下层存在多追随者的分层次线性诱导决策问题及算法

本文讨论上层决策给定的条件下，下层存在多追随者的多目标分层次诱 导决策问题．在线性情况下，此类问题的最优解可在有界多面体区域的某个端点实 现；应用罚函数理论，原决策问题转换为一个在有界多面体区域求连续凸函数最大值 的最优化问题．建议采用的计算方法较为简单，容易实现，而且能够保证求出问题的 全局最优解．

A Multi-Follower Linear Hierarchical Decision Making Problem and Its Solution Method

This paper deals with a two-level decision making problem with the presence of multiple followers. In linear case, the optimal solution to this tape of problem is achievable at one of the vertices of the bounded polyhedral region of the feasible decisions. Using penalty function, the two-level problem is transformed to a special optimization problem where a continuous convex function is maximized within the bounded polyhedral region. The transformed problem can be solved efficiently using a cutting plane algorithm and the solution is a globally optimal one.