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Multi-mine Better Than Multiple Mines

for Orebody Modelling and Strategic Mine Planning Symposium, Perth, November 2004

by: Geoff HallB.Sc., M. App. Sci., M.A.C.S., M.A.C.M.

Senior Developer, Whittle team, Gemcom Software International Inc.

Phone & fax: 03 9878 6888

Email: [email protected]

Abstract:

It is not uncommon for a number of open cut mines to share infrastructure in the mining

value chain. This sharing offers economies of scale, and presents additional scheduling options, but

also increases the complexity of design and scheduling. How do you best investigate and optimize

this type of scenario in order to yield maximum economic benefit?

As a senior developer in the Whittle team, the author has been involved in the creation of a

modelling and optimization system which caters for multiple integrated mines. The objectives of the

system design were:

* To provide a process, supported by effective tools, which enables mine planners to

maximize the economic benefit of multi-mine operations.

* To provide a modelling and optimization environment that allows multiple integrated mines

to be planned and scheduled effectively, including adaptation of optimization engines to the multi-

mine situation.

This paper describes the benefit the Whittle Multi-mine option can bring to such a complex

operation and the features that enable that benefit.

mailto:[email protected]

mailto:[email protected]




Table of Contents

Introduction..........................................................................................................................................3

Multiple mines .....................................................................................................................................3

The background................................................................................................................................3

The Whittle Multi-mine solution .....................................................................................................4

Example case study..............................................................................................................................5

Example data....................................................................................................................................5

Treat as single mine .........................................................................................................................5

Optimal Pit ...................................................................................................................................5

Pushbacks and Mine schedule......................................................................................................5

Three asides..................................................................................................................................6

Treat as multi-mine ..........................................................................................................................6Modifying constraints ......................................................................................................................7

Processing capacity ......................................................................................................................7

Mining capacity............................................................................................................................8

Milawa algorithm.............................................................................................................................8

Conclusions......................................................................................................................................9

References ............................................................................................................................................9

Appendix I: Glossary .........................................................................................................................10




Introduction

It is not uncommon for a number of open cut mines to share infrastructure in the mining value

chain. This sharing presents scale economies, and presents additional scheduling options, but also

increases the complexity of design and scheduling. How do you best investigate and optimize this

type of scenario in order to yield maximum economic benefit?

Multiple mines could be treated in Whittle, to a certain extent, before the Whittle Multi-mine option

was introduced. The simplest approach was to model each mine in isolation and then produce a

schedule manually. Several people, Tom Tulp (Tulp, 1997), David Whittle (Whittle, 2001) and

Chris Desoe from AMDAD developed techniques that removed some of the restrictions associated

with treating multiple mines as a single model within the Whittle environment. None of these

processes could entirely remove the restrictions and they all required complex setup procedures.

Within their limits, however, they worked and they all enjoyed success in a restricted number of

situations.

The Multi-mine option allows the flexibility of choice of optimal pit and pushbacks for each mine

independent of the other mines in the model, while still producing a schedule automatically across

all mines.

There are a few terms that can be used in conflicting ways. To avoid confusion, these terms,“mine”, “pit”, “shell” and “operation” and are defined in the glossary (Appendix I) along with a

more extensive list of terms used in this paper.

Multiple mines

The background

A multiple mine operation has more than one mine sufficiently close together that they share

infrastructure and are planned as a single study. The past approaches to modelling this situation

identified in the introduction either fail to address the benefits of producing a joint schedule, or limit

the definition of the individual mines so that they do not use their optimal pit or pushbacks tailored

to that mine.

Planning the mining schedule of a single mine is reasonably well understood. While the process is

complex, tools exist to assist the user in creating an optimal open pit shape from a model of an ore

body. Tools also exist to assist in planning a mining schedule from the chosen pit. The difficulty in




the multiple mine situation in particular, is in defining the best pushbacks and finding the best

mining schedule. The Whittle product uses the Net Present Value (NPV) of a mine to drive both

the identification of the optimal pit and the creation of the mining schedule.

The optimal pit is found using the Lerchs-Grossmann (LG) algorithm (Lerchs & Grossmann, 1965).

The method for determining the optimal pits is the same for a single mine or a set of mines. This,however, is just the start of the solution. The material to be removed from each mine can be

extracted in any one of a number of ways, all of which can result in dramatically different NPVs for

the mine.

The creation of a mining sequence involves defining some useful pushbacks for those mines then

mining those pushbacks in such a way that maximises the potential value of an operation.

