Friends, you may like to see the presentation on the above topic, starts with the examples showing conventional models of ore bodies being biased representations of reality – so why do we hope conventional mine planning optimizers should work well. Then the presentation moves on to stochastic optimization and our recent research outcomes and real applications in mining complexes and major improvements in strategic mine planning. Hope you will have a look and questions are most welcome. Roussos

1. Simultaneous Stochastic Optimization of
Mining Complexes and Mineral Value Chains
Roussos Dimitrakopoulos
New digital technologies for the
smart(er) management of technical risk
COSMO Stochastic Mine Planning Laboratory - http://cosmo.mcgill.ca/
Technical Conference, April 4-7, 2017

2. Content
2
• Introduction
• Modelling mining complexes with risk management
• Stochastic optimization and formulations (concepts)
• Applications
• Comparisons to reality
• Conclusions

3. Production Forecast
1 5 10Year
Estimated Orebody Model Deterministic Design
Is this design the
optimal / ‘best’?
Can a single estimated
model represent a mineral
deposit?
(Grade variability,
uncertainty)
Are we able to meet
expected forecasts?
Orebody Modelling
Mine Design &
Production Scheduling
Financial &
Production Forecasts
3
Introduction – Deterministic workflow

4. Periods (years)
Million$
Production Forecast
1 5 10Year
Estimated Orebody Model Deterministic Design
Is this design the
optimal / ‘best’?
Can a single estimated
model represent a mineral
deposit?
(Grade variability,
uncertainty)
Are we able to meet
expected forecasts?
Will production forecasts on ore,
metal, FCF … be reached?
Are we really maximizing NPV?
What is the risk of deviating from
the LOM forecasts?
Orebody Modelling
Mine Design &
Production Scheduling
Financial &
Production Forecasts
4
Introduction – Deterministic workflow

5. Periods (years)
Million$
Production Forecast
1 5 10Year
Estimated Orebody Model Deterministic Design
Is this design the
optimal / ‘best’?
Can a single estimated
model represent a mineral
deposit?
(Grade variability,
uncertainty)
Are we able to meet
expected forecasts?
Will production forecasts on ore,
metal, FCF … be reached?
Are we really maximizing NPV?
What is the risk of deviating from
the LOM forecasts?
Accounting for uncertainty (and variability)
• A group of simulated orebody models can describe the variability and
uncertainty in a mineral deposit, which can be incorporated through new
stochastic optimization of mine designs and production schedules.
• Stochastic optimizers use a group of simulated orebody realizations and
capture/capitalize on spatial grade variability and uncertainty to manage
uncertainty and INCREASE value.
Orebody Modelling
Mine Design &
Production Scheduling
Financial &
Production Forecasts
5
Introduction – Deterministic workflow

6. Introduction - Estimation vs Simulation
• Estimated Orebody Model
Model characteristics:
o Large number of blocks
o Multiple domains
o 20 simulations: 557 million nodes
27 million mining blocks
Quantifying Uncertainty
3 simulated scenarios of the same
section (SMU grade)
A mature, well
drilled and
understood
gold deposit
• Simulated Orebody Models. This is a
Monte Carlo simulation …

7. 7
2
4
6
8
10
12
0
5
10
15
20
25
30
35
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Grade(g/t)
OreTonnage(Mt*10)
Cutoff grade (g/t)
Grade-tonnage Curves – Gold Deposit
The representation of a mineral deposit and related attributes –
estimated vs simulated - MATTERS … see next slide…
Traditional Orebody Models - Limits & Shortcomings
Simulated grades
Estimated ( - - -, - - - ) vs simulated models ( , ) as inputs to …
SMU Size Blocks

8. Prob.
5
10
15
20
25
0 5 10 15 20 25 30 35 40 45 50
Pit Shells
NPVA$*106
(i=8%)
Simulated
Realizations – Risk Analysis
Forecast from
Estimated Deposit
Most probable NPV is A$16.5M, 25 % less
than the conventional (deterministic)
estimate
0
A recall:
The expected project NPV has only 2-4% probability to
be realized
Introduction - Estimation vs Simulation does it Matter?
Why this? As per the previous grade-tonnage graph, estimation
misrepresents volumes of different grade ranges … and more …

