  We investigate new methods for generating Lagrangian cuts to solve two-stage
stochastic integer programs. Lagrangian cuts can be added to a Benders
reformulation, and are derived from solving single scenario integer programming
subproblems identical to those used in the nonanticipative Lagrangian dual of a
stochastic integer program. While Lagrangian cuts have the potential to
significantly strengthen the Benders relaxation, generating Lagrangian cuts can
be computationally demanding. We investigate new techniques for generating
Lagrangian cuts with the goal of obtaining methods that provide significant
improvements to the Benders relaxation quickly. Computational results
demonstrate that our proposed method improves the Benders relaxation
significantly faster than previous methods for generating Lagrangian cuts and,
when used within a branch-and-cut algorithm, significantly reduces the size of
the search tree for three classes of test problems.