The Whittle Multi-mine solution

The model file of the Multi-mine option uses a single block model definition which identifies each

mine in the block model separately. You are able to define the pushbacks and choose the optimum

pit for each mine separately, then create a schedule that considers all of the mines together. This

technique allows each mine to be designed to its full potential because its optimum pit is

independent of any other mine. During the scheduling process, however, there are benefits from

considering the mines as multiple sources of ore. The scheduler is able to decide when to choose

material from the mines such that the value of the operation is maximised.

The key benefits of the Multi-mine option are that it gives you independence between mines:

• pushbacks can be determined that are ideal for an individual mine,

• the final pit for each mine is separate,

• the order of processing of the mines can be changed easily, and

• mining limits can be tailored for individual mines.

In addition, the material movements in each mine can be tracked separately and extra controls have

been added to allow per-mine constraints.

By using Whittle to find the theoretical maximum value of the operation, it is possible to cost the

decisions that are made along the way as progress is made to a final design for the operation.

Sometimes, this means that Whittle presents information that justifies a change in approach because

of the increased value that is realisable when that change is implemented.




Example case study

Example data

The data comes from the “BlueSky” project which was originally developed as a multi-mine

example by Chris Wharton and is based on the “Marvin” data developed by Norm Hanson for his

students at RMIT University and used in the “Whittle Challenge”, a one day add-on to the

“Optimizing With Whittle” conference in 1999.

It has two mines, called NorthPark (mine 1) and SouthBorder (mine 2). SouthBorder is the standard

Marvin mine with three rock-types: OX (a surface oxide), MX (a mixed ore) and PM (the primary

ore). NorthPark has been modified from the original Marvin with the OX and PM rock-type

tonnages being summed together (called SL) and MX being renamed to RF.

The SouthBorder rock-types have their rock-type Cost Adjustment Factor (CAF) greater than one to

indicate a harder rock than in the original Marvin.

The slopes of both mines have been modified from the original Marvin and also made different

from each other.

All rock-types have gold and copper elements.

Treat as single mine

Optimal Pit

The creation of the optimal pit for each mine proceeds as in the single mine case because the LG

algorithm (in a single model file) will treat the mines as independent entities (provided the resultant

pits do not touch).

Pushbacks and Mine schedule

Before we explore designs for a practical and realistic mine design and schedule, it is useful to look

at the operation as a single mine case to provide some indicator values. The initial run introduces

the period tonnages involved and forms a framework for developing further refinements.

Key aspects of this run are:

• liberal mining rate (chosen to ensure mining limit is never, or rarely a limiting factor. In this

example 80 million tonnes (mt) per annum (pa))




• conservative processing throughput (chosen to ensure this is the limiting factor and reflects

“reasonable” mine life - 20 mt pa)

With the above limits and reasonable estimates of the costs required to support the above rates, the

Pit by Pit Graph node indicates that the maximum best case NPV that can be achieved is $272m.

This is the pit containing 693m tonnes total with a mine life of 24 years (Table 1, line 1).

We have arbitrarily chosen to develop four pushbacks. This is a decision that can be explored

further when there are definite costs of starting a new pushback. The more pushbacks you have, the

closer you can get to the Whittle “Best case” scenario. When the costs of a pushback are included

in the analysis, you can very quickly see when the cost of adding a pushback outweighs the return.

When we add four pushbacks (letting the Pushback Chooser (Whittle 2004a) decide them for us),

the optimal pit is 488mt with a value of $186m over a nearly 19 year mine life (Table 1, line 2).

Three asides

1. The use of geometric values 1 in defining the revenue factor range generates a good range of

pits, giving good starting pits and still keeps the overall number of pits to consider to a

minimum.

2. By including the actual cost of establishing pushbacks in an operation, one can determine

whether using more pushbacks would improve the value of the operation.

3. The slopes of each mine in an operation could be quite different. Since Whittle has the

capability to model these without the use of the Multi-mine option, they will not be

discussed further in this paper.

Treat as multi-mine

Without the Multi-mine option above, the chosen pushbacks are the same for every mine. The

optimal pit is chosen by its pit number and that is also the same for every mine.

Each mine is different, therefore one would expect the ideal pushbacks for each mine to be

different. Using the Multi-mine model we can run the Pushback Chooser separately for each mine.

This approach can be used because the Pushback Chooser only uses the relative differences between

NPVs in deciding where to put the pushback boundaries.

