A cutting-plane approach for large-scale capacitated multi-period facility location using a specialized interior-point method

• 成果类型: Article
• 署名作者: Castro, Jordi; Nasini, Stefano; Saldanha-da-Gama, Francisco
• 署名单位: Universitat Politecnica de Catalunya; Centre National de la Recherche Scientifique (CNRS); IESEG School of Management; Universidade de Lisboa
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-016-1067-6
• 发表日期: 2017
• 页码: 411-444
• 关键词: accelerating benders decomposition; lagrangian decomposition; algorithm

摘要

We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization problems is exploited by the interior-point method, allowing the (either exact or inexact) efficient solution of large instances. The consequences of different modeling conditions and problem specifications on the computational performance are also investigated both theoretically and empirically, providing a deeper understanding of the significant factors influencing the overall efficiency of the cutting-plane method. The methodology proposed allowed the solution of instances of up to 200 potential locations, one million customers and three periods, resulting in mixed integer linear optimization problems of up to 600 binary and 600 millions of continuous variables. Those problems were solved by the specialized approach in less than one hour and a half, outperforming other state-of-the-art methods, which exhausted the (144 GB of) available memory in the largest instances.