Published on February 28, 2014
Is There a Role for Lerchs-Grossman Optimization in Industrial Minerals and Aggregates Mine Planning? Kwame Awuah-Offei Associate 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) 2
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 3
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 4
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.) 5
Sand & Gravel Case Study 6
Objectives of the Optimization • To define economic horizons of the ultimate pit • To determine pricing strategy 7
Input Data Parameter Average Sales Price Value $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 8
Default Price – 0% Discount 9
Price Discount = 10% 10
Price Discount = 20% 11
Price Discount = -10% 12
Price-Reserve Curve Prive vs. Reserve Curve 70 Reserve (million tons) 60 50 40 30 20 10 0 $9.00 $9.50 $10.00 $10.50 $11.00 $11.50 $12.00 $12.50 $13.00 $13.50 Average Sales Price ($/ton) 13
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) 14
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