2023/12/27 by Xiaoyu Luo, Mingming Xu, Luo, Xiaoyu +3
Business, Management and Accounting · Computer Science · Decision Sciences · #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Search Problems #Risk and Portfolio Optimization #Supply Chain and Inventory Management
paper · pdf · doi:10.48550/arxiv.2312.16445
openalex publication_date 2023/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.