9. Introduction - Cross Disciplinary Learning ?
Other fields of Engineering: Industry practice in
Petroleum Reservoir Engineering has moved away from
estimation models since the late 1980’s (stemming from
the Stanford University related research - Prof. A. Journel)
Oil recovery
forecasting
(EOR) –
Production
forecasts:
Examples
Forecasts come
from multiphase
flow simulation
Estimation does no longer exists in reservoir forecasting
Average in ≠ Average out …. P90 in ≠ P90 out ……
A Chevron
example-1990
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1
HB
Injected Pore Volume
NormalizedOilRecovery
Estimated
reservoir
properties
Simulated
reservoir
properties
Intevep 1992

10. Simulated Orebody Models
Sim. 1
s=1
Sim. 2
s=2
Sim. S
s=S 1 5 10Year
Stochastic Design & Production Schedule
10
Probabilistic Reporting
A set of simulations describe
geological uncertainty and
grade variability
A “single” mine design and
production schedule
accounting for and managing
uncertainty
A better NPV is always
obtained through the use of
stochastic mine planning in
comparison with conventional
methods
……
Stochastic
Orebody Modelling
Stochastic Mine Design &
Production Scheduling
Financial & Production
Forecasts
Introduction – Stochastic workflow

11. Simulated Orebody Models
Sim. 1
s=1
Sim. 2
s=2
Sim. S
s=S 1 5 10Year
Stochastic Design & Production Schedule
11
Probabilistic Reporting
A set of simulations describe
geological uncertainty and
grade variability
A “single” mine design and
production schedule
accounting for and managing
uncertainty
A better NPV is always
obtained through the use of
stochastic mine planning in
comparison with conventional
methods
……
If we can optimize mine designs with the established deterministic
tools, we can also develop and optimize with stochastic optimizers:
Stochastic Mine Planning
1. Lower risk in meeting financial and production forecasts.
2. Higher value for less risk.
3. Larger pit limits.
4. More metal.
Stochastic
Orebody Modelling
Stochastic Mine Design &
Production Scheduling
Financial & Production
Forecasts
Introduction – Stochastic workflow

12. Approaches to Uncertainty
Using estimated (expected value) models as inputs to
an optimizer will give somehow misleading results
• A known probability property: 𝐸 𝑓 𝑥 ≠ 𝑓 𝐸 𝑥
• This becomes even more significant in the context of a mining
complex with compound non-linearities
• Any framework that considers uncertainty is better than one
that ignores it
• An example follows

13. Approaches to Uncertainty
• An Example:
Calculating the economic value of a block using a
marginal cut-off grade

14. Deterministic Approach to Uncertainty
Copper price: $4410/t ($2/lb Cu)
Recovery: 90%
Processing cost: $6/t
Mining cost: $2/t
Block tonnage: 14465 t
$ 𝑉𝑎𝑙𝑢𝑒 =
$4410 ⋅ 0.9 ⋅
0.118
100
⋅ 14465 − $2 + $6 ⋅ 14465 = $ − 47974 if processed as ore
−$2 ⋅ 14465 = $ − 28930 if processed as waste
This block’s estimated grade lies below the marginal cut-off grade.
A deterministic optimizer will only mine this block as waste, with a
value of $-28930.
A block’s economic value, according to a
deterministic optimizer
Estimated
(expected) grade:
0.118% Cu

