Partial Benders Decomposition: General Methodology and Application to Stochastic Network Design
提出部分Benders分解方法，通过在主问题中纳入场景子问题的显式信息，克服传统Benders分解主问题松弛过弱的缺陷，应用于随机多商品网络设计问题，显著提升计算效率、解质量和稳定性。
Benders decomposition is a broadly used exact solution method for stochastic programs, which has been increasingly applied to solve transportation and logistics planning problems under uncertainty. However, this strategy comes with important drawbacks, such as a weak master problem following the relaxation step that confines the dual cuts to the scenario subproblems. In this paper, we propose a partial Benders decomposition methodology, based on the idea of including explicit information from the scenario subproblems in the master. To investigate the benefits of this methodology, we apply it to solve a general class of two-stage stochastic multicommodity network design models. Specifically, we solve the challenging variant of the model where both the demands and the arc capacities are stochastic. Through an extensive experimental campaign, we clearly show that the proposed methodology yields significant benefits in computational efficiency, solution quality, and stability of the solution process.