Theory and Applications of Stochastic Bilevel Mixed-Integer Programming

双层规划对两个自主且可能相互冲突的决策者（领导者和追随者）之间的等级关系进行建模。每个决策者控制着一组不同的变量，决策是按顺序做出的。首先，上级决策由领导做出，然后下级决策由下属做出。跟随者受到领导者决策的影响，而跟随者的决策反过来又影响领导者。传统的双层规划模型是确定的，尽管许多现实生活中的问题包含不确定的参数。随机规划可以用来对不确定条件下的优化问题进行建模。然而，该框架不能自然地扩展到双层程序，因为它涉及单个决策级别。本文的主要目的是采用一种新的方法，从模型、理论和方法三个方面对“双层随机规划”进行研究。因此，我们的方法结合并扩展了双层规划和随机规划的研究。

Bilevel programs model the hierarchical relationship between two autonomous and possibly conflicting decision makers: the leader and the follower. Each decision maker controls a distinct set of variables, and the decisions are made sequentially. First, the upper-level decisions are made by the leader, after which the lower-level decisions are made by the follower. The follower is affected by the decisions of the leader, while the follower's decisions in return affect the leader. Conventional bilevel programming models are deterministic, although many real life problems include uncertain parameters. Stochastic programming can be used to model optimization problems under uncertainty. However, that framework does not naturally extend to bilevel programs as it involves a single decision level. The main goal of the present work is to take a new approach and study "bilevel stochastic programs" in terms of modeling, theory and methodology. Our approach thus combines and expands the research on bilevel programming and stochastic programming.