15. Stochastic Approach to Uncertainty
$ 𝑉𝑎𝑙𝑢𝑒 =
$4410 ⋅ 0.9 ⋅
𝑔
100
⋅ 14465 − $2 + $6 ⋅ 14465 if processed as ore
−$2 ⋅ 14465 if processed as waste
A stochastic optimizer may choose to mine this block with an expected value of
$21457. However, this is a risky block if we wish to feed a mill up to its capacity
Stochastic optimizers account for this risk, in addition to its potential value
Simulation #1
0% Cu
Simulation #2
0% Cu
Simulation #3
0% Cu
Simulation #4
0% Cu
Simulation #5
0.59% Cu
Average grade is
0.118% Cu
$-28930 $-28930 $-28930 $-28930 $223008
Expected Block Value:
𝟒 ⋅ $𝟐𝟖𝟗𝟑𝟎 + $𝟐𝟐𝟑𝟎𝟎𝟖
= $𝟐𝟏𝟒𝟓𝟕
A block’s economic value, according to a
stochastic optimizer

16. Some Questions:
• why should we still think that conventional mine
planning can provide “optimal” mine plans and
production schedules?
• why should we still think Life-of-Mine plans will
materialize?
• why should we still think we do the best
assessments, valuations or forecasts possible?
• do we really provide the best possible
decision support information?

17. The objective function now is …..
Maximize (s11x1
1+s21x2
1+….
s12x1
1+s22x2
1+….) … …
Subject to
s11x1
1+s21x2
1+…. = b1
s11x1
p+s21x2
p+…. = b1
s12x1
p+s22x2
p+…. = b1
s1rx1
p+s2rx2
p+…. = b1
Stochastic Integer Programming
Simulated model 1
Simulated model 2
Simulated model r
Period 1
Period p
s4
1
s1
1 s2
1 s3
1
s4
1
s1
1 s2
1 s3
1
s4
1
s1
1 s2
1 s3
1
s4
n
s1
n s2
n s3
n
Stochastic Mine Planning (start)

18. Economic Mining Block Value, when optimizing,
is driven by the economic values of the blocks
mined rather than the products produced.
$ VALUE for A MINING BLOCK
=
(METAL*RECOVERY*PRICE - ORE*COSTP)
- ROCK*COSTM
Stochastic Mine Planning (later on)
CHANGE CONTEXT and USE ONLY
geological attributes: Material Types, Grades ….

19. Simultaneous Stochastic
Optimization of
Mining Complexes
- Mineral Value Chains
for
Decision Support
Extending models
& capitalizing on synergies

20. Mine A
Mine B
Mine C
Mining Complexes & Mineral Value Chains
A mining complex may be seen as an integrated business starting from the
extraction of materials to a set of sellable products delivered to various customers
and/or spot market
Simultaneous optimization of the mining complex/value chain

21. Mine A
Mine B
Mine C
Mining Complexes & Mineral Value Chains
A mining complex may be seen as an integrated business starting from the
extraction of materials to a set of sellable products delivered to various customers
and/or spot market
Simultaneous optimization focuses on
the
$ value of products sold
rather than the
$ value of individual blocks

22. Simultaneous Optimization
*Tmax is the maximum plant feed tonnage
Objectives:
1. Maximize NPV
2. Satisfy SiO2:MgO blend
3. Minimize deviations from
plant capacity target
A
B
Example:
Nickel laterite mineral value chain - Blending policy optimization

23. Nickel Laterite Complex – Risk Analysis of Deterministic Design
Deterministic model
Simulation 1
…
Simulation N
…
Orebody simulations quantify:
• Volumetric uncertainty
• Multi-element uncertainty
Simultaneous Optimization

24. Nickel Laterite Complex – Deterministic Simultaneous Optimization
(36 days) (36 days)
Simultaneous Optimization

25. Nickel Laterite Complex – Risk Analysis of Deterministic Design
(36 days) (36 days)
Simultaneous Optimization

26. Simultaneous Stochastic Optimization
1 10 20 30Period
Ni Simulations Nickel Laterite Mine Production Schedule
SiO2 Simulations
MgO Simulations
…
…
…

27. 1.2
1.4
1.6
1.8
2.0
2.2
2.4
0 10 20 30 40
PlantFeedSiO2:MgO
Period
Plant Silica-to-Magnesia Ratio - Stochastic Solution
0%
20%
40%
60%
80%
100%
120%
140%
160%
180%
200%
0 10 20 30 40
DryTonnes(%Max.Capacity)
Period
Plant Feed Tonnage - Stochastic Solution
Nickel Laterite Complex - Simultaneous Stochastic Optimization
(36 days) (36 days)
Simultaneous Stochastic Optimization

