IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2021i1p100-d713236.html
   My bibliography  Save this article

Stochastic Final Pit Limits: An Efficient Frontier Analysis under Geological Uncertainty in the Open-Pit Mining Industry

Author

Listed:
  • Enrique Jelvez

    (Advanced Mining Technology Center, Delphos Mine Planning Laboratory & Department of Mining Engineering, University of Chile, Santiago 8370451, Chile)

  • Nelson Morales

    (Civil, Geology and Mining Engineering Department, Polytechnique Montréal, Montreal, QC H3T 1J4, Canada)

  • Julian M. Ortiz

    (The Robert M. Buchan Department of Mining, Queen’s University, Kingston, ON K7L 3N6, Canada)

Abstract

In the context of planning the exploitation of an open-pit mine, the final pit limit problem consists of finding the volume to be extracted so that it maximizes the total profit of exploitation subject to overall slope angles to keep pit walls stable. To address this problem, the ore deposit is discretized as a block model, and efficient algorithms are used to find the optimal final pit. However, this methodology assumes a deterministic scenario, i.e., it does not consider that information, such as ore grades, is subject to several sources of uncertainty. This paper presents a model based on stochastic programming, seeking a balance between conflicting objectives: on the one hand, it maximizes the expected value of the open-pit mining business and simultaneously minimizes the risk of losses, measured as conditional value at risk, associated with the uncertainty in the estimation of the mineral content found in the deposit, which is characterized by a set of conditional simulations. This allows generating a set of optimal solutions in the expected return vs. risk space, forming the Pareto front or efficient frontier of final pit alternatives under geological uncertainty. In addition, some criteria are proposed that can be used by the decision maker of the mining company to choose which final pit best fits the return/risk trade off according to its objectives. This methodology was applied on a real case study, making a comparison with other proposals in the literature. The results show that our proposal better manages the relationship in controlling the risk of suffering economic losses without renouncing high expected profit.

