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Impacts of Grade Distribution and Economies of Scale on Cut-off Grade and Capacity Planning

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Abstract

Strategic mine planning centers on solving cut-off grade selection, capacity planning, and block sequencing. Even though significant knowledge has been accumulated on mine planning over the last decades, there is still potential to add value to mineral sourcing by addressing various aspects. To this end, this paper addresses two issues. The effects of (1) grade/metal distribution within a mineral deposit and (2) the economies of scale (EoS) are explored in cut-off grade selection and capacity planning. In doing so, the interdependency between cut-off grade selection and capacity planning is also considered. A case study is implemented on a metallic deposit whose grade distribution exhibits lognormal distribution to detect if grade/metal distribution influences cut-off grade selection. Also, based on the same ore tonnage and metal quantity, six different datasets are generated with different shape and scale factors. The research outcomes indicate that deposits with lower shape and scale factors of lognormal distribution are more sensitive to metal price and discount rate changes because slight cut-off grade variations significantly change net present value (NPV). While the NPV of the deposit with the largest shape factor is $3,208,112,841 with a cut-off grade of 0.058 oz/tonne, the NPV of the deposit with the smallest shape factor is $93,617,240 with a cut-off grade of 0.027 oz/tonne. Furthermore, the case study is directed to investigate the effect of EoS on a project’s value, with a specific emphasis on the ratio of variable cost to total cost (capacity factor). Two different regression analyses are conducted based on the proposed model for optimal capacity planning and cut-off grade selection, respectively. In the first one, the absolute standardized beta values for EoS of mining and mineral processing costs are 0.736 and 0.425, meaning that capacity planning is highly sensitive to the EoS of mining and mineral processing operating costs. Meanwhile, the absolute standardized beta value for grade variability is 0.054 which means that the effects of grade variability and metal distribution are almost negligible for capacity planning. However, EoS is the most critical variable for capacity optimization. In the second regression analysis, the standardized beta values for grade variability and EoS of mineral processing operating cost are 0.573 and 0.522, so their effects on cut-off grade selection become vital.

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Funding

This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) (Fund number: 236482—NSERC RGPIN-2019–04763). The authors are grateful for this support.

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  1. Department of Mining and Materials Engineering, McGill University, 3450 Rue University, Montreal, QC, H3A 0E8, Canada

    Mehmet Balci & Mustafa Kumral

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Correspondence to Mustafa Kumral.

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Article Highlights

• Cut-off grade selection and capacity planning are essential for strategic mine planning.

• This paper aims to demonstrate the impacts of grade/metal distribution within a mineral deposit and the economies of scale on cut-off grade selection and capacity planning.

• Lognormal distribution parameters and capacity factors are crucial to quantify grade/metal variability and the economies of scale, respectively.

• While the impact of the economies of scale is evident in both cut-off grade selection and capacity planning, grade/metal distribution only affects cut-off grade selection.

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Balci, M., Kumral, M. Impacts of Grade Distribution and Economies of Scale on Cut-off Grade and Capacity Planning. Mining, Metallurgy & Exploration (2024). https://doi.org/10.1007/s42461-024-00982-8

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