28. Modelling Mining Complexes
with Uncertainty
New mathematical models

29. • Adaptable two-stage stochastic integer programming model
with CAPEXs:
max
1
𝕊
𝑡∈𝕋 𝑠∈𝕊 𝑎∈𝔸
𝑝 𝑎,𝑡 ⋅ 𝑣 𝑎,𝑡,𝑠 −
1
𝕊
𝑡∈𝕋 𝑠∈𝕊 𝑎∈𝔸
𝑐 𝑎,𝑡
+
⋅ 𝑢 𝑎,𝑡,𝑠 + 𝑐 𝑎,𝑡
−
⋅ 𝑙 𝑎,𝑡,𝑠
Attributes of interest
• Revenues from
metal sale
• Mining, processing &
stockpiling costs
Penalties for deviations from targets
• Mining, stockpile, processing
capacities
• Blending constraints
• Deleterious elements
Simultaneous Stochastic Optimization Formulation
−
𝑡∈𝕋 𝑘∈𝕂
𝑝 𝑘,𝑡 ⋅ 𝑤 𝑘,𝑡
Change of capacities depends on:
• Quantity purchased (𝑤 𝑘,𝑡′)
• Constraint increase (𝜅 𝑎,𝑘)
• Life of equipment (𝜆 𝑘)
• Lead time (𝜏 𝑘)CAPEX

30. • Adaptable two-stage stochastic integer programming model
with CAPEXs:
max
1
𝕊
𝑡∈𝕋 𝑠∈𝕊 𝑎∈𝔸
𝑝 𝑎,𝑡 ⋅ 𝑣 𝑎,𝑡,𝑠 −
1
𝕊
𝑡∈𝕋 𝑠∈𝕊 𝑎∈𝔸
𝑐 𝑎,𝑡
+
⋅ 𝑢 𝑎,𝑡,𝑠 + 𝑐 𝑎,𝑡
−
⋅ 𝑙 𝑎,𝑡,𝑠
Attributes of interest
• Revenues from
metal sale
• Mining, processing &
stockpiling costs
Penalties for deviations from targets
• Mining, stockpile, processing
capacities
• Blending constraints
• Deleterious elements
Simultaneous Stochastic Optimization Formulation
1. Risk reduction.
2. Risk deferral (geological risk discounting).
0%
20%
40%
60%
80%
100%
120%
140%
160%
0 10 20 30 40
Tonnage(%Capacity)
Period
Plant Feed Tonnage
1.3
1.4
1.5
1.6
1.7
1.8
1.9
0 10 20 30 40
SiO2:MgO
Period
Plant Silica-to-Magnesia Ratio

31. Modelling Mining Complexes with Risk Management
Sulfides - Mine 1
• Metal tonnes
• Total tonnes
Sulfides - Mine 2
• Metal tonnes
• Total tonnes
Processing Stream A
1. Total metal
2. Total tonnes
3. Head grade
4. Recovery
5. Throughput
6. Metal recovered
Customer #1 (Contract)
1. Metal
2. Metal value
Customer #2
(Exchange)
1. Metal
2. Metal value
Destination policies
Processing streams
Production schedule
𝜉𝑠
Decisions,
GEOMET…
All move here
No Economic
Values for
Mining Blocks
Used
Uncertainty can be
quantified at any
stage
Product Value

32. 32
• Computationally prohibitive optimization models,
IN THE PAST.
Mine 1
400,000 blocks
400 destination decisions/y
30 years
30 simulations
• 9,000 joint scenarios
• 18,750,000 scheduling decision variables
• 62,500 destination policy variables
• 540,000 processing stream variables
Mine 2
50,000 blocks
40 destination decisions/y
10 years
15 simulations
Mine 3
250,000 blocks
100 destination decisions/y
25 years
20 simulations
Stockpile
Mill 1 Mill 2 Waste
Algorithmic Optimization with Metaheuristics

