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Aggregation heuristic for the open-pit block scheduling problem

Author

Listed:
  • Jélvez, Enrique
  • Morales, Nelson
  • Nancel-Penard, Pierre
  • Peypouquet, Juan
  • Reyes, Patricio

Abstract

In order to establish a production plan, an open-pit mine is partitioned into a three-dimensional array of blocks. The order in which blocks are extracted and processed has a dramatic impact on the economic value of the exploitation. Since realistic models have millions of blocks and constraints, the combinatorial optimization problem of finding the extraction sequence that maximizes the profit is computationally intractable. In this work, we present a procedure, based on innovative aggregation and disaggregation heuristics, that allows us to get feasible and nearly optimal solutions. The method was tested on the public reference library MineLib and improved the best known results in the literature in 9 of the 11 instances of the library. Moreover, the overall procedure is very scalable, which makes it a promising tool for large size problems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:249:y:2016:i:3:p:1169-1177
    DOI: 10.1016/j.ejor.2015.10.044
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    References listed on IDEAS

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    1. W. Lambert & A. Newman, 2014. "Tailored Lagrangian Relaxation for the open pit block sequencing problem," Annals of Operations Research, Springer, vol. 222(1), pages 419-438, November.
    2. 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.
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    5. 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.
    6. Hansen, Pierre & Mladenovic, Nenad, 2001. "Variable neighborhood search: Principles and applications," European Journal of Operational Research, Elsevier, vol. 130(3), pages 449-467, May.
    7. Alexandra M. Newman & Enrique Rubio & Rodrigo Caro & Andrés Weintraub & Kelly Eurek, 2010. "A Review of Operations Research in Mine Planning," Interfaces, INFORMS, vol. 40(3), pages 222-245, June.
    8. 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. 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).
    2. Hooshmand, F. & Mirarabrazi, F. & MirHassani, S.A., 2020. "Efficient Benders decomposition for distance-based critical node detection problem," Omega, Elsevier, vol. 93(C).
    3. Samavati, Mehran & Essam, Daryl & Nehring, Micah & Sarker, Ruhul, 2017. "A local branching heuristic for the open pit mine production scheduling problem," European Journal of Operational Research, Elsevier, vol. 257(1), pages 261-271.
    4. Amin Mousavi & Erhan Kozan & Shi Qiang Liu, 2016. "Comparative analysis of three metaheuristics for short-term open pit block sequencing," Journal of Heuristics, Springer, vol. 22(3), pages 301-329, June.
    5. Samavati, Mehran & Essam, Daryl & Nehring, Micah & Sarker, Ruhul, 2018. "A new methodology for the open-pit mine production scheduling problem," Omega, Elsevier, vol. 81(C), pages 169-182.
    6. Zeng, Lanyan & Liu, Shi Qiang & Kozan, Erhan & Corry, Paul & Masoud, Mahmoud, 2021. "A comprehensive interdisciplinary review of mine supply chain management," Resources Policy, Elsevier, vol. 74(C).
    7. Armstrong, Margaret & Lagos, Tomas & Emery, Xavier & Homem-de-Mello, Tito & Lagos, Guido & Sauré, Denis, 2021. "Adaptive open-pit mining planning under geological uncertainty," Resources Policy, Elsevier, vol. 72(C).
    8. Samavati, Mehran & Essam, Daryl & Nehring, Micah & Sarker, Ruhul, 2017. "A methodology for the large-scale multi-period precedence-constrained knapsack problem: an application in the mining industry," International Journal of Production Economics, Elsevier, vol. 193(C), pages 12-20.
    9. 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.
    10. Moreno, Eduardo & Rezakhah, Mojtaba & Newman, Alexandra & Ferreira, Felipe, 2017. "Linear models for stockpiling in open-pit mine production scheduling problems," European Journal of Operational Research, Elsevier, vol. 260(1), pages 212-221.
    11. Cinna Seifi & Marco Schulze & Jürgen Zimmermann, 2021. "Solution procedures for block selection and sequencing in flat-bedded potash underground mines," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(2), pages 409-440, June.
    12. César Flores-Fonseca & Rodrigo Linfati & John Willmer Escobar, 2022. "Exact algorithms for production planning in mining considering the use of stockpiles and sequencing of power shovels in open-pit mines," Operational Research, Springer, vol. 22(3), pages 2529-2553, July.
    13. Zhang, Jian & Nault, Barrie R. & Dimitrakopoulos, Roussos G., 2019. "Optimizing a mineral value chain with market uncertainty using benders decomposition," European Journal of Operational Research, Elsevier, vol. 274(1), pages 227-239.

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