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A two-step mathematical programming framework for undercut horizon optimization in block caving mines

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  • Noriega, Roberto
  • Pourrahimian, Yashar
  • Ben-Awuah, Eugene

Abstract

The definition of caving economic limits is one of the initial steps in the planning and design of caving projects. This paper proposes a binary optimization framework to integrate the caving envelope and production schedule that maximizes the net present value of the project under technical constraints that model the caving operation mechanics. The constraints considered in the framework are mining capacities, draw rates, maximum and minimum column heights, horizontal and vertical precedences, undercut development rates and the maximum relative adjacent height of draw between columns. An early-start algorithm is used to reduce the number of decision variables and a sliding-time heuristic is applied to significantly reduce the computing time. The framework is implemented in a MATLAB environment with CPLEX as the optimization engine. A case study is presented for the section of a copper deposit, where different horizons were evaluated to select the optimal undercut level and define the caving envelope and initial production schedule. Results were obtained in under 20 min, which allows the method to be efficiently used to evaluate multiple scenarios.

Suggested Citation

  • Noriega, Roberto & Pourrahimian, Yashar & Ben-Awuah, Eugene, 2020. "A two-step mathematical programming framework for undercut horizon optimization in block caving mines," Resources Policy, Elsevier, vol. 65(C).
    • Handle: RePEc:eee:jrpoli:v:65:y:2020:i:c:s0301420719302909
    DOI: 10.1016/j.resourpol.2020.101586
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    References listed on IDEAS

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    1. Adrien Rimélé, M. & Dimitrakopoulos, Roussos & Gamache, Michel, 2018. "A stochastic optimization method with in-pit waste and tailings disposal for open pit life-of-mine production planning," Resources Policy, Elsevier, vol. 57(C), pages 112-121.
    2. Underwood, Robert & Tolwinski, Boleslaw, 1998. "A mathematical programming viewpoint for solving the ultimate pit problem," European Journal of Operational Research, Elsevier, vol. 107(1), pages 96-107, May.
    3. Lamghari, Amina & Dimitrakopoulos, Roussos, 2016. "Progressive hedging applied as a metaheuristic to schedule production in open-pit mines accounting for reserve uncertainty," European Journal of Operational Research, Elsevier, vol. 253(3), pages 843-855.
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    Cited by:

    1. Saavedra, Francisco & Morales, Nelson & Nelis, Gonzalo & Gómez, René, 2023. "A fast method to find smooth economic envelopes for block and panel caving mines," Resources Policy, Elsevier, vol. 83(C).

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