Decision Rule Bounds for Two-Stage Stochastic Bilevel Programs

Abstract

We study two-stage stochastic bilevel programs where the leader chooses a binary here-and-now decision and the follower responds with a continuous wait-and-see decision. Using modern decision rule approximations, we construct lower bounds on an optimistic version and upper bounds on a pessimistic version of the leader's problem. Both bounding problems are equivalent to explicit mixed-integer linear programs that are amenable to efficient numerical solution. The method is illustrated through a facility location problem involving sellers and customers with conflicting preferences.