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Implementing a parametric maximum flow algorithm for optimal open pit mine design under uncertain supply and demand

Author

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  • M W A Asad

    (COSMO Stochastic Mine Planning Laboratory, McGill University, Canada)

  • R Dimitrakopoulos

    (COSMO Stochastic Mine Planning Laboratory, McGill University, Canada)

Abstract

Conventional open pit mine optimization models for designing mining phases and ultimate pit limit do not consider expected variations and uncertainty in metal content available in a mineral deposit (supply) and commodity prices (market demand). Unlike the conventional approach, a stochastic framework relies on multiple realizations of the input data so as to account for uncertainty in metal content and financial parameters, reflecting potential supply and demand. This paper presents a new method that jointly considers uncertainty in metal content and commodity prices, and incorporates time-dependent discounted values of mining blocks when designing optimal production phases and ultimate pit limit, while honouring production capacity constraints. The structure of a graph representing the stochastic framework is proposed, and it is solved with a parametric maximum flow algorithm. Lagragnian relaxation and the subgradient method are integrated in the proposed approach to facilitate producing practical designs. An application at a copper deposit in Canada demonstrates the practical aspects of the approach and quality of solutions over conventional methods, as well as the effectiveness of the proposed stochastic approach in solving mine planning and design problems.

Suggested Citation

  • M W A Asad & R Dimitrakopoulos, 2013. "Implementing a parametric maximum flow algorithm for optimal open pit mine design under uncertain supply and demand," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(2), pages 185-197, February.
    • Handle: RePEc:pal:jorsoc:v:64:y:2013:i:2:p:185-197
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    Citations

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    Cited by:

    1. Rimélé, Adrien & Dimitrakopoulos, Roussos & Gamache, Michel, 2020. "A dynamic stochastic programming approach for open-pit mine planning with geological and commodity price uncertainty," Resources Policy, Elsevier, vol. 65(C).
    2. Madziwa, Lawrence & Pillalamarry, Mallikarjun & Chatterjee, Snehamoy, 2023. "Integrating stochastic mine planning model with ARDL commodity price forecasting," Resources Policy, Elsevier, vol. 85(PB).
    3. Madziwa, Lawrence & Pillalamarry, Mallikarjun & Chatterjee, Snehamoy, 2023. "Integrating flexibility in open pit mine planning to survive commodity price decline," Resources Policy, Elsevier, vol. 81(C).
    4. Kizilkale, Arman C. & Dimitrakopoulos, Roussos, 2014. "Optimizing mining rates under financial uncertainty in global mining complexes," International Journal of Production Economics, Elsevier, vol. 158(C), pages 359-365.
    5. Paithankar, Amol & Chatterjee, Snehamoy & Goodfellow, Ryan & Asad, Mohammad Waqar Ali, 2020. "Simultaneous stochastic optimization of production sequence and dynamic cut-off grades in an open pit mining operation," Resources Policy, Elsevier, vol. 66(C).
    6. Madziwa, Lawrence & Pillalamarry, Mallikarjun & Chatterjee, Snehamoy, 2022. "Gold price forecasting using multivariate stochastic model," Resources Policy, Elsevier, vol. 76(C).
    7. Yasrebi, Amir Bijan & Hezarkhani, Ardeshir & Afzal, Peyman, 2017. "Application of Present Value-Volume (PV-V) and NPV-Cumulative Total Ore (NPV-CTO) fractal modelling for mining strategy selection," Resources Policy, Elsevier, vol. 53(C), pages 384-393.
    8. 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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