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Robust, flexible and operational mine designstrategies
B. Groeneveld
*
1
, E. Topal
2
and B. Leenders
3
Strategic planning in mining is an important value accretive process. One of the most essentialaspects during the planning phase is determining the correct system design. A traditional minedesign process develops a fixed system for one set of conditions or expected values. Analternative is to develop a robust system that deals with variation, by handling a range ofconditions within the optimisation process. Conversely, a flexible design can be generated whichchanges the system dynamically over time in response to change. It is hypothesised that a flexibledesign generates more value than a robust design which in turn generates more value than atraditional design. However, due to constant change, a fully flexible design is not practical.Ideally, a hybrid of the two methods would be optimal. An operational design is proposed as amanual solution to this problem. This paper compares these different new design methodologies.
Keywords:
Strategic planning, Decision making, Mine design, Robust mine design, Flexible mine design
Introduction
Decision making in mining operations can take manyyears due to the period of time required to explore anddevelop a large deposit. During the study and construc-tion period, many uncertainties can unfold and multipleeconomic cycles may occur. Making decisions based onsingle point estimates of the future limits ﬂexibility,potentially resulting in premature foreclosure of anoperation. By considering changing conditions (bothupwards and downwards movements) in the decisionmaking process, a company is able to include ﬂexibilityin an operation allowing value to be maximised. Currentmethodologies impair a decision maker’s ability to justify this additional ﬂexibility.Building ﬂexibility into an operation provides acompany with the ability to quickly respond to change;however, ﬂexibility comes at a price. For example, anoperation of building a crusher to feed a processingplant has an initial plan to produce at 6 Mtpa. Anoption exists to build the allowance for a plantexpansion to 8 Mtpa (by increasing the size of thefoundations and footings to allow physical room forlarger equipment). However, when the decision to buildthe plant is made, to minimise initial capital investment,this ﬂexibility is removed. One year into the operation,the sale price of the product doubles and costs slightlyincrease, while all other variables hold. In this environ-ment, it is considered favourable to expand theoperation; however, due to the cost cutting decision,this ﬂexibility was removed from the plant and to makethe matter worse, production needs to be maintained sothe only option is to build a new crusher. Unfortunately,this will come at a signiﬁcant capital cost and time tobuild; reducing the overall value of the operation hadthis ﬂexibility initially been incorporated. This upfrontﬂexibility is difﬁcult to justify with current decisionmaking tools. Advances in an area broadly known asreal options ‘in’ projects (ROIP) are beginning toaddress this gap (de Neufville
et al.
, 2005; de Neu-fville, 2006; Wang and de Neufville, 2005, 2006; Cardin
et al.
, 2008; Groeneveld
et al.
, 2009).Real options ‘in’ projects are located midway betweenﬁnancial real options analysis (which does not deal withengineering system ﬂexibility) and traditional engineeringapproaches (which do not deal with ﬁnancial ﬂexibility).An analysis done using ROIP methods allows the designof a system under uncertainty to be studied. Through theanalysis process, the value of each design option can betested.Having this information allows thedecision makerto make an informed decision on what ﬂexibility to in-corporate in the ﬁnal design.Previous papers using ROIP methods have shown thevalue of this technique (Cardin
et al.
, 2008; Groeneveld
et al.
, 2009; Groeneveld and Topal, 2011). Cardin
et al.
(2008) implemented this technique for mining projectswith a Chilean mine in the ‘Cluster Toki’ region. In thepaper, a methodology is implemented where operatingplans are varied by truck ﬂeet capacity and crusher sizein response to changing prices. For each price scenario,the optimal operational plan is selected. The applicationof this method resulted in
y
30% more project valuethan current estimates. This paper provides a strongbasis on which to grow ROIP theory in mining. Thoughthere are several deﬁciencies in the model. The approachlimits the ﬂexibility by only including a handful of staticoperational plans; it assumes that the schedule of material moved is ﬁxed, fails to deal with variation in
1
Telfer Mine, Newcrest Mining Limited, Melbourne, Vic., Australia
2
Mining Engineering Department, Western Australia School of Mines,Curtin University of Technology, Kalgoorlie, WA, Australia
3
Strategic Development, Rio Tinto Iron Ore, Perth, WA, Australia
*
Corresponding author, email benjamin.groeneveld@gmail.com
20
2012 Institute of Materials, Minerals and Mining Published by Maney on behalf of the Institute and The AusIMMReceived 20 March 2011; accepted 29 October 2011DOI 10.1179/1743286311Y.0000000018
Mining Technology
2012
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ore grade and recovery and fails to consider options inthe main value adding stages of a mining operation.Groeneveld
et al.
