This presentation discusses using stochastic modeling in mine planning to account for uncertainties in material type and grade. Traditional direct block scheduling is compared to a stochastic approach. A case study of a copper deposit with oxide and sulphide zones shows that considering geological uncertainties through 20 simulated models improved the net present value by 4% compared to the average case, reducing risk from 9% to 8% probability. Moving forward, more robust algorithms and multistage approaches could further improve mine planning under uncertainty.

1. IV SIMPOSIO INTERNACIONAL
DE PLANEAMIENTO DE MINADO
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TRADITIONAL VERSUS
STOCHASTIC MINE PLANNING
UNDER MATERIAL TYPE AND
GRADE UNCERTAINTIES
M. SC. ALEXANDRE MARINHO
MiningMath
DR. LUIS MARTINEZ TIPE
R&O Analytics

2. Outline
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Introduction
Modelling
Results
Conclusions
Current Work

3. Direct Block Scheduling
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Block values for each
possible destination
Image taken from Micromine
Multi-period scheduling with
blending and stockpiling
Image taken from Micromine

4. Stochastic Mine Planning with DBS
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Block values for each model
and possible destination
Multi-period scheduling
under uncertainty with
blending and stockpiling
1 3 5 7 9 11 13 15 17
Indicators with risk profiles

5. Case Study
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Sulphide zone Oxide zone
Slope angle, degrees 55 47
Density, t/m³ 2.7 2.2
• Copper deposit with oxide and sulphide zones
• Uncertainty represented by 20 simulated models
• Blocks with 40x40x20m³

6. Material Type Uncertainty
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7. Destination and Recovery
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Oxi
de
Bloc
k
Sulp
hide
Bloc
k
Mill
Sulphur Leach
Oxide Leach
Drops to 12%
Drops to 10%
Recovery 92%Recovery 81%

8. Economic Parameters
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5000.00
Long term copper price, $/t of copper 5000.00
Refining cost, $/t of copper 150.00
Mining cost, $/t mined 3.50
Stockpile rehandling cost, $/t rehandled 0.50
Mill processing cost, $/t processed 5.10
Sulphur leach processing cost, $/t processed 1.90
Oxide leach processing cost, $/t processed 0.50
Yearly discount rate, % 10

9. Production Rates - Average case
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Setup
Number
Capacities (Mt)
NPV (M$)Mill Sulphur
Leach
Oxide Leach
1 20 0 0 2467
2 0 20 20 3400
3 10 10 10 3085
4 8 8 16 3188
5 6 10 18 3264
6 4 12 20 3349
7 3 13 21 3376
8 2 14 22 3432
9 1 15 23 3422
10 0 16 24 3419
~0.4% less NPV
1Mt in the mill ~ 2Mt in the leach plants

10. Expected Productions
Stochastic
Case
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Average
Case

11. CU risk profiles
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12. Yearly risk profile for cumulative project NPV
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13. Conclusions – Stochastic Modelling
Ability to model uncertainties from different sources
simultaneously.
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14. Conclusions – Results
• The average case overestimated the project NPV in 37%.
• Considering geological uncertainties, the project NPV
improved by 4%, with the uncertainty reducing from 9 to 8%
with 80% probability.
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15. Conclusions – Moving Forward
• Application of a robust algorithm for direct block scheduling (pessimistic,
updateable).
• A multistage view could also be implemented (optimistic, assumes perfect
knowledge once the first block is extracted).
• So, what would be “the realistic view”? We should look deeper into
mining policies and procedures, not only mine plans.
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16. Contacts
Visit our website
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Direct Block Scheduling – LinkedIn Group
www.linkedin.com/groups/8552888
Thank you!
Alexandre Marinho Luis Martinez
alexandre.marinho@miningmath.com lmartinez@randoanalytics.com
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