IIE Simulation Competition Dalhousie University

8/17/2019 IIE Simulation Competition Dalhousie University

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Institute of Industrial Engineering ArenaStudent Simulation Competition

Spotted Dog Gold Mine Operations Simulation

Submitted to Alexandre Ouellet on December 31st, !1

Submitted "#$ %aul &enton, 'ra(is &oster and )iara *eiler

Dal+ousie ni(ersit#

!


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Executive Summary

'+e Spotted Dog Mine is an open pit gold mine located in -estern nited States. Operations at t+e mine

include drilling, blasting, loading/+auling material, 0eco(ering gold from ore, and dumping -aste.

American Mining Ser(ices AMS2 is responsible for pro(iding reliable dump truc transportation

bet-een t+e loading s+o(els and t+e (arious material destinations at t+e mine.

Operations at t+e Spotted Dog Mine are sc+eduled to ad(ance t+roug+ four p+ases in t+e coming #ears.

4auling distances for t+e trucs -ill gro- -it+ eac+ p+ase. AMS must determine t+e optimal number of

trucs re5uired for eac+ of t+e four stages in order to maximi6e profits b# exceeding production targets

and maintaining a +ig+ le(el of truc utili6ation.

1


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'+is report documents t+e problem sol(ing approac+ t+at -as used to arri(e at a set of recommendations

for expanding trucing capacit# as time goes for-ard. '+e follo-ing steps -ere taen to arri(e at a

reliable set of solutions$

• An Arena model -as constructed to capture rele(ant s#stem c+aracteristics.• '+e model -as (alidated based on anal#tical solutions and field data.

• '+e model -as run under a (ariet# of potential scenarios to determine t+e optimal number of

trucs at eac+ p+ase of operations.

• '+e results -ere anal#6ed according to e# performance indicators for t+e s#stem.

• A set of recommendations -ere put toget+er based on t+e anal#sis of t+e simulation model.

pon running t+e simulation -it+ t+e pro(ided +aul profiles for eac+ stage, t+e optimal number of trucs

-as determined to be 3! trucs in %+ases 1 and , 31 trucs in %+ase 3, and 33 trucs in %+ase 7. It is

recommended t+at AMS pro(ide t+is amount of trucs for p+ases of operation in order to ac+ie(e t+e

+ig+est expected profit.


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Table of Contents

Executi(e Summar#..................................................................................................................................... i

)ist of 'ables.............................................................................................................................................. iii

)ist of &igures............................................................................................................................................ iii1.!2 %roblem Statement...........................................................................................................................1

1.12 8e# %erformance Indicators................................................................................................ ........

1.2 %roblem Scope.............................................................................................................................3

.!2 Met+odolog# and Assumptions........................................................................................................3

.12 Input Data....................................................................................................................................3

.2 Model Specifications................................................................................................................... 7

3.!2 Experimental Design...................................................................................................................... .9

7.!2 0esults.............................................................................................................................................:

7.12 %+ase 1.........................................................................................................................................;

7.2 %+ase .........................................................................................................................................<

7.32 %+ase 3.........................................................................................................................................=

7.72 %+ase 7.......................................................................................................................................1!

9.!2 Anal#sis.........................................................................................................................................11

9.12 *arm>p %eriod........................................................................................................................ 11

9.2 ?umber of 0eplications............................................................................................................. 11

:.!2 @erification and @alidation...................................................................................................... ......1

:.12 S+o(el constraint producti(it# approximation$..........................................................................13

:.2 S+o(el constraint producti(it# -it+ s+o(el failures...................................................................13

:.32 ?umerical Calculation...............................................................................................................13

:.72 'ruc constraint producti(it# approximation.............................................................................13

:.92 ueuing t+eor# (alidation..........................................................................................................17

;.!2 Implementation %lan...................................................................................................................... 19

Gradient Speed 0eduction Calculation................................................................................1<Appendix C > Mont+l# 'ruc Operating Cost Estimation..........................................................................1

Appendix D B Expected %rofit 'ables........................................................................................................

