带有限反馈下层的二层规划问题的部分合作模型

运筹学学报 ›› 2012, Vol. 16 ›› Issue (3): 84-92.

带有限反馈下层的二层规划问题的部分合作模型

刘兵兵^1,2, 万仲平¹

1. 武汉大学数学与统计学院
2. 安庆师范学院数学与计算科学学院

收稿日期:2010-12-17 修回日期:2012-05-10 出版日期:2012-09-15 发布日期:2012-09-18
通讯作者: 刘兵兵
基金资助:
基金项目: 国家自然科学基金(No. 71171150); 安徽省高校优秀青年人才基金项目(No. 2009SQRZ121)

A partial cooperation model for bilevel programming problems with finite reactions follower

LIU Bingbing^1,2, WAN Zhongping¹

1. School of Mathematics and Statistics, Wuhan University 2. School of Mathematics and Computing Science, Anqing Normal University

Received:2010-12-17 Revised:2012-05-10 Online:2012-09-15 Published:2012-09-18
Contact: LIU Bingbing

摘要/Abstract

摘要： 对下层最优反馈为离散有限多个的二层规划问题的部分合作模型进行探讨. 当下层的合作程度依赖于上层的决策变量时, 给出一个确定合作系数函数的一般方法, 进而得到一个新的部分合作模型. 在适当地假设下, 可保证所给的部分合作模型一定可以找到比悲观解要好的解, 并结合新的部分合作模型对原不适定问题进行分析, 得到了一些有益的结论. 最后以实际算例说明了所给部分合作模型的可行性.

关键词: 二层规划, 有限反馈, 部分合作模型, 合作系数, 乐观模型, 悲观模型

Abstract: Bilevel programming problem provide a framework to deal with decision processes involving two decision makers with a hierarchical structure. The leader at the upper level of the hierarchy and the follower at the lower level seek to optimize their individual objective functions and control their own set of decision variables. Bilevel programming problem involves two optimization problems where the constraint region of the upper level problem is implicitly determined by another optimization problem. Bilevel programming problem is frequently encountered with in the fields of economy, industry, transportation, military, and so on. In this paper, we investigate the partial cooperation model for the bilevel programming problem in which the optimal reactions of the lower level problem is discrete and finite. We develop a general method for ascertaining the cooperation ratio in the partial cooperation model when the cooperation degree of the follower depends on the decision variables of the leader. Furthermore, we develop a new partial cooperation model of which the optimal is better than of the pessimistic model under suitable conditions. Then we derive some meaningful results based the proposed partial cooperation model. Finally, we show that the proposed partial cooperation model is feasible by two numerical examples.

Key words: bilevel programming, finite reactions, partial cooperation model, cooperation ratio, optimistic model, pessimistic model

中图分类号:

90C05

刘兵兵,万仲平. 带有限反馈下层的二层规划问题的部分合作模型[J]. 运筹学学报, 2012, 16(3): 84-92.

LIU Bingbing, WAN Zhongping. A partial cooperation model for bilevel programming problems with finite reactions follower[J]. Operations Research Transactions, 2012, 16(3): 84-92.

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