  Bilevel optimization formulates hierarchical decision-making processes that
arise in many real-world applications such as in pricing, network design, and
infrastructure defense planning. In this paper, we consider a class of bilevel
optimization problems where the upper-level problem features some integer
variables while the lower-level problem enjoys strong duality. We propose a
dedicated Benders decomposition method for solving this class of bilevel
problems, which decomposes the Benders subproblem into two more tractable,
sequentially solvable problems that can be interpreted as the upper and the
lower-level problems. We show that the Benders subproblem decomposition carries
over to an interesting extension of bilevel problems, which connects the
upper-level solution with the lower level dual solution, and discuss some
special cases of bilevel problems that allow sequence-independent subproblem
decomposition. Several novel schemes for generating numerically stable cuts,
finding a good incumbent solution, and accelerating the search tree are
discussed. A computational study demonstrates the computational benefits of the
proposed method over a state-of-the-art bilevel-tailored branch-and-cut method,
a commercial solver, and the standard Benders method on standard test cases and
the motivating applications in sequential energy markets.
