  We propose to generate Lagrangian cut for two-stage stochastic integer
program by batch, in contrast to the existing methods which solve each
Lagrangian subproblem at every iteration. We establish two convergence
properties of the proposed algorithm. Then we demonstrate that the improvement
in the lower bound achieved by incorporating the Lagrangian cut adheres to the
`triangle inequality', thereby showcasing the superiority of our proposed
method over existing approaches. Moreover, we suggest acquiring Lagrangian cuts
for unresolved scenarios by averaging the coefficients of the acquired
Lagrangian cuts, ensuring the quality of this cut with a certain probability.
Computational study demonstrates that our proposed algorithm can significantly
improve the lower bound of the linear relaxation of the Bender master problem
more quickly with much fewer Lagrangian cuts.
