Theory and Applications of Stochastic Bilevel Mixed-Integer Programming

点击翻译按钮获取中文摘要

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.