33. The Twin Creeks
Gold Mining Complex, Nevada

34. Twin Creeks (TC) gold mining complex
34
Mega Pit Sulfide ore
Au SS CO3 Corg
Vista Pit Oxide ore
Au

35. Twin Creeks (TC) gold mining complex
35
Sage Autoclave
Juniper Mill
Waste Dumps
Oxide Leach
Gold
Sulphide piles
Oxide stockpiles
Vista Pit
Mega Pit
Extraction
Capacity
TRJV Mill 5 Mag
Other Sources
Blending is
crucial!

36. Base Case
Long-term Production Schedule
& Risk Analysis
Twin Creeks Gold Mining Complex, Nevada

37. Base Case long-term production schedule
37
• Long-term plan (from 2013) provided by TC
• Based on the estimated orebody model:
• Autoclave is used at full capacity during LOM
• Blending requirements are satisfied
• Evaluated with a set of stochastic orebody model
scenarios
• Will the forecasts from the Bass Case be met
in the presence of geological (supply) uncertainty

38. Base Case - Sources of supply uncertainty
38
Mega Pit
Sulphide Stockpiles
TRJV
Stochastic simulations
Historical data
Sage Autoclave
Mill 5 Mag
Other Sources
Vista Pit
Juniper Mill
Oxide Leach
Stochastic simulations

39. Simulations of stockpile SM-F2
39
0%
10%
20%
30%
40%
50%
60%
70%
80%
SM-F SH-F, SL-F or SS-F No F-Material
Percentageoftotalblocks(204)
Material type
In all simulations of stockpile SM-F2
less than 25% of blocks can be
classified as SM-F material

40. Base Case forecast P10 P50 P90
2013 2014 2015 2016 2017 2018
MillionOz
Year
Cumulative gold recovered – First 6 years
6%
Base Case - Gold recovery & Risk analysis

41. Base Case - DCF & Risk analysis
41
0%
10%
20%
30%
40%
50%
60%
2013 2014 2015 2016 2017 2018
CDCF(%)
Year
Cumulative DCF – First 6 years
9%
Base Case forecast P10 P50 P90

42. Base Case - Blending: SS and Acid
• Sulfide sulfur is not a major problem
• Carbonate materials demand excessive amounts
of acid and above legal limits
42
3.5
3.7
3.9
4.1
4.3
4.5
2013 2015 2017 2019 2021 2023 2025
%
Year
Sulfide sulfur
Estimation Scenarios Limits
0
20
40
60
80
100
2013 2015 2017 2019 2021 2023 2025
ThousandTons
Year
Acid consumption

43. Stochastic Production Schedule
Fitted to - Constrained
by the
Existing Pit Designs
Twin Creeks Gold Mining Complex, Nevada

44. 44
• Fit to the existing pit designs and accessibility
constraints; guarantee a minimum mining width for
accessibility of mining equipment and so on
• Reduce unnecessary displacement of equipment
by connecting cluster of blocks on a bench within
the same period
• Ensure slope and mining capacity constraints are
respected
• Blending, stockpiling and processing decisions are
re-optimized to satisfy requirements
Modified (practical) stochastic schedule

45. 45
Modified (practical) stochastic schedule
Raw Schedule
Select Pit
Select top
bench
Does it need
correction?
Connect cluster of blocks
guaranteeing mining width
and respecting mining rates
Re-optimize blending,
stockpiling and processing
decisions
Mark bench as
corrected
Is there a
lower bench?
Yes
No
Select higher bench
without correction
Is there
another pit?
No
Yes
Yes
Modified Schedule No

46. Modified stochastic schedule – Mega Pit
Full View
Modified
(practical)
Stochastic
plan
Base case
plan
Bench 3400 Bench 2460
Stochastic vs conventional schedules:
Substantially different parts of the pit are mined at the same year
Colours represent production years
46

