A continuous framework for open pit mine planning |
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Authors: | Felipe Alvarez Jorge Amaya Andreas Griewank Nikolai Strogies |
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Institution: | 1.Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (CNRS UMI 2807),Universidad de Chile,Santiago,Chili;2.DFG Research Center Matheon “Mathematics for Key Technologies”,Berlin,Germany;3.Humboldt Universit?t zu Berlin,Berlin,Germany |
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Abstract: | This paper proposes a new mathematical framework for the open pit mine planning problem, based on continuous functional analysis.
The main challenge for engineers is to determine a sequence of nested profiles maximizing the net present value of the mining
operation. The traditional models for this problem have been constructed by using binary decision variables, giving rise to
large-scale combinatorial and Mixed Integer Programming problems. Instead, we use a continuous approach which allows for a
refined imposition of slope constraints associated with geotechnical stability. The framework introduced here is posed in
a suitable functional space, essentially the real-valued functions that are Lipschitz continuous on a given two dimensional
bounded region. We derive existence results and investigate qualitative properties of the solutions. |
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