Appendix E B tili6ation 'ables................................................................................................................7

Appendix & B %roducti(it# Slope Calculation...........................................................................................:

3


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List of Tables

'able 1 > Experiment Summar# 'able.............................................................................................. ...........:'able > Expected %rofit %+ase 12, Selection.............................................................................................;'able 3 > Expected %rofit %+ase 2, Selection.............................................................................................<'able 7 > Expected %rofit %+ase 32..................................................................................................... ........=

'able 9 > Expected %rofit %+ase 72...........................................................................................................1!'able : > 'rial 0un 0esults....................................................................................................................... .11'able ; > Implementation %lan...................................................................................................................19'able < > 0epresentati(e Data Distributions..............................................................................................1;'able = > p+ill Speed &actor.................................................................................................................... 1<'able 1! > %it 0amp Do-n+ill Speed &actor..............................................................................................!'able 11 > Dump 0amp Do-n+ill Speed &actor........................................................................................!'able 1 > Expected %rofit %+ase 12......................................................................................................... 'able 13 > Expected %rofit %+ase 2......................................................................................................... 'able 17 > Expected %rofit %+ase 72......................................................................................................... 3'able 19 > Expected %rofit %+ase 32......................................................................................................... 3'able 1: > Asset tili6ation %+ase 2........................................................................................................7

'able 1; > Asset tili6ation %+ase 12........................................................................................................7'able 1< > Asset tili6ation %+ase 72........................................................................................................9'able 1= > Asset tili6ation %+ase 32........................................................................................................9

List of Figures

7


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&igure 1 > Arena Animation of Spotted Dog Gold Mine %it.........................................................................1&igure > Expected Mont+l# %rofit %+ase 12......................................................................................... ....;&igure 3 > Asset tili6ation %+ase 12..........................................................................................................;&igure 7> Expected Mont+l# %rofit %+ase 2..............................................................................................<

&igure 9 > Asset tili6ation %+ase 2.......................................................................................................... Expected Mont+l# %rofit %+ase 32......................................................................................... ....=&igure ; > Asset tili6ation %+ase 32..........................................................................................................=&igure < > Expected Mont+l# %rofit %+ase 72...........................................................................................1!&igure = > Asset tili6ation %+ase 72........................................................................................................1!&igure 1! > Model Comparison..................................................................................................................1&igure 11 > "irt+>Deat+ %rocess.................................................................................................... ............17&igure 1 > Gradeabilit#/Speed/0impull....................................................................................................1<&igure 13 > Standard 0etarding, Continuous..............................................................................................1=&igure 17 > Standard 0etarding, 19!! m....................................................................................................!


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1.0) Problem Statement

'+e Spotted Dog Mine is an open pit gold mine located in t+e -estern nited States. '+e mine operates

using a truc>s+o(el s#stem. 0oc is extracted from t+e mine using t+ree large mining exca(ators,

commonl# referred to as s+o(els. '-o s+o(els exca(ate ore material, -+ile t+e t+ird exca(ates -aste

material. '+e roc is classified after extraction, according to t+e estimated gold concentrations in t+e

mined roc. &ort# percent of t+e ore material is classified as ore, lea(ing sixt# percent classified as

leac+. All of t+e -aste material is classified as -aste. 'rucs +aul t+e material to one of t+ree locations

according to t+e material classification. Ore material is +auled to t+e crus+er -+ere t+ere are t-o

unloading spots, -+ile leac+ and -aste material is +auled to t+eir respecti(e dumps. 'rucs arri(e at t+e

s+o(els, are loaded -it+ material, +aul t+e material to its destination and t+en return to t+e next a(ailable

s+o(el to repeat t+e process.

'+ese operations of drilling,

blasting, loading and +auling

are contracted out to

American Mining Ser(ices,

Inc. AMS2.

AMS is paid according to

t+e amount of material

+auled eac+ mont+ t+e more

material +auled, t+e more AMS

is paid. If too man# trucs are onsite, lines -ill form at t+e (arious stations, resulting in a decrease of

truc utili6ation. AMS must pro(ide a number of trucs t+at -ill balance bot+ t+ese considerations. In

addition, t+e nature of an open pit mine is to expand o(er time. '+e Spotted Dog Mine breas its

expansion into four p+ases. '+e distance trucs -ill be re5uired to +aul material out of t+e mine -ill

increase -it+ eac+ p+ase. As suc+, t+e number of trucs pro(ided in eac+ p+ase is expected to increase as

-ell.