(2009) outlined a methodology fordetermining a ﬂexible mine design by dynamicallyincluding design options in the optimisation in orderto maximise value. Multiple ‘states of the world’ weresimulated and the optimal design for each state wasdetermined. A dataset of results was formed from theoutput of each simulated scenario. From this dataset, acumulative probability graph was produced, commonlyknown as a value at risk graph. This resulting curverepresents a theoretical maximum achievable value.However, this assumes that a decision maker can makeperfect decisions. In reality, this is impracticable.An alternative is to produce a single ﬁxed design whichhandles optimally handles change. This is achieved bytaking the full set of uncertainties into the optimisationand developing a ﬁxed design that optimally handles thechanging uncertainties. The resultant design would be arobust design as it would best handle variation. Since theoptimisation includes high price and low price scenarios,it will attempt to produce a design that minimises anylosses and maximise any potential upside, while consider-ing that these are extreme scenarios and the mainscenarios are around the average. Note that this designisfundamentallydifferenttoadesignjustgeneratedbasedon the average value and this will be shown in theillustrative case study.However, a robust design proposes that a ‘set andwatch’ approach is taken by management. Therefore, itfails to value active management of an operation. So, aﬂexible model proposes constant change which is notpracticable and a robust model does not allow manage-ment decisions. To overcome these limitations, it isproposed that an operational design be generated wherethe initial periods have a ﬁxed ‘robust’ design and thelater years have a ﬂexible design where management hasthe ability to have multiple options in the pipeline.This paper compares these different design methodol-ogies. A summary of the methodology used for generat-ing the designs is outlined followed by the mathematicalformulation of the robust design under uncertainty, usingmixed integer programming (MIP) and Monte Carlosimulation (MCS) techniques. Furthermore, an opera-tional design is proposed as a solution to the limitationsof the robust and ﬂexible design methodologies. Finally,the different design methodologies are compared againsteach other and a traditional design approach, in an illu-strative case study.
Methodology
It is proposed that for these different design scenarios, acombination of MCS and MIP techniques be utilised.Uncertainties (or stochastic parameters) are simulatedthrough MCS as inputs to the MIP model. The MIPmodel allows for ‘go’ or ‘no go’ decisions to bemodelled. An optimised MIP model therefore deter-mines the optimal execution timing of design options fora set of uncertainties (‘states of the world’).
Design options
Four categories of system design options are incorpo-rated in the model. These are mine options, preproces-sing stockpile options, processing plant options andcapacity constraint options. Mine options represent thephysical extraction capacity that is required to movematerial from the ground. This constraint may be anannual tonnage constraint or an effective ﬂat haulconstraint which considers the time required to movematerial. Preprocessing stockpiles are stores of materialafter extraction from the ground, either for long termlow grade scenarios, ﬂuctuating demand scenarios or forwaste material storage. Processing plant options repre-sent the physical and/or chemical process that isundertaken to ‘recover’ ore from the gangue material.Capacity constraint options represent physical capacityconstraints at any point in the network. These mayrepresent attributes such as port capacity, loadingfacilities, crusher capacities or conveyor capacities.
Resource representation
The representation of the resource in the model is byparcels of material which contain multiple grade bins.These parcels are designed to represent a physicalconstraint on the resource, such that they must be fullymined before mining a parcel lower in the physicalsequence. A parcel may be made up of one or moregrade bins. The average grade of a parcel is the weightedaverage of the grade bins. A grade bin represents aquantity of material at a speciﬁed grade. The size of theparcels can be determined by the modeller, but eachparcel requires a binary variable in the model forscheduling which increases the solution time of themodel. However, the grade bins within a parcel are anattempt to provide a level of detail that maintains theselectivity of the model.
Flow paths
A ﬂow path represents a route for material to travel.Multiple processing plants/routes can be included andproducts can be generated at any point in the network.Different routes through the network are termed ‘ﬂowpaths’. To explain this concept, further consider Fig. 1.Examples of ﬂow paths in Fig. 1 include the pathfrom the resource (R) to mine 1 (M1) to stockpile 1 (S1)to plant 1 (P1) through circuit 1 (C1) to product A whichwould be RM1S1P1C1A, the path from the resource (R)to mine 1 (M1) to waste stockpile 1 (W1) which wouldbe RM1W1, the path from the resource (R) to mine 1(M1) to stockpile 1 (S1) to plant 4 (P4) through circuit 2(C2) to product B (B) which would be RM1S1P4C2Band the path from the resource to mine 3 (M3) tostockpile 1 (S1) to plant 3 (P3) through circuit 1 (C1) toproduct A (A) which would be RM3S1P3C1A. This isonly a small number of the potential paths through thenetwork.
