Hierarchical Benders Decomposition for Open-Pit Mine Block Sequencing

• 成果类型: Article
• 署名作者: Vossen, Thomas W. M.; Wood, R. Kevin; Newman, Alexandra M.
• 署名单位: University of Colorado System; University of Colorado Boulder; United States Department of Defense; United States Navy; Naval Postgraduate School; Colorado School of Mines
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2016.1516
• 发表日期: 2016
• 页码: 771-793
• 关键词: branch-and-price; nested decomposition; programming model; algorithm; implementations

摘要

The open-pit mine block sequencing problem (OPBS) models a deposit of ore and surrounding material near the Earth's surface as a three-dimensional grid of blocks. A solution in discretized time identifies a profit-maximizing extraction (mining) schedule for the blocks. Our model variant, a mixed-integer program (MIP), presumes a predetermined destination for each extracted block, namely, processing plant or waste dump. The MIP incorporates standard constructs but also adds not-so-standard lower bounds on resource consumption in each time period and allows fractional block extraction in a novel fashion while still enforcing pit-wall slope restrictions. A new extension of nested Benders decomposition, hierarchical Benders decomposition (HBD), solves the MIP's linear-programming relaxation. HBD exploits time-aggregated variables and can recursively decompose a model into a master problem and two subproblems rather than the usual single subproblem. A specialized branch-and-bound heuristic then produces high-quality, mixed-integer solutions. Medium-sized problems (e.g., 25,000 blocks and 20 time periods) solve to near optimality in minutes. To the best of our knowledge, these computational results are the best known for instances of OPBS that enforce lower bounds on resource consumption.