@ariabilit# is also an important part of Spotted Dog Mine operations. '+is includes t+e speeds t+at trucs

tra(el, t+e rate t+at trucs are loaded/unloaded, as -ell as s+o(el breado-n rates and repair times. In

order to incorporate t+is (ariation and determine t+e number of trucs re5uired to +aul material at eac+

stage, an Arena model -as built. '+is model -as (alidated and ran under a (ariet# of experiments to

determine t+e optimal amount of trucs for eac+ p+ase of operations.

Figure 1 - rena nimation of S!otte" #og $ol" %ine Pit


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1.1) &ey Performance 'n"icators

*+en sol(ing an# problem, criteria are re5uired in order to e(aluate and compare solutions. '+ree e#

performance indicators 8%I2 -ere identified to anal#6e results from t+e Spotted Dog Mine simulation.

All model (ariations -ill be e(aluated using t+ese 8%I$

Profit(

%rofit refers to AMS re(enue multiplied b# t+e pro(ided pa# factor of %& F !.


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1.) Problem Sco!e

As -it+ an# s#stem, t+e mining operations at t+e Spotted Dog Mine +a(e an in+erent (ariabilit#.

Specificall# to t+is s#stem, (ariabilit# includes extracted material classification, o(erall production, truc

tra(el speeds and loading/unloading times. If (ariabilit# is not accounted for in a model, decision maers

+a(e a limited abilit# to understand and account for t+e s#stems true be+a(iour. '+is limits t+eir abilit# to

mae a -ell informed decision. Arena is designed to account for t+e stoc+astic nature of t+ese processes,

so it -as used to build a model to anal#6e t+e problem described in Section 1.!.

Se(eral aspects of mining operations at t+e Spotted Dog Mine -ere deemed to be out of scope for t+is

proJect. '+e maret demand for gold is not included in t+e model, nor is staffing re5uirements. In

addition, t+e re5uired operations to process material before exca(ation and after unloading are out of

scope. As suc+, onl# t+e material +andling aspect of t+e mine is modelled. Section .! describes all t+e

assumptions made t+roug+out t+e construction of t+e model in furt+er detail.

.0) %et,o"ology an" ssum!tions

'+roug+out t+e construction of t+e Arena model, numerous assumptions -ere made. '+ese assumptions

can be classified into t-o categories B input data and model specifications. Input data refers to t+e

distributions pro(ided to Arena in order to control (arious acti(ities, -+ile model specifications refer to

assumptions t+at influenced t+e mae>up of t+e model.

.1) 'n!ut #ata

Data regarding loaded truc speeds, empt# truc speeds, s+o(el failure rates, s+o(el repair times, s+o(el

loading times and truc dumping times -ere pro(ided to describe operating conditions at t+e Spotted Dog

Mine. As distributions representing data sets is more representati(e t+an exact past data, t+e Arena Input

Anal#6er -as used to determine t+e most accurate distributions t+at s+ould be used in t+e model. 0esults

from t+is anal#sis are presented in Appendix A.

'+e ;=3& Mining 'ruc specifications indicate t+e maximum unloaded speed of t+e truc is :! m/+, or

1!!! m/min. Some of t+e data pro(ided included (alues abo(e t+is speed t+ese data points -ere

considered outliers and remo(ed from t+e dataset. It -as assumed t+at all of t+e trucs speeds -ere

collected -+ile trucs -ere tra(elling on flat ground and calculated b# di(iding total time b# total

distance tra(elled. '+e specifications also indicated t+at truc speeds must decrease -+en tra(ersing

do-n+ill to pre(ent t+e braes from o(er+eating. sing t+e Standard 0etarding grap+s in Appendix ", a

factor of


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'+e truc specifications also indicated t+at -+en loaded trucs are tra(elling up+ill, t+eir speed s+ould

also be reduced. sing t+e pro(ided gradeabilit# grap+, a factor for speed reduction -as calculated to be

. As suc+, t+e speed of loaded trucs tra(elling up+ill is +alf t+at of loaded trucs tra(elling on flat

ground.

