灰色多随从二层线性规划问题及其解法  

A Grey Linear Bilevel Programming Problem with Multiple Independent Followers and Its Algorithm

作　　者：刘兵兵[1] 郭亚君[2] 

机构地区：[1]安庆师范学院数学与计算科学学院,安徽安庆246133 [2]河北科技师范学院数学与信息科技学院,河北秦皇岛066004

出　　处：《吉林大学学报（理学版）》2011年第4期625-632,共8页Journal of Jilin University:Science Edition

基　　金：安徽省高校优秀青年人才项目基金(批准号:2009SQRZ121)

摘　　要：针对多随从二层线性规划问题,结合灰色特征,提出了灰色独立多随从二层线性规划问题.建立了该问题的数学模型,并证明了漂移型灰色独立多随从二层线性规划问题等价于漂移型灰色二层线性规划问题.对于漂移型灰色独立多随从二层线性规划问题,基于单纯形法设计了一种求解算法.数值算例表明该算法是可行有效的.Based on the linear bilevel programming problem with multiple independent followers and the characteristic of grey system,a grey linear bilevel programming problem with multiple independent followers（GLBMIF） was put forward,and its model was given.We showed that the drifting grey linear bilevel programming problem with multiple independent followers（GLBMIF（θ）） is equivalent to the drifting grey linear bilevel programming problem.An algorithm based on simplex method was developed to solve the GLBMIF（θ）.A numerical example shows that the proposed algorithm is feasible and effective.

关 键 词：二层线性规划 灰色理论 独立多随从 单纯形方法 

分 类 号：O221.1[理学—运筹学与控制论] N941.5[理学—数学]