Is There a Role for Lerchs-Grossman Optimization in Industrial

Minerals and Aggregates Mine Planning?

Kwame Awuah-OffeiAssociate Professor

Missouri University of Sc. & Tech

Pit Optimization

• Optimization problem that selects the blocks to be mined to maximize pit value while respecting all constraints

• Two most popular methods:– Floating cone

– Lerchs-Grossman (LG)

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Objective

1. To discuss the challenges and benefits of implementing LG optimization in industrial minerals and aggregates (IM&A)

2. Make recommendations for when it is useful

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Challenges in IM&A

• Lack of resources to engage in detailed strategic mine planning

• Long mine lives make it difficult to estimate costs and prices

• Difficulty estimating value as a function of grade

• Multiple products with complicated value relationships

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Benefits in Mine Planning

• Establish economic boundaries of pit (including surface/underground boundary)

• Determine optimal mining phases

• Evaluate effect of pricing policy on reserves

• To determine optimal location of facilities (waste dumps, plant etc.)

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Sand & Gravel Case Study

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Objectives of the Optimization

• To define economic horizons of the ultimate pit

• To determine pricing strategy

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Input Data

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Parameter Value

Average Sales Price $11.97/ton

Ore Cost $5.94/ton

Stripping Cost $1.70/yd3

Density of Material 0.06 tons/ft3

Slope 1.5:1

Grade 1-wash loss

Discount Values (%) -10, 0, 10, & 20

Default Price – 0% Discount

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Price Discount = 10%

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Price Discount = 20%

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Price Discount = -10%

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Price-Reserve CurvePrive vs. Reserve Curve

0

10

20

30

40

50

60

70

$9.00 $9.50 $10.00 $10.50 $11.00 $11.50 $12.00 $12.50 $13.00 $13.50

Average Sales Price ($/ton)

Rese

rv

e (

mil

lio

n t

on

s)

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Summary & Recommendations

• In industrial minerals & aggregates pit optimization might still be useful in strategic mine planning

• Using qualified consultants for training or strategic mine planning can address lack of resources

• Clearly define what you intend to get out of this step

• IM&A experience is crucial to properly define value (iterations may be necessary)

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