.) %o"el S!ecifications

A simulation model -as needed to model t+e complex and d#namic be+a(ior of t+e stoc+astic processes

at t+e Spotted Dog Gold Mine. '+e processes and t+eir interactions -ere mapped, and an Arena model

-as created to approximate t+em. '+e replication lengt+s and resource sc+edules are based on t-o nine

+our s+ifts per da#, and a mont+l# pa#ment sc+edule. In order to compare t+e benefits of purc+asing

additional trucs, a @"A controller uses a MS Excel spreads+eet to dri(e a set of experiments and reco(er

continuous responses from t+e s#stem based on t+e controls defined b# t+e experiment. '+ese

experiments are described in Section 3.!. Se(eral met+odologies and assumptions -ere used in order to

create a simplified, #et representati(e model. '+ese are summari6ed belo-$

S,ovel Process %o"el

*it+ sufficientl# +ig+ number of trucs, t+e s+o(els -ill be t+e constraint to production at t+e mine. '+e

s+o(elling process sei6es t-o resources, a truc and a s+o(el2, dela#s for a random loading time, releases

t+e s+o(el, and t+e truc proceeds to deli(er t+e loaded material to its destination. '+e s+o(el model

maes use of t+e follo-ing assumptions about t+e s#stem$

• An infinite suppl# of crus+ed roc is a(ailable for t+e s+o(els to exca(ate

• S+o(el loading times account for all c+anges in position t+at a s+o(el maes -it+in a p+ase

• External demand for gold and t+e proportion of -aste to ore is assumed to be constant. '+is

results in a permanent allocation of one s+o(el mining gold ore, and t-o s+o(els mining -aste

• S+o(el operators are sc+eduled for t-o = +our s+ifts a da#

• Eac+ s+o(el +as a dedicated repair cre-. *+en t-o failures occur simultaneousl# t+e# are still

repaired according to t+e same distribution

Trucing/auling Process %o"el

'+e number of trucs in t+e s#stem is t+e (ariable t+at is optimi6ed. At t+e start of a replication, t+e

number of trucs for t+e current polic# of t+e experiment is loaded into t+e s#stem. 'rucs are resources

t+at onl# become a(ailable -+en t+e# are KreturnedL to t+e empt# truc 5ueue beside t+e s+o(els in t+e

mine pit. A truc is sei6ed b# a s+o(el, sent to a destination, and t+en returns empt# to t+e 5ueue. '+e

follo-ing assumptions -ere made -+en modelling t+e trucing process$

• 'ruc dri(ers are considered al-a#s a(ailable


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• S+o(els stop operations at = +ours -+ile t+e rest of t+e s#stem continues to -or until it is empt#

• 'rucs +aul material at t+e full capacit# of 9! tonnes

• '+ere are no capacit# constraints associated -it+ roads, ramps, or intersections in t+e model

• 'rucs do not experience failures

• 0oute times are calculated b# di(iding effecti(e distance b# a stoc+astic (elocit# effecti(e

distances are defined in Appendix "

#estination Process %o"el

%rocessing at t+e destination uses t+e follo-ing set of assumptions to simplif# t+is aspect of t+e model$

• One distribution is fit to a set of data and used to model dumping at all destinations

• '+ere are no capacit# restrictions on leac+ -aste dumps

• Ore production targets consist of t+e amount of bot+ leac+ and ore material +auled eac+ mont+

• '+e pa# factor is calculated according to t+e total amount of ore material and -aste material

+auled b# trucs eac+ mont+

• '+e effecti(e grade of eac+ ramp is estimated to ne(er be greater t+an 19

• '+e mont+l# aggregate truc cost is N9!,!!! see Appendix C

.0) Ex!erimental #esign

'+e run controller for t+e model can feed a set of control parameters into t+e model at t+e start of eac+

replication, and output data out of t+e model at t+e end of t+e replication. '+e different scenarios to be

considered are represented as sets of (alues for t+e control parameters, -+ic+ can be defined in a

spreads+eet t+at is lined to t+e model t+roug+ t+e run controller.

Due to t+e small computational si6e of t+e model, and t+e need to onl# optimi6e one control (ariable, a

brute force approac+ is used to run t+e model under a range of different truc 5uantities. '+e experiments

in 'able 1 -ere run to produce results for anal#sis.


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Table 1 - Ex!eriment Summary Table

Experiment 0ange of 'rucs Experiment

parameters

?umber of

replications da#s2/

truc 5uantit#

&ilename

%+ase 1 'ruc

Optimi6ation

1,9,1!,19,!,3,9,;,=,3!

