Integrating Short- and Long-term Mine Planning through Stochastic Optimization and

Future data-Application and Comparisons

Arja Jewbali

Newmont Mining corporation

Content

• Introduction

• Quantifying geological uncertainty

• Simulating short- scale orebody variability

• Stochastic production scheduling

• Production scheduling with simulated ‘future’ data

• Application at gold mine

• Comparisons and the value of the approach

• Conclusions

Risk in Mining: Australasian Examples

About 85% of discrepancies are due to poor understanding/modelling of the orebody being mined (After Baker and Giacomo, 1998)

1st year of production

• 60% of mines had an average rate of production LESS

THAN 70% of planned rate

• In the first year after start up, 70% of mills or

concentrators had an average rate of production LESS

THAN 70% of design capacity

• Key contributor to mining risk felt in all downstream

phases: Geology and reserves

Risk in Mining: A World Bank Survey (after Vallee, 2000)

Conventional vs Stochastic Approaches

Traditional view Unknown,

true answer

Single, often precise, wrong answer

Cashflows, cost/ounce, metal, reserves, …

Prob

abili

ty

1

Orebody Model

Single estimated model

Risk oriented view

Multiple probable models

Financial and Production Forecasts

Mine Design & Production Scheduling

Mining Process or Transfer Function

Accurate uncertainty

Prob

abili

ty

1 Accurate uncertainty quantification

Prob

abili

ty

1

Cashflows, cost/ounce, metal, reserves, …

Quantitative Models of Geological Uncertainty:

Monte Carlo or stochastic or geostatistical

conditional simulations

Quantification of Uncertainty about a Gold Deposit Monte Carlo Simulations

Lode 1502 Simulation #1

Future Drilling Data

Production sequencing with simulated grade control drilling

Mine Production Scheduling

• Short- and long- term mine production scheduling are based on exploration data

• Exploration data which does not capture the short-scale behavior of the orebody

• Grade control drilling: Available at time of mining not at the time of planning

• Integrate short scale behavior of the orebody at the time of planning with “future” grade control drilling?

• What is the value in doing so?

‘Future’ Grade Control Data

Exploration data Grade control data

Bench/Section of pit already mined out

Define relationship

Exploration data Simulate grade control data

Bench/Section of pit NOT yet mined out

Updating Existing Orebody Models with New Data

Simulated grade control drilling

Update

Stochastic Optimization & Production Scheduling

Using quantified geological uncertainty

Discounting geological risk while sequencing

A Stochastic Integer Programming Formulation

P N S P Rt t s t t s t ti i r r r r

t=1 i=1 s=1 t=1 r=1

Max E(NPV) X - ( Cu Yu + Cl Yl )∑∑ ∑∑∑

P= number of periods: 4-monthly periods for 4 years = 12 N= number of blocks: 5,626 blocks of 30 x 30 x 7.5 m S= number of simulated orebody models: 20 used R= number of targets: 2 grade and ore production

Binary variable tiE(NPV)

tiX

Expected NPV for block i mined in period t

trYu Excess amount produced compared to the target

s trCu Cost to penalize excess production

trYl Deficient amount produced compared to the target

s trCl Cost to penalize deficient production

Stochastic Integer Programming - SIP

……

Ore Grade 1 Metal …

Orebody Model 1 A production

schedule

Orebody Model 2

Orebody Model R

Ore Grade 2 Metal …

Ore Grade R Metal …

- TARGET [ ]

- TARGET [ ]

- TARGET [ ]

Deviation 1

Deviation 2

Deviation R

1 2 3

4

Managing Risk Between Periods

Met

al q

uant

ity

(100

0 K

g)

Ct=Ct-1 * RDFt-1 RDFt=1/(1+r)t

r – orebody risk discount rate

Deviations from production target

RDF – risk discounting factor

0

0.5

1

1.5

2

2.5

3

0 1 2 3 40

1 2 3

1

2

3

Periods

Application and Comparisons at a Gold Mine

• Exploration and grade control data • Variable at short distances: grade control at 5 x 7 m • Standard resource model (MIK) and “layer cake”

schedule • Reconciliations: Producing more than predicted

2000

2200

Y=99824

P1

P2 P3

P4

P5

Scheduling and Simulated ‘Future’ Data

Existing Stochastic LOM Scheduling Process

Proposed Multistage Approach with Short-scale Information

Simulation of orebody models from exploration data

Stochastic optimization and generation of production schedules

Updating of the existing orebody models with the future data

Stage 1

Quantification of risk and analysis of schedule Stage 4

Simulation of high density ‘future’ grade control information

Stochastic optimization and generation of production schedules

Stage 2

Stage 3

• Stage 1: ‘Future’ Grade Control Data

• Stage 2: Updating of Existing Simulated Models

Simulations Without and With Future Data

Y=99870

Y=99967

50200 50600

2240

2000

<0.8 0.8-1.2 1.2-1.6 1.6-2.2

>2.2

AU g/t

50600 50200

2240

2000 Y=99870

Y=99967

50200 50600

2240

2000

50600 50200

2240

2000

Based on exploration data

Based on simulated grade control data

Recoverable Reserves

Grade tonnage curve for the updated models

0.0

20.0

40.0

60.0

80.0

100.0

120.0

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8M

illio

ns

Cutoff grade g/t

Tonn

age

0

2

4

6

8

10

12

Gra

de g

/t

MIK modelSimulations

Grade tonnage curve

0.0

20.0

40.0

60.0

80.0

100.0

120.0

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8

Mill

ions

Cutoff grade g/t

Tonn

age

0.00

2.00

4.00

6.00

8.00

10.00

12.00

Gra

de g

/t

Based on exploration data

Based on simulated future grade control data

Stage 3: Stochastic Production Schedule Stage 4: Risk Analysis

Schedule (quarters) – Simulations based on Exploration Data

MIK model Average of the simulations Simulations

Mill target

Y=99824

P1

P2 Y=99824

Viability of the derived schedule given grade control information

Average of the simulations Simulations

Mill target

Schedule (quarters) – Simulations based on Simulated Future Grade Control

MIK model Average of the simulations Simulations

Mill target

Scheduling and Simulated Future Data

Mine’s Schedule

SIP & Simulated Orebody (exploration based)

SIP & Future data (grade control based)

Period (years) 2005

2007 2008 2009

1 2

4

Period (years)

2007 2008 2009

Period (years)

2006 2007

2009

1 2 3

5

Y=99824

P1

P2

P3

P4

2000

2200

Y=99824

P1

P2 P3

P4

P1

P2

P3

P5

P1

P2 P3

P5

Y=99824

P1

P2

Y=99824

P1

P2

Scheduling and Simulated Future Data

Simulations (exploration

data)

Updated simulations (future data)

Mines schedule

(future data)

Ore Tonnes (Mt)

14 18

10

Metal Tonnes (Mgrams)

52

55

38

Cumulative NPV (Million AUD)

552 560

330

Y=99824

P1

P2 P3

P4

Y=99824

P1

P2 P3

P4

P1

P2 P3

P5

P1

P2 P3

P5

Y=99824

P1

P2 Y=99824

P1

P2

Mines schedule

Exploration based schedule

Grade control based schedule

THANK YOU