  The use of Lagrangian cuts proves effective in enhancing the lower bound of
the master problem within the execution of benders-type algorithms,
particularly in the context of two-stage stochastic programs. However, even the
process of generating a single Lagrangian cut is notably time-intensive. In
light of this challenge, we present a novel framework that integrates
Lagrangian cut generation with an adaptive partition-based approach, thereby
mitigating this time-related drawback to a considerable extent. Furthermore, we
also discuss the dominance relationship between the generated partition-based
Lagrangian cut and the Lagrangian cut for the original problem. To provide
empirical evidence of our approach's efficacy, we undertake an extensive
computational study encompassing instances involving even up to a thousand
scenarios. The results of this study conclusively demonstrate the superiority
and efficiency of the proposed methodology.