31,3,33,37,39,3:,3;,3

Optimi6ation

1,9,1!,19,!,3,9,;,=,3!

31,3,33,37,39,3:,3;,3

Optimi6ation

1,9,1!,19,!,3,9,;,=,3!

31,3,33,37,39,3:,3;,3

Optimi6ation

1,9,1!,19,!,3,9,;,=,3!

31,3,33,37,39,3:,3;,3

determine t+e optimal number of trucs in eac+ p+ase. '+ese results are presented in t+e follo-ing

subsections, eac+ -it+ an Expected Mont+l# %rofit table, grap+ and an Asset tili6ation grap+. '+e

figures of Expected Mont+l# %rofit and Asset tili6ation s+o- t+e relations+ip bet-een t+e number of

trucs pro(ided b# AMS, and t+e ser(ice le(el t+at -ould be ac+ie(ed, as t+e +ig+er t+e ser(ice le(el, t+e

more AMS -ill be paid.

'+e Expected Mont+l# %rofit grap+ displa#s t+e relations+ip bet-een t+e number of trucs and t+e profit

AMS s+ould expect to recei(e. '+e met+od used to calculate costs in t+ese grap+s is re(ie-ed in

Appendix C. '+e Expected Mont+l# %rofit table s+o-s a selection of t+e number of truc (alues as -ell

as correlating expected profit. '+e +ig+est expected profit (alue for eac+ p+ase is +ig+lig+ted in dar

green, -+ile t+e second +ig+est (alue is +ig+lig+ted in lig+t green. '+e complete tables are displa#ed in

Appendix D. '+e Asset tili6ation grap+ s+o-s t+e trade>off bet-een truc utili6ation and s+o(el

utili6ation. '+e number of trucs and t+e truc utili6ation le(el at t+e s+o(el and truc utili6ation

intersection is +ig+lig+ted. '+e tables used to create t+ese grap+s can be found in Appendix E. In eac+

p+ase, t+e +ig+est expected profit -as ac+ie(ed -+en s+o(el utili6ation reac+ed its maximum and truc

utili6ation -as at approximatel#


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.1) P,ase 1

'+e follo-ing grap+s and table s+o- t+e results of t+e simulation for %+ase 1 of t+e mine.

! 9 1! 19 ! 9 3! 39 7! 79N!

N1!,!!!,!!!

N!,!!!,!!!

N3!,!!!,!!!

N7!,!!!,!!!

N9!,!!!,!!!

N:!,!!!,!!!

N7


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! 9 1! 19 ! 9 3! 39 7! 79

!.!!

!.!

!.7!

!.:!

!.

1.!!

1.!

sset *tili+ation 3P,ase 1)

S+o(el tili6ation

'ruc tili6ation

4umber of Trucs

*tili+ation

Figure - sset *tili+ation 3P,ase 1)

.) P,ase

! 9 1! 19 ! 9 3! 39 7!

N!

N1!,!!!,!!!N!,!!!,!!!

N3!,!!!,!!!

N7!,!!!,!!!

N9!,!!!,!!!

N:!,!!!,!!!

N;!,!!!,!!!

N9,;!!,:79.


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Table - Ex!ecte" Profit 3P,ase )6 Selection

! 9 1! 19 ! 9 3! 39 7! 79

!.!!

!.!

!.7!

!.:!

!.

1.!!

1.!

sset *tili+ation 3P,ase )

S+o(el tili6ation

'ruc tili6ation

4umber of Trucs

*tili+ation

.) P,ase


ure : - sset *tili+ation 3P,ase )

Figure ; - Ex!ecte" %ont,ly Profit 3P,ase )

7 Trucs E8Profit9

9 N79,9:3,


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! 9 1! 19 ! 9 3! 39 7! 79

N!

N1!,!!!,!!!

N!,!!!,!!!

N3!,!!!,!!!

N7!,!!!,!!!N9!,!!!,!!!

N:!,!!!,!!!

N;!,!!!,!!!

N9:,737,9!1.;9

Ex!ecte" %ont,ly Profit 3P,ase )

%rofit

0e(enue

Costs

4umber of Trucs

%ont,ly 5alues

Table - Ex!ecte" Profit 3P,ase )

7 Trucs E8Profit9

= N9,;:,3;3.1.!!!