Stockpiling
Stockpiling is used in mine operations for many reasonsincluding blending of material, storage of excess mineproduction, storage of waste material and storage of lowgrade ore for future production. When material isstockpiled, the grade and tonnage of the material isknown. However, as the material is mixed on thestockpile, the grade and the tonnage become unknown.Since the quantity of material in the stockpile isunknown before the optimisation, this gives rise to anon-linear constraint. To solve this problem, virtualgrade bins are created in the stockpile. These grade binshave a maximum and minimum grade of material whichcan enter the bin. As material is added to a stockpile, it
Groeneveld et al.
Robust, flexible and operational mine design strategies
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will be fed into a grade bin that has a suitable graderange. Many grade bins can be created without adver-sely affecting the performance of the model which limitsthe averaging effect.
Stochastic parameters
The model incorporates uncertainty around the inputparameters by MCS. Each simulation of values repre-sents a ‘state of the world’ that is equally probable in thefuture. Various parameters can be incorporated in themodel, for example price, capital cost, operating cost,equipment utilisation, recovery and time to build.Running a set of simulations is intended to give arepresentative sample of the future ‘states of the world’.
Models
Three different models have been proposed in order to justify increased ﬂexibility to determine a ﬂexible design,a robust design and an operational design. All modelsuse MCS and MIP techniques to determine a systemdesign. The fundamental difference between the modelsis that under a robust design, multiple ‘states of theworld’ are considered together, while a ﬂexible designconsiders just one ‘state of the world’ at a time. Anoperational design is developed by determining a ﬁxeddesign for the ﬁrst couple of periods and having aﬂexible design for periods after that. The ﬂexible designmodel has been published previously in (Groeneveld
et al.
, 2009; Groeneveld and Topal, 2011). The robustmodel is outlined in this paper and the operational planis a new hybrid of these two models with the maindifference that the design in the initial years is ﬁxed.That is no binary value exits for design options in theinitial periods.
Flexible design
Some researchers (Groeneveld
et al.
, 2009; Groeneveldand Topal, 2011) have previously outlined a methodol-ogy for undertaking ﬂexible mine design. The basis of these models was to optimise a design for a given singlestate of the world. This was achieved by includingmining, plant and capacity constraint design options inthe system and allowing the MIP model to internallyhandle the design options. MCS was used to generatethese different ‘states of the world.’This methodology assumes that a decision makermakes optimal decisions based on the knowledge of allstates of the project over time (i.e. what price and costsoccurred over time). In reality, forecasting the exact ﬁnalstate of a project is difﬁcult if not impossible. Theproposed methodology provides information and insightthat can be used by the decision maker in conjunctionwith other tools to make timely, informed and valueadding decisions.
Robust design
A new robust design methodology is proposed in thispaper to develop a design that better handles all ‘statesof the world’ as opposed to just a single design. It usesthe same concepts and assumption developed in theﬂexible design model but differs by considering numer-ous states at once. A robust design is achieved by solvingone ‘large’ MIP model that generates one design frommultiple possible options. In essence, this design is theone which handles a range of conditions the best out of all possible options.
Operational design
An operational design methodology is proposed as apractical alternative to overcome the limitations of therobust and ﬂexible methods. Essentially, an operationaldesign is where the initial years of a fully ﬂexible designhave been ﬁxed by the modeller. This allows manage-ment to make decisions today to enable the business tobe an ‘ongoing’ concern. By not ﬁxing future decisions,management can maintain ﬂexibility in order to beneﬁtfrom any upside potential and minimise any downsiderisk. As this method incorporates future ﬂexibility intothe analysis, the impact of the initial ﬁxed decisions canbe tested and tweaked in order to maximise value.
Robust model formulation
The developed MIP model optimises the system designfor a risk neutral investor for all simulated ‘states of theworld’. Each design option can impact capital commit-ment, revenue generated and operating expenses. Theoptimisation process seeks to determine the design withthe highest equally weighted net present value for allgiven ﬁnancial and technical scenarios. An outline of themathematical formulation is provided below.
Notation
Indices
b
a grade bin of material within a parcel
d
product type
e
dependent options
f
flow path of material through the designnetwork
1 Example network of design options showing numerous ﬂow paths
Groeneveld et al.
Robust, flexible and operational mine design strategies
22
Mining Technology
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g
grade element of material within a resource
j
bin of material within a stockpile: this binwill have a maximum and minimum grade of material which can enter
l
design options
m
mining options within the set of designoptions
n
simulated ‘state of the world’
p
parcel of material
r
required rate of return on the project
t
time period step (periods do not need to beequal)
s
stockpiling options within the set of designoptions
y
tolerance factor for the deviation of themining of a bin within a parcelCapitalised indices are the maximum value or upperlimit of that index.