47. 47
Modified stochastic schedule – Vista Pit
Full View
Modified
(practical)
Stochastic
plan
Base case
plan
Bench 0500 Bench 0360
Colours represent production years
Stochastic vs conventional schedules:
Substantially different parts of the pit are mined at the same year

48. Modified (practical) stochastic schedule
P50 Base Case (mine’s) P10 P50 P90

49. • Sulfide sulfur is well controlled
• Acid requirement is below the maximum
consumption allowed in the long-term plan
49
P50 Base Case (mine’s) Scenarios Limits
Modified (practical) stochastic schedule

50. 50
0%
20%
40%
60%
80%
100%
120%
2013 2015 2017 2019 2021 2023 2025
CDCF(%)
Year
Cumulative DCF - LOM
7%
P50 Base Case (mine’s) P10 P50 P90
Modified (practical) stochastic schedule

51. 51
0%
10%
20%
30%
40%
50%
60%
70%
2013 2014 2015 2016 2017 2018
CDCF(%)
Year
Cumulative DCF – First 6 years
9%
P50 Base Case (mine’s) P10 P50 P90
Modified (practical) stochastic schedule

52. • Stochastic optimization of the TC mining complex leads to
solutions with increased cashflows, more metal, grade risk
management and blending control
• The stochastic solution shows significant improvement
after been modified for equipment mobility and
accessibility to fit pre existing mine designs:
• Increases expected recovered gold by 7% (9% by
2018)
• Does not exceed the acid consumption at the autoclave
• Increases expected NPV by 7% (9% by 2018)
TC Mining Complex Comments
52

53. Please note:
The Base Case assessments do not account for the
costs of not meeting requirements, such as acid
consumption and others, thus differences in
comparisons and assessments are even larger …
Again: The stochastic schedule presented is fully
practical and in all its aspects, as required by the long
producing Mega and Vista pits.
• What if the stochastic LOM plan was done earlier in
the life of the TC mining complex?
TC Mining Complex Comments
53

54. What if the stochastic scheduler
finds a
different and larger ultimate pit?
Twin Creeks Gold Mining Complex, Nevada

55. Stochastic schedule - More ore, larger pit
55
1 extra year of ore to the
autoclave
0
1
2
3
4
5
2013 2015 2017 2019 2021 2023 2025 2027
MillionTons
Year
Sage autoclave processed tons
P50 Base Case Scenarios
Mega Pit – Bench 3940
Conventional Stochastic

56. Stochastic schedule - More ore, larger pit
56
0
1
2
3
4
5
6
7
8
2013 2015 2017 2019 2021 2023 2025 2027
MillionOz
Year
Cumulative gold recovered - LOM
12%
0
0.9
1.8
2.7
3.6
2013 2014 2015 2016 2017 2018
MillionOz
Year
Cumulative gold recovered – First 6 years
14%
P50 Base Case P10 P50 P90

57. If the technologies presented here were
applied at the early(er) parts of the life of
this mining complex,
even more more Au would be recovered
and even higher cashflows generated
Twin Creeks Gold Mining Complex, Nevada

58. Initial Geomet Applications at the
Escondida Mining Complex
58

59. Integrating Geometallurgy at Escondida
Escondida
Norte
Escondida
Leach pad
Bio-Leach
LC - 120Ktpd
LS - 130Ktpd
OGP1 - 160Ktpd
C1
C4
C3
Copper
Cathodes
Concentra
te to Port
C5
C2
Grades
- Cu
- Fe
- As
- Au
UNCERTAINTY
Geology
Geometallurgy
Hardness
- SPi
- BWI
Recovery
Throughput
Material Type
- Oxides
- Mixed
- Sulphides
Energy
consumption
Mining Mode

60. • Effect on the mines: Change to a denser blast net to increase crushability
• Effect on the processing stream:
• 5 primary compression crushers receive material from the two mines and send it
through conveyor belts to the plants.
• The smaller the input rock, the faster the material will pass through the
crusher  higher throughput
+ blast
holes
16bh 
18bh
Idea: increase blasting in hard rock zones to reduce
negative effects on the processing stream.
Mining Costs
Crusher’s
Capacity
Mining Operation Modes

