1482页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Science Foundation [CMMI-0653909] 

主　　题：programming: stochastic 

摘      要：In this paper, we introduce the extended affinely adjustable robust counterpart to modeling and solving multistage uncertain linear programs with fixed recourse. Our approach first reparameterizes the primitive uncertainties and then applies the affinely adjustable robust counterpart proposed in the literature, in which recourse decisions are restricted to be linear in terms of the primitive uncertainties. We propose a special case of the extended affinely adjustable robust counterpart-the splitting-based extended affinely adjustable robust counterpart-and illustrate both theoretically and computationally that the potential of the affinely adjustable robust counterpart method is well beyond the one presented in the literature. Similar to the affinely adjustable robust counterpart, our approach ends up with deterministic optimization formulations that are tractable and scalable to multistage problems.