Parameters
C
l,t,n
the capital cost of option
l
in time
t
for trial
nD
d,t,n
the capacity of product
d
in time
t
for trial
nD
l,t,n
the disposal cost of option
l
in time
t
for trial
nDT
the lag time between these relationships (i.e.build option two, three periods after optionone)
FD
l,t,n
the fixed cost saved from not operatingoption
l
from time
t
for trial
n
to the end of the project life
T F
l,t,n
the fixed cost of operating option
l
from time
t
for trial
n
to the end of the project life
T GL
g,d
the lower grade limit of grade
g
product
d GL
j
the lower grade limit of bin
j GU
g,d
the upper grade limit of grade
g
product
d GU
j
the upper grade limit of bin
j G
p,b
the grade of parcel
p
bin
bG
g,l,n
the grade
g
through plant
l
for trial
nG
g,s,j
the calculated average, maximum or mini-mum metal units of grade
g
in stockpile
s
inbin
j K
l,t,n
the capacity of option
l
in time
t
for trial
nK
s,t,n
the stockpile capacity of stockpile
s
in time
t
for trial
nM
p,b,l,t,n
the mining cost from parcel
p
to bin
b
through mine option
l
in time
t
for trial
nP
g,d,t,n
the sale price of grade element
g
for product
d
in time
t
for trial
n
(in $/metal unit)
R
l
the recovery of material through circuit
l R
s,j
the calculated average, maximum or mini-mum recovery for all material in stockpile
s
bin
j R
p,b
the available resource of parcel
p
bin
bR
p
z
1
the available resource of the successor parcel
p
z
1V
l,t,n
the variable cost of option
l
in time
t
for trial
n
Variables
G
g,d,t,n
the metal units of grade
g
produced forproduct
d
in time
t
for trial
nID
l,t
1, if option
l
is disposed in time
t
;0, otherwise
:
XI
s,j,t,n
the flow in from stockpile
s
bin
j
in time
t
fortrial
nXO
s,j,t,n
the flow out from stockpile
s
bin
j
in time
t
for trial
nX
p,b,f,t,n
the tonnage from parcel
p
bin
b
through flowpath
f
in time
t
for trial
nX
f,t,n
the tonnage mined through flow path
f
intime
t
for trial
nX
p,b,t,n
the tonnage mined from parcel
p
bin
b
intime
t
for trial
nX
p
z
l,b,t,n
the tonnage mined from the successor parcel
p
z
1 bin
b
in time
t
for trial
nY
e,t
the dependent option
e
of
Y
l,t
Y
l,t
1, if option
l
is executed in time
t
;0, otherwise
:
Y
p,t,n
1, if pushback
p
is fully minedintime
t
for trial
n
;0, otherwise
:
( )
Formulation
Objective function
The objective function seeks to maximise the equallyweighted before tax net present value (NPV) for allsimulated ‘states of the world’
X
nn
~
1
1
N
X
Tt
~
1
11
z
r
ð Þ
t
X
D,Gd
~
1,g
~
1
P
d,g,t,n
G
g,d,t,n
{
(X
P,B,Fp
~
1,b
~
1,f
~
1
j
l
[
f
V
l,t,n
X
p,b,f,t,n
{
X
P,B,Fp
~
1,b
~
1,f
~
1 l
[
f
j j
l
[
m
M
p,b,l,t,n
X
p,b,f,t,n
{
X
Ll
~
1
C
l,t,n
Y
l,t
{
X
Ll
~
1
F
l,t,n
Y
l,t
{
X
Ll
~
1
j
t
=
1
D
l,t,n
ID
l,t
z
X
Ll
~
1
j
t
=
1
FD
l,t,n
ID
l,t
359=;
(1)The constraints in the model can be divided into ﬁvecategories: resource, option, stockpiling, product andﬂow balance constraints.
Resource constraints
X
Tt
~
1
X
p,b,t,n
{
R
p,b
ƒ
0
V
p
,
b
,
n
(2)
X
B,tb
~
1,tt
~
1
X
p,b,tt,n
ƒ
X
Bb
~
1
R
p,b
Y
p,t,n
V
p
,
t
,
n
(3)
X
p
z
1,b,t,n
ƒ
R
p
z
1
X
ttt
~
1
Y
p,tt,n
V
p
,
t
,
n
(4)
X
Tt
~
1
Y
p,t,n
ƒ
1
V
p
,
n
(5)
X
Bb
~
1
1
R
p,b
X
p,b,t,n
{
1
R
p,b
X
p,b,t,n
ƒ
c
%
V
p
,
b
,
t
,
n
(6)
X
Bb
~
1
1
R
p,b
X
p,b,t,n
{
1
R
p,b
X
p,b,t,n
§
{
c
%
V
p
,
b
,
t
,
n
(7)The resource constraints in the model limit whatquantities and grades of material can be produced bythe system. The amount of material extracted from amining grade bin in a pit has an upper bound based onthe resource model which is constrainted by equa-tion (2). Scheduling constraints are encorporated by
Groeneveld et al.
Robust, flexible and operational mine design strategies
Mining Technology
2012
VOL
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23

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