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A continuous framework for open pit mine planning

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  • Felipe Alvarez
  • Jorge Amaya
  • Andreas Griewank
  • Nikolai Strogies

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. Copyright Springer-Verlag 2011

Suggested Citation

  • Felipe Alvarez & Jorge Amaya & Andreas Griewank & Nikolai Strogies, 2011. "A continuous framework for open pit mine planning," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(1), pages 29-54, February.
    • Handle: RePEc:spr:mathme:v:73:y:2011:i:1:p:29-54
    DOI: 10.1007/s00186-010-0332-3
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    References listed on IDEAS

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    1. Dorit S. Hochbaum & Anna Chen, 2000. "Performance Analysis and Best Implementations of Old and New Algorithms for the Open-Pit Mining Problem," Operations Research, INFORMS, vol. 48(6), pages 894-914, December.
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    Cited by:

    1. EKELAND, Iver & QUEYRANNE, Maurice, 2014. "Optimal pits and optimal transportation," LIDAM Discussion Papers CORE 2014052, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Jélvez, Enrique & Morales, Nelson & Nancel-Penard, Pierre & Peypouquet, Juan & Reyes, Patricio, 2016. "Aggregation heuristic for the open-pit block scheduling problem," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1169-1177.

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