8
box plots and measured by the similar relative standard
deviations. Note that the NPV represents the LOM dis-
counted operating cash flows—if a $750M capital cost was
subtracted from all cases, the NPV differences vs the base
case would change from –15%/–10%/–5%/0%/+9% to
–29%/–18%/–10%/0%/+18%.
The mining sensitivity cases (Figure 7, second group
of 3 bars) show that more value is at risk in Case C if the
maximum vertical advance is slowed from 8 to 6 benches/
yr vs reducing the maximum mining rate from 10 to 8 Mt/
yr. The mean NPV impact of slower vertical advance would
be greater than the orebody uncertainty impact of moving
from mean NPV to 25th percentile NPV.
Input models and stochastic vs deterministic optimiza-
tion had little impact on NPV when stochastic evaluation is
used to consistently evaluate the resulting mine plans against
the same conditional simulations (Figure 7, third group of
six bars). For Case C, mine plans were virtually identical
and mainly constrained by vertical advance whether the
plans were created with deterministic optimization from
OK or IK model inputs or created from stochastic optimi-
zation with CS inputs. For Case B, deterministic optimiza-
tion with the OK inputs yielded a slightly lower NPV when
evaluated against the CS models, because the OK model
had less selectivity and thus encouraged a slower mining
rate when no stockpiling was allowed. Note that the NPV
reported from the lower selectivity OK model was signifi-
cantly lower than the IK or CS values, but when the OK
based mine plan is consistently evaluated against the same
CS realizations, the NPV is within 3% of the CS plan’s
NPV for Case B and within 0.5% of the CS plan’s NPV for
Case C (see Hoerger and Dagdelen, 2024 for details on OK
low planned NPV vs realized NPV).
Other Risks
Conditional simulations provide an effective means for
showing mine plan risks due to orebody uncertainty. The
case study used the same model to show potential impacts
(but not likelihood) due to not achieving planned vertical
advance or mining rates. However, many other risks may
not be easily modeled in terms of impact or likelihood.
Other risks which would have a significant impact to achiev-
ing a mine plan include geotechnical events, major weather
events, failure to achieve planned slope angles, systematic
biases between the geostatistical model vs reality and opti-
mistic plan assumptions [Bowater, 2022]. Unfortunately,
most of these other risks will not only add uncertainty to
plan outcomes, but also add an unfavorable bias.
CONCLUSIONS
This paper has shown how geostatistical conditional simu-
lations can be used for stochastic evaluation of mine plans
to show how orebody uncertainty can translate into grade
uncertainty and ultimately into production and cash flow
risk. The MILP model demonstrated for stochastic evalu-
ation of production schedules is closely related to MILP
models that can be used for deterministic optimization or
stochastic optimization of production schedules. However,
stochastic evaluation can be used to provide risk analysis
for existing mine plans regardless of how they were created.
Orebody uncertainty is a key driver of differences between
LOM NPV: Sensitivity Analysis
Mean NPV 1337 1425 1496 1578 1727 1578 1493 1536 1454 1496 1496 1570 1578 1578
%Diff vs C -15% -10% -5% 0% 9% 0% -5% -3% -8% -5% -5% 0% 0% 0%
Rel Std Dev 6.9% 7.1% 6.8% 6.7% 6.4% 6.7% 6.6% 6.7% 6.8% 6.8% 6.7% 6.6% 6.7% 6.7%
Strategy Sensitivity Mining Sensitivity Input model sensitivity
No stockpile case
Input model sensitivity
With stockpile case
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
A2: 0.02
const cut
A4: best
const cut
B: var
cut-off
C: B +
stkpil
D: C +
leach
.C: 8b/yr,
10Mt/yr
E: 6b/yr,
10Mt/yr
F: 8b/yr,
8Mt/yr
.G: B w/
ok input
B: ik
input
H: B w/
CS input
I: C w/
ok input
C: ik
input
J: C w/
CS input
Figure 7. NPV sensitivities to strategic options, mining shortfalls and different input models
NPV
($M)
box plots and measured by the similar relative standard
deviations. Note that the NPV represents the LOM dis-
counted operating cash flows—if a $750M capital cost was
subtracted from all cases, the NPV differences vs the base
case would change from –15%/–10%/–5%/0%/+9% to
–29%/–18%/–10%/0%/+18%.