1 “Geometric values” is a technique for defining revenue factors that produces a greater number of pits at the smaller pitend of the range than at the larger pit end (Whittle 2004b). It is useful for defining the starter pit and early pushbacks.




Once we have the pushbacks for each mine, we can explore schedules using input from both mines

(each with its own pushbacks) and costings and limits that can be a combination of global and per

mine attributes. Note that individual mine constraints are only available with the Multi-mine

option.

The user can now explore the opportunities available to vary the schedule based on the order inwhich the mines are considered as well as the previous variables associated with pushbacks in a

single mine.

At this point it useful to note which mines are the biggest contributors. This will help drive the

decision as to the order in which we should mine the mines. In this example, the significantly

bigger contribution comes from the NorthPark mine, so we will consider it first in the order (Fig 1).

Using the Milawa algorithm will improve the NPV if an inappropriate ordering of mines is chosen,

but it cannot necessarily find the best NPV.

With each mine having its own (four independent) pushbacks and considering NorthPark first, we

end up with a schedule (Fig 2) developing an NPV of $197m from a combined tonnage of 569 mt

(Table 1, line 3). This is an increase of $11m with addition of 81 mt over the previous result which

is a direct result of being able to start with individually optimized mines.

The following steps are not specific to the Multi-mine option when only global limits are applied,

but significant gains in NPV may be available by exploring variations in the processing and mining

limits.

Modifying constraints

When analysing the effects of constraints, you should ensure that constraints further back in the

process are not making an adverse impact on downstream processes. For the illustrative purposes

of this paper, selling limits are ignored (the last step in the Whittle limits) and we’ll deal with the

two main limits back up the process stream: the processing capacity, then the mining capacity.

Processing capacity

We have started with a generous mining limit, so the impact of extending the processing capacity

can be considered without a tight mining limit confusing the results.




We consider the situation whereby spending an extra $55m we can add 10 mt pa to the processing

capacity, increasing it to 30 mt pa. 2

The result of this analysis is that we can increase the NPV from the previous analysis to $280m with

the same tonnage (Table 1, Line 4). The change is that the mine life is now less than 14 years as

compared to over 20 years previously. The increase in NPV is due to being able to earn the moneysooner. Note that at this point, mining limits have not been touched and so the mining cost (quoted

per tonne) is unchanged.

Mining capacity

From Fig 2 we can see that there are some periods that have mined considerably more material than

is required in that period. The pattern is similar after the processing capacity is increased.

Let us consider what would happen if we reduced our mining capacity to 60 mt which allows us tosave $30m. 3

We see that we can add $26m to the value of the mine, increasing the NPV to $306m (Table 1, Line

5) even though we don’t fill the mill in periods 5 and 12 (by a small amount). (Fig 3)

Milawa algorithm

The study up until now has only used fixed lead. This has been for a couple of reasons. The fixed

lead approach gives results very quickly which allows us to explore many possible “what if”

scenarios and gives a good feel for the performance of the mine under differing conditions. As we

get closer to what we think might be a final solution, we use the Milawa algorithm 4 to see what

extra benefits we can realise out of this mining operation.

The result using Milawa NPV raises the value another $30m to $336m (Table 1, Line 6). Now the

mill is kept full (until the end of the mine). Milawa is now changing the order of processing in the

mines to achieve a greater NPV. This becomes more obvious when the mining limit is reduced

even further to 50 mt pa (Fig 4).

The next result, from a Milawa Balanced run, shows that we can balance our mining (and keep the

mill filled) at a cost of dropping the value of the operation to $246m (Table 1, Line 7; Fig 5).

2 In a real study, several scenarios would be considered to explore the benefits of increasing production. Somequestions that would need answers are, “Should we increase production?” “If we do, by how much?” “What are therisks involved?” This example is chosen to illustrate one such scenario.3 As with the processing capacity, this is an example of a single variation, which in practice would be one of severalvariations studied.4 The Milawa algorithm is a proprietary algorithm that modifies the selection of material available from every open

pushback to produce a schedule that improves the NPV. “Milawa NPV” focuses on improving NPV, “MilawaBalanced” focuses on keeping the mining rate balanced.




From Figs 4 and 5, by inspection, it looks like the increased mining in the early years of the Milawa

Balanced solution is contributing to some early costs of mining which do not occur in the Milawa

NPV solution.

