Integrated open pit pushback selection and production capacity optimization

Journal of Mining Science, 2011

T. Elkington and R. Durham

3rd presentation of surface mining and sustainable developmentProfessor: OsanlooNovember 20, 2012Satar Mahdevari

Amirkabir University of TechnologyDepartment of Mining and Metallurgical Engineering

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1. Introduction 2. Methodology3. MIP Formulation4. Case study5. Conclusions

Outlines

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Introduction

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Strategic mine planning for open pit mines typically involves solving the problems of:

What should be mined? Where it should be sent? When this should be done?

There have been two main broad methodologies for optimizing these problems “block level resolution” and “aggregation” approaches.

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Introduction

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This paper utilizes an aggregation approach in a new formulation for simultaneously optimizing production rates and pushback selection, along with scheduling, stockpiling, and cut-off grades.

Open pit strategic mine planning is processed of two steps: First, nested pit shells are generated over a range of prices Second, selection of pushbacks from the available nested

pit shells is built in an MIP scheduling formulation

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MIP FormulationThere are nine main types of decision variables used in this model.

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Objective Function

The objective of the optimization model is to maximize NPV.

Phbgt discounted net revenue from directly processed materialYhbgt discounted net revenue from processed stockpile materialXhbgt costs from material added to stockpileWhcbt costs from miningMCt units of mining capacityPCt units of processing capacity

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Constraints

Quantity Constraints

Product Constraints

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Pit Shell to Pushback Allocation Constraints

Pushback Constraints

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Material Flow Constraints

Sequencing Constraints

Stockpile Constraints

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Key Assumptions

Pushback selection is determined by allocating parcels in each pit shell to a pushback.The ultimate pit outline is defined as the outline of the final pushback.The schedule optimization defines the portion of each panel that is mined in each period.Cut-off grade optimization is implicitly defined by the material contained within the grade groups selected for processing.It is assumed that material can be removed from the stockpile in any period after it has been placed there.Each unit of production capacity must be purchased at a given unit cost. It is assumed that the relationship between production capacity and cost is linear.

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Case study A hypothetical copper orebody with approximately 160 000 blocks was used to

demonstrate the proposed methodology. To begin, a pit optimization was completed with the Whittle strategic mine

planning package. Overall 31 nested pit shells were generated using a parameterized copper price,

ranging from 30 to 200 percent of the base case price and resulting in 454 parcels.

Three pushbacks containing a minimum of 80 Mt of total material, Maximum advance of six benches per year per pushback, Unlimited stockpiling capacity, A discount rate of 10 %, A capital cost of $25/ tpa of processing capacity, A capital cost of $5/ tpa of mining capacity.

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An optimization completed at the base case price of $3,300/t CuThe NPV of this scenario is $1,031 million

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Three strategies were considered for comparison:

1) stockpile optimization base case (Scenario SP OPT)2) marginal cut-off grade with no stockpiles (COG MARG)3) optimized cut-off grade with no stockpiles (COG OPT)

The predicted NPV of the COG OPT scenario is $995 million, and the COG MARG scenario is $917 million. This represents a decrease in NPV of 3.5 % and 11.1 % from the SP OPT scenario, respectively.

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1- SP OPT2- COG MARG3- COG OPT

SP OPT is able to operate at full processing capacity for the life of the mine, whereas the other cases both had processing shortfalls in some periods, and consequently revenue shortfalls, which may result in liquidity issues.

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1- SP OPT2- COG MARG3- COG OPT

The most flexible method (SP OPT), which allows stockpiling and cut-off grade to vary implicitly, produces the highest NPV with the lowest capital expenditure associated with processing capacity.

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Price uncertainty

A significant source of uncertainty is commodity price.The influence of this parameter on strategy selection must be well understood to avoid suboptimal project outcomes.

Five scenarios were considered:– The base case price (Scenario A)– 20 % below the base case price (L)– 20 % above the base case price (H)– The price falls from the H case to the A case over 5 years (HA)– The price increases from the L case to the A case over 5 years (LA)

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(a) Low price scenario (L) production schedule(b) High price scenario (H) production schedule(c) High to average price scenario (HA) production schedule(d) Low to average price scenario (LA) production schedule

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Processing rate schedule, by price scenario

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Stockpile size versus cumulative tonnes mined profile, by price scenario

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Direct processing cut-off grade versus cumulative tonnes mined profile, by price scenario

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Conclusions

This paper demonstrated a new MIP method of simultaneously optimizing mining and processing capacities, intermediate pushback, and ultimate pit outline selection in conjunction with optimized scheduling, cut-off grade and stockpiling.

The cut-off grade and stockpiling affects the optimal production capacities, as well as NPV.

The main strategic aspects affected by price were the ultimate pit outline and production capacities.

Future work will focus on incorporating uncertainty, both market and geological, into this planning framework.

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Thank you for your attention