The mining sensitivity cases (Figure 7, second group
of 3 bars) show that more value is at risk in Case C if the
maximum vertical advance is slowed from 8 to 6 benches/
yr vs reducing the maximum mining rate from 10 to 8 Mt/
yr. The mean NPV impact of slower vertical advance would
be greater than the orebody uncertainty impact of moving
from mean NPV to 25th percentile NPV.
Input models and stochastic vs deterministic optimiza-
tion had little impact on NPV when stochastic evaluation is
used to consistently evaluate the resulting mine plans against
the same conditional simulations (Figure 7, third group of
six bars). For Case C, mine plans were virtually identical
and mainly constrained by vertical advance whether the
plans were created with deterministic optimization from
OK or IK model inputs or created from stochastic optimi-
zation with CS inputs. For Case B, deterministic optimiza-
tion with the OK inputs yielded a slightly lower NPV when
evaluated against the CS models, because the OK model
had less selectivity and thus encouraged a slower mining
rate when no stockpiling was allowed. Note that the NPV
reported from the lower selectivity OK model was signifi-
cantly lower than the IK or CS values, but when the OK
based mine plan is consistently evaluated against the same
CS realizations, the NPV is within 3% of the CS plan’s
NPV for Case B and within 0.5% of the CS plan’s NPV for
Case C (see Hoerger and Dagdelen, 2024 for details on OK
low planned NPV vs realized NPV).
Other Risks
Conditional simulations provide an effective means for
showing mine plan risks due to orebody uncertainty. The
case study used the same model to show potential impacts
(but not likelihood) due to not achieving planned vertical
advance or mining rates. However, many other risks may
not be easily modeled in terms of impact or likelihood.
Other risks which would have a significant impact to achiev-
ing a mine plan include geotechnical events, major weather
events, failure to achieve planned slope angles, systematic
biases between the geostatistical model vs reality and opti-
mistic plan assumptions [Bowater, 2022]. Unfortunately,
most of these other risks will not only add uncertainty to
plan outcomes, but also add an unfavorable bias.
CONCLUSIONS
This paper has shown how geostatistical conditional simu-
lations can be used for stochastic evaluation of mine plans
to show how orebody uncertainty can translate into grade
uncertainty and ultimately into production and cash flow
risk. The MILP model demonstrated for stochastic evalu-
ation of production schedules is closely related to MILP
models that can be used for deterministic optimization or
stochastic optimization of production schedules. However,
stochastic evaluation can be used to provide risk analysis
for existing mine plans regardless of how they were created.
Orebody uncertainty is a key driver of differences between
LOM NPV: Sensitivity Analysis
Mean NPV 1337 1425 1496 1578 1727 1578 1493 1536 1454 1496 1496 1570 1578 1578
%Diff vs C -15% -10% -5% 0% 9% 0% -5% -3% -8% -5% -5% 0% 0% 0%
Rel Std Dev 6.9% 7.1% 6.8% 6.7% 6.4% 6.7% 6.6% 6.7% 6.8% 6.8% 6.7% 6.6% 6.7% 6.7%
Strategy Sensitivity Mining Sensitivity Input model sensitivity
No stockpile case
Input model sensitivity
With stockpile case
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
A2: 0.02
const cut
A4: best
const cut
B: var
cut-off
C: B +
stkpil
D: C +
leach
.C: 8b/yr,
10Mt/yr
E: 6b/yr,
10Mt/yr
F: 8b/yr,
8Mt/yr
.G: B w/
ok input
B: ik
input
H: B w/
CS input
I: C w/
ok input
C: ik
input
J: C w/
CS input
Figure 7. NPV sensitivities to strategic options, mining shortfalls and different input models
NPV
($M)