We can now consider “tuning” the mining capacity to improve the Milawa Balanced result. In this

example we can achieve a Milawa Balanced schedule (Fig 6) that is a significant improvement overthe “un-tuned” result yielding a value of $328m (Table 1, Line 8).

Conclusions

The optimal pits for individual mines can be determined without the Multi-mine option in Whittle.

The LG algorithm will develop each mine independently.

The basic approach to a multi-mine study is similar to a single mine study with all the single mine

features being available in the multi-mine situation.

The differences arise when the key benefits of the Multi-mine option are used:

• pushbacks can be determined that are ideal for an individual mine,

• the final pit for each mine is separate,

• the order of processing of the mines can be changed easily, and

• mining limits can be tailored for individual mines.

The Multi-mine option can add significant value to a multiple mine operation.

References

Lerchs, H, Grossmann, I F, 1965. Optimum Design of Open-Pit Mines, Joint C.O.R.S. and

O.R.S.A. Conference, Montreal, May 27-29, 1964, in Transactions, C.I.M., pp.17-24.

Tulp, T, 1997. Multiple Ore Body Systems in Proceedings of Optimizing with Whittle Conference ,Perth, 1997.

Whittle, D, 2001. Multi-pit scheduling in Four-X. Whittle Programming internal document

published on user group list server and available on request .

Whittle Programming Pty Ltd, 2004a. Pushback Chooser. Whittle version 3.2 Help .

Whittle Programming Pty Ltd, 2004b. Revenue factors. Whittle version 3.2 Help .




Appendix I: Glossary

Cost Adjustment Factor (CAF)

This is a term that is used as a multiplicand in a cost calculation. A factor of 1.0 has no affect on

the associated cost. The cost to which this CAF applies will always be mentioned in the context of

its use.

Discounting

A dollar that we get today is more valuable to us than a dollar that we expect to get next year.

When estimating the value of a project, it is common to reduce expected future cash flows by a

certain percentage per year, to allow for interest and risk, etc. This process is called discounting.

Mine

A reserve that can be or is being mined independently of any other reserve.

Net Present Value (NPV)

The NPV is the present value of the expected future cash flows minus the present value of the costs.

Operation

The term used in this paper to describe the group of mines that is being studied as a multi-mine

scenario.

PitOne of the possible shapes for a mine. All of the possible shapes produced by Whittle are nested

from smallest to largest.

Pushback

A pushback is an intermediate pit outline that is mined to, before mining to another pushback or to

the final pit outline.

Revenue Factor (RF)

This is the factor by which the revenue for each block is scaled in order to produce one of the nested pits. The factor operates on the element prices.

Shell

The difference between two adjacent pits.



Discounted cashflow contribution from each mine

0

100

200

300

400

500

600

700

800

900

1000

1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 19 20 21 22 23 24

Pit

T o n n e s

( m )

0

50

100

150

200

250

300

350

400

$ ( m )

Tonnes:wasteTonnes:process$:SouthBorder $:NorthPark

Fig 1: Cash flow contribution from each mine

Two mines, independent pushbacks

010

20

30

40

50

60

1 3 5 7 9 11 13 15 17 19 21

Period

T o n n e s

( m ) Tonnes:waste:South

Tonnes:waste:NorthTonnes:input:SouthTonnes:input:North

Fig 2: Two mines, independent pushbacks




Increased processing , decreased mining

0

10

20

30

40

50

60

1 3 5 7 9 11 13 15

Period

T o n n e s

( m )

Tonnes:waste:SouthTonnes:waste:NorthTonnes:input:SouthTonnes:input:North

Fig 3: Increased processing, decreased mining

Milawa NPV (50mt minin g limit)

0

10

20

30

40

50

60

1 3 5 7 9 11 13 15

Period

T o n n e s

( m ) Tonnes:waste:SouthTonnes:waste:NorthTonnes:input:SouthTonnes:input:North

Fig 4: Milawa NPV




Milawa Balanced (un-tuned)

0

10

20

3040

50

60

1 3 5 7 9 11 13

Period

T o n n e s

( m )

Tonnes:waste:SouthTonnes:waste:NorthTonnes:input:SouthTonnes:input:North

Fig 5: Milawa Balanced

Milawa Balanced (tuned)

0

10

20

30

40

50

60

1 3 5 7 9 11 13

Period

T o n n e s

( m ) Tonnes:waste:South

Tonnes:waste:NorthTonnes:input:SouthTonnes:input:North

Fig 6: “Tuned” Milawa Balanced




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