Theory and Applications of Stochastic Bilevel Mixed-Integer Programming

双层规划模型的层次关系之间的两个自治和可能发生冲突的决策者：领导者和追随者。每个决策者控制一组不同的变量，决策是按顺序进行的。首先，上级决策由领导者做出，然后下级决策由追随者做出。追随者受到领导者决定的影响，而追随者的决定反过来影响领导者。传统的双层规划模型是确定性的，虽然许多真实的生活问题包括不确定的参数。随机规划可以用来模拟不确定性下的优化问题。然而，该框架并不自然地扩展到双层计划，因为它涉及一个单一的决策层。本文的主要目的是从建模、理论和方法等方面对“双层随机规划”进行新的研究。因此，我们的方法结合和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.