Suggested Citation

  • Enrique Jelvez & Nelson Morales & Julian M. Ortiz, 2021. "Stochastic Final Pit Limits: An Efficient Frontier Analysis under Geological Uncertainty in the Open-Pit Mining Industry," Mathematics, MDPI, vol. 10(1), pages 1-16, December.
  • Handle: RePEc:gam:jmathe:v:10:y:2021:i:1:p:100-:d:713236
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/1/100/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/1/100/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bala G. Chandran & Dorit S. Hochbaum, 2009. "A Computational Study of the Pseudoflow and Push-Relabel Algorithms for the Maximum Flow Problem," Operations Research, INFORMS, vol. 57(2), pages 358-376, April.
    2. Dorit S. Hochbaum, 2008. "The Pseudoflow Algorithm: A New Algorithm for the Maximum-Flow Problem," Operations Research, INFORMS, vol. 56(4), pages 992-1009, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Enrique Jelvez & Julian Ortiz & Nelson Morales Varela & Hooman Askari-Nasab & Gonzalo Nelis, 2023. "A Multi-Stage Methodology for Long-Term Open-Pit Mine Production Planning under Ore Grade Uncertainty," Mathematics, MDPI, vol. 11(18), pages 1-19, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Renaud Chicoisne & Daniel Espinoza & Marcos Goycoolea & Eduardo Moreno & Enrique Rubio, 2012. "A New Algorithm for the Open-Pit Mine Production Scheduling Problem," Operations Research, INFORMS, vol. 60(3), pages 517-528, June.
    2. Li, Xiangyong & Aneja, Y.P., 2017. "Regenerator location problem: Polyhedral study and effective branch-and-cut algorithms," European Journal of Operational Research, Elsevier, vol. 257(1), pages 25-40.
    3. Amina Lamghari & Roussos Dimitrakopoulos & Jacques Ferland, 2015. "A hybrid method based on linear programming and variable neighborhood descent for scheduling production in open-pit mines," Journal of Global Optimization, Springer, vol. 63(3), pages 555-582, November.
    4. Lamas, Patricio & Goycoolea, Marcos & Pagnoncelli, Bernardo & Newman, Alexandra, 2024. "A target-time-windows technique for project scheduling under uncertainty," European Journal of Operational Research, Elsevier, vol. 314(2), pages 792-806.
    5. Armin Fügenschuh & Marzena Fügenschuh, 2008. "Integer linear programming models for topology optimization in sheet metal design," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(2), pages 313-331, October.
    6. Nancel-Penard, Pierre & Morales, Nelson & Cornillier, Fabien, 2022. "A recursive time aggregation-disaggregation heuristic for the multidimensional and multiperiod precedence-constrained knapsack problem: An application to the open-pit mine block sequencing problem," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1088-1099.
    7. Kwame Awuah-Offei & Sisi Que & Atta Ur Rehman, 2021. "Evaluating Mine Design Alternatives for Social Risks Using Discrete Choice Analysis," Sustainability, MDPI, vol. 13(16), pages 1-15, August.
    8. Das, Ranajit & Topal, Erkan & Mardaneh, Elham, 2023. "A review of open pit mine and waste dump schedule planning," Resources Policy, Elsevier, vol. 85(PA).
    9. Jélvez, Enrique & Morales, Nelson & Nancel-Penard, Pierre & Cornillier, Fabien, 2020. "A new hybrid heuristic algorithm for the Precedence Constrained Production Scheduling Problem: A mining application," Omega, Elsevier, vol. 94(C).
    10. Gonzalo Muñoz & Daniel Espinoza & Marcos Goycoolea & Eduardo Moreno & Maurice Queyranne & Orlando Rivera Letelier, 2018. "A study of the Bienstock–Zuckerberg algorithm: applications in mining and resource constrained project scheduling," Computational Optimization and Applications, Springer, vol. 69(2), pages 501-534, March.
    11. Whittle, D. & Brazil, M. & Grossman, P.A. & Rubinstein, J.H. & Thomas, D.A., 2018. "Combined optimisation of an open-pit mine outline and the transition depth to underground mining," European Journal of Operational Research, Elsevier, vol. 268(2), pages 624-634.
    12. Madziwa, Lawrence & Pillalamarry, Mallikarjun & Chatterjee, Snehamoy, 2023. "Integrating stochastic mine planning model with ARDL commodity price forecasting," Resources Policy, Elsevier, vol. 85(PB).
    13. Daniel Espinoza & Marcos Goycoolea & Eduardo Moreno & Alexandra Newman, 2013. "MineLib: a library of open pit mining problems," Annals of Operations Research, Springer, vol. 206(1), pages 93-114, July.
    14. Alipour, Hossein & Muñoz, Mario Andrés & Smith-Miles, Kate, 2023. "Enhanced instance space analysis for the maximum flow problem," European Journal of Operational Research, Elsevier, vol. 304(2), pages 411-428.
    15. Roberto Asín Achá & Dorit S. Hochbaum & Quico Spaen, 2020. "HNCcorr: combinatorial optimization for neuron identification," Annals of Operations Research, Springer, vol. 289(1), pages 5-32, June.
    16. Kiyomi Kawamoto & Eric Y. Yamashita, 2024. "Urbanization and social capital networks among regions for natural disaster resilience," Environment Systems and Decisions, Springer, vol. 44(3), pages 514-526, September.
    17. Lin, Jingsi & Asad, Mohammad Waqar Ali & Topal, Erkan & Chang, Ping & Huang, Jinxin & Lin, Wei, 2024. "A novel model for sustainable production scheduling of an open-pit mining complex considering waste encapsulation," Resources Policy, Elsevier, vol. 91(C).
    18. Xiangyong Li & Y. P. Aneja, 2020. "A new branch-and-cut approach for the generalized regenerator location problem," Annals of Operations Research, Springer, vol. 295(1), pages 229-255, December.
    19. Baumann, P. & Hochbaum, D.S. & Yang, Y.T., 2019. "A comparative study of the leading machine learning techniques and two new optimization algorithms," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1041-1057.
    20. Al-Takrouri, Saleh & Savkin, Andrey V., 2013. "A decentralized flow redistribution algorithm for avoiding cascaded failures in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 6135-6145.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2021:i:1:p:100-:d:713236. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.