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Math Meth Oper Res (2011) 73:2954 DOI 10.1007/s00186-010-0332-3
 

Summary: Math Meth Oper Res (2011) 73:29­54
DOI 10.1007/s00186-010-0332-3
ORIGINAL ARTICLE
A continuous framework for open pit mine planning
Felipe Alvarez · Jorge Amaya ·
Andreas Griewank · Nikolai Strogies
Received: 2 February 2010 / Accepted: 29 September 2010 / Published online: 17 October 2010
© Springer-Verlag 2010
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 con-
structed 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 geotechni-
cal 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.
Keywords Mine planning · Continuous optimization · Calculus of variations ·

  

Source: Alvarez, Felipe - Departamento de Ingeniería Matemática, Universidad de Chile

 

Collections: Mathematics; Engineering