Hierarchical Benders decomposition for open-pit mine block sequencing

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Author
Vossen, Thomas W.M.
Wood, R. Kevin
Newman, Alexandra M.
Date
2016Metadata
Show full item recordAbstract
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.
Description
The article of record as published may be found at http://dx.doi.org/10.1287/opre.2016.1516
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
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