61. Real-World Reconciliation Study
at a Copper Mine
and
Over 13 Years of Production

62. Copper Mining Complex: Reconciliation
Original data:
• Exploration drillholes
• Feasibility study (FS)
estimated model
• Original FS Whittle
LOM Schedule
Risk assessment and
management:
• Orebody simulations
created from original
exploration drillholes
• Stochastic LOM
schedule over same
years as FS.
Reconciliation with
operations:
• Blasthole model, 5m
spacing (gathered
between Y1 – Y13)
1 2
3
4
Estimated Model
(Deterministic)
Geological Interpretation
+
Kriging
Deterministic Mine Scheduling
Whittle
sim60
sim01
Simulated Models
(Categorical + Grade Simulations)
Risk Analysis
Probabilistic analysis for ROM,
Grade, Metal, NPV
sim60
sim01
Simulated Models
(Categorical + Grade Simulations) Stochastic Mine Scheduling
COSMO Simultaneous Stochastic Optimizer
1 2
3
4
Risk Analysis
Probabilistic analysis for ROM,
Grade, Metal, NPV
Blasthole Model
Conventional Framework
Stochastic Framework
Reconciliation from the feasibility study to 13 years of production

63. Reconciliation Study, Schedules vs Blast Holes
P50: Stochastic Schedule
BHs: Blast Holes
NCL: Conventional Schedule

64. Optimizing with
Joint Supply (metal)
and
Demand (commodity price)
Uncertainty

65. 1 2 34
Spot
Market
Contracts & Value Chain Optimizers
• Objective function
Maximize 𝑆𝑥𝑆′ 𝑡
1
1+𝛾 𝑡 𝑅𝑒𝑣𝑒𝑛𝑢𝑒𝑡,𝑠 − 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛𝐶𝑜𝑠𝑡𝑡,𝑠 −
Joint metal (S) and commodity price (S’) uncertainty

66. Contract Design: Numerical Results
66
Profit
Price
Expected with contract
Expected without contract
Worst-case (with contract)
Worst-case (without contract)
Contract demand = 0
Optimal contract price – for a given mining complex under
joint metal and commodity price uncertainty
of
the new contract
Range of new contract prices that add value
given supply and remand uncertainty

67. Conclusions
• Stochastic optimization in mine planning starts with
realistic representations of mineral deposits and
their related uncertainties.
• Simultaneous stochastic optimization coordinates
LOM production schedules, destination policies and
processing streams.
• Focus on value of products sold rather than
materials mined.
• Decentralized approach for evaluating processing
streams permits detailed modelling, including
geometallurgical responses.

68. Conclusions
• Nickel laterite example shows ability to create multi-
element blending policies while considering
uncertainty and variability of material properties.
• Gold mining complex demonstrates ability to
simultaneously optimize production with
less risk and higher NPV.
• Copper reconciliation study – Feasibility study vs
stochastic schedule compared to blast holes over 13
years demonstrates major improvements in
forecasting through stochastic mine planning.

69. Conclusions
• Escondida study shows new ongoing developments
in dealing with geomet in simultaneous stochastic
optimization of mining complexes.
• Joint supply and demand uncertainty adds new
dimensions to mine planning.
• The basis of and future needs for all presented is a
natural part of digital technologies and big data …
as it has always been.

70. Conclusions
• Ongoing research not presented includes:
• Extending further the framework for the simultaneous
stochastic optimization of mining complexes.
• Smarter self-learning decision support systems
integrating incoming sensor data, and link to both short
and long term production planning.
• Hyper-heuristic methods for solving much larger
mathematical optimization formulations faster.
• High-order stochastic simulation methods for mineral
deposits (focus on the spatial connectivity of extreme
values that drive production sequencing).

71. COSMO Industry Members
Thanks are in order to our
And
Funding Agencies