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Determination of optimum cut-off grade of an open-pit metalliferous deposit under various limiting conditions using a linearly advancing algorithm derived from dynamic programming

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  • Biswas, Pritam
  • Sinha, Rabindra Kumar
  • Sen, Phalguni
  • Rajpurohit, Sohan Singh

Abstract

In the process of planning an open-pit, the determination of optimum cut-off grade plays a vital role. The classical approach of Lane's algorithm yields infinitely many solutions when the metal price is very high and mining, milling and refining costs are low. This problem has been addressed through a new algorithm. This study deals with the optimization of cut-off grade of a real-life case study of an open-pit copper mine in India considering fixed annual production of mine, mill and refinery facilities. However, the optimization ignores uncertainty in input parameters. The optimization has been carried out with the objective of maximizing the discounted total profit in terms of Net Present Value (NPV). As the process of determination of optimum cut-off grade of the deposit is dependent on many parameters which can suitably be addressed using a linearly advancing algorithm derived from dynamic programming approach. Considering a precision of 0.01% in the grade interval, the optimum cut-off grades, the amount of metal produced per ton and the NPV have been evaluated. Accordingly, the optimum cut-off grade of the Malanjkhand copper deposit has been found to be 0.32% amounting to a maximum NPV of ₹ 12123 million. The calculation reveals that the life of mine is 37.5 years and the average mill head grade optimises to 1.12%. The results also reveal that the present value of net cash-flow increases in the initial years, reaches a maximum value at a certain mid-life time and then declines with the depletion of the reserve. The NPV finally reaches a zero value at the end of mine life corroborating the general trend as seen in other mining organisations.

Suggested Citation

  • Biswas, Pritam & Sinha, Rabindra Kumar & Sen, Phalguni & Rajpurohit, Sohan Singh, 2020. "Determination of optimum cut-off grade of an open-pit metalliferous deposit under various limiting conditions using a linearly advancing algorithm derived from dynamic programming," Resources Policy, Elsevier, vol. 66(C).
    • Handle: RePEc:eee:jrpoli:v:66:y:2020:i:c:s0301420719307883
    DOI: 10.1016/j.resourpol.2020.101594
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    References listed on IDEAS

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    1. Dehghani, Hesam & Bogdanovic, Dejan, 2018. "Copper price estimation using bat algorithm," Resources Policy, Elsevier, vol. 55(C), pages 55-61.
    2. Khan, Asif & Asad, Mohammad Waqar Ali, 2019. "A method for optimal cut-off grade policy in open pit mining operations under uncertain supply," Resources Policy, Elsevier, vol. 60(C), pages 178-184.
    3. Ahmadi, Mohammad Reza & Bazzazi, Abbas Aghajani, 2019. "Cutoff grades optimization in open pit mines using meta-heuristic algorithms," Resources Policy, Elsevier, vol. 60(C), pages 72-82.
    4. Ahmadi, Mohammad Reza & Shahabi, Reza Shakoor, 2018. "Cutoff grade optimization in open pit mines using genetic algorithm," Resources Policy, Elsevier, vol. 55(C), pages 184-191.
    5. Asad, Mohammad Waqar Ali & Dimitrakopoulos, Roussos, 2013. "A heuristic approach to stochastic cutoff grade optimization for open pit mining complexes with multiple processing streams," Resources Policy, Elsevier, vol. 38(4), pages 591-597.
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    1. Biswas, Pritam & Sinha, Rabindra Kumar & Sen, Phalguni, 2023. "A review of state-of-the-art techniques for the determination of the optimum cut-off grade of a metalliferous deposit with a bibliometric mapping in a surface mine planning context," Resources Policy, Elsevier, vol. 83(C).
    2. Khan, Asif & Asad, Mohammad Waqar Ali, 2021. "A mixed integer programming based cut-off grade model for open-pit mining of complex poly-metallic resources," Resources Policy, Elsevier, vol. 72(C).

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