Integrating Benders Decomposition and Pure Cutting Plane Method for Solving Stochastic Integer Program

• Main Authors: Rao, Cheng-Yu, 饒承毓
• Other Authors: Chen, Sheng-I
• Format: Others
• Language: en_US
• Published: 2019
• Online Access: http://ndltd.ncl.edu.tw/handle/3sffyc

碩士 === 國立交通大學 === 工業工程與管理系所 === 107 === Benders decomposition is a commonly-used approach for solving large-scale mathematical programming problem. The application in stochastic programming is known as L-shaped method proposed for solving two-stage stochastic programs by taking advantage of its specific structure. The algorithm utilizes the parametric lower bound of second-stage objective value to obtain the optimal solution iteratively. However, the approach fails to generate the lower bound for the integer recourse problem and it may not converge to optimal due to the relaxation solution provides a week lower bound. This study focuses on a general case of two-stage stochastic programs, in which decision variables in both stages are integers. We integrate the L-shaped method and Gomory cutting plane to obtain an approximate solution. A finite cutting plane method is posted to the second-stage problem to strengthen the lower bound for the recourse cost function. The result demonstrates that the proposed method is capable to obtain a high quality solution for problem instances whose extensive forms are unsolvable by merely using the conventional branch-and-cut method. We perform a computational analysis and suggest the best cutting plane strategy used in the proposed algorithm.