S+o(el tili6ation 'ruc tili6ation

4umber of Trucs

*tili+ation

Figure < - sset *tili+ation 3P,ase )


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.) P,ase


! 9 1! 19 ! 9 3! 39 7! 79

N!

N!,!!!,!!!

N7!,!!!,!!!

N:!,!!!,!!!

N

N:!,79!,199.79

Ex!ecte" %ont,ly Profit 3P,ase )

%rofit

0e(enue

Costs

4umber of Trucs

%ont,ly 5alues

Table : - Ex!ecte" Profit 3P,ase )

7 Trucs E8Profit9

31N9;,:;9,:::.9

7

3N9=,

:

33N:!,79!,199.7

9

37N:!,9,::!.;

=

39N:!,!


18/37

! 9 1! 19 ! 9 3! 39 7! 79

!

!.

!.7

!.:

!.<

1

1.


S+o(el tili6ation

'ruc tili6ation

4umber of Trucs

*tili+ation

Figure > - sset *tili+ation 3P,ase )

:.0) nalysis

'+e conclusions from t+e results presented in Section 3.! are dependent on AMSs polic# on truc

utili6ation. If an increased profit -it+ lo-er truc utili6ation is acceptable, AMS s+ould emplo# 3! trucs

in %+ases 1 and , 31 trucs in %+ase 3 and 33 trucs in %+ase 7. 4o-e(er, if AMS desires a certain

t+res+old for truc utili6ation to be met, Appendix E s+ould be consulted. &or instance, if AMS -is+es

t+eir trucs to maintain

trucs in %+ase 3 and 33 trucs in %+ase 7 -ould be desirable. Alternatel#, if t+e# -is+ to meet certains+o(el utili6ation standards and eep a constant flo- of production2, Appendix E s+ould again be

consulted.

:.1) ?arm-*! Perio"

'+e Spotted Dog Mine operates t-o 1! +our s+ifts eac+ da#. As t+ese are discrete time blocs, a -arm>up

period is not re5uired for t+e simulation. '+e mine onl# +as 1< +ours of effecti(e operations, so it is

assumed t+at an# -aste and ore in a truc -ill lea(e t+e s#stem, and t+e trucs -ill immediatel# be

a(ailable to t+e s+o(els once operations start ane-.

:.) 4umber of 2e!lications

'+e number of replications is important to determine for statistical accurac# in t+e model. '+e larger t+e

number of replications, t+e smaller t+e confidence inter(al, and t+e more accurate t+e model is. 4o-e(er,

t+e more replications re5uired, t+e longer t+e model taes to run.


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'o determine t+e appropriate number of replications, a trial run of 3! mont+s -as conducted for 3! trucs

during %+ase 7. '+e pa# for eac+ mont+ -as calculated, and t+e =9 confidence inter(al -as calculated.

It -as decided t+at t+is confidence inter(al s+ould be no larger t+an 1 t+en t+e a(erage (alue of mont+l#

pa#. '+is (alue -as c+osen because t+e optimal number of trucs can be c+anged -it+ slig+t (ariations in

t+e model. '+e results from t+is trial run are displa#ed in 'able :.

Table ; - Trial 2un 2esults

5ariable 5alue

Alp+a 1.=:

A(erage N 3,:99,!1:.;

Standard De(iation N


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! 9 1! 19 ! 9 3! 39 7! 79

!

!!

7!!

:!!

1!!!

1!!

%o"el Com!arison( Ex!ecte" #aily Loa"s #elivere" 3P,ase )

Simulated Amount 'ruc Constraint Approximation

S+o(el Constraint Approximation ueueing '+eor# Approximation

S+o(el Constraint Approximation -/ &ailures

4umber of Trucs

vg. Loa"s #elivere" #ay

A mining operation +as some c+aracteristics t+at allo- for accurate anal#tic models in certain

circumstances. '+e (alidation p+ase of model creation compared a (ariet# of anal#tic and simplified

numerical models to t+e output of t+e simulation model. '+is comparison is summari6ed b# &igure 1!

belo-$

Eac+ of t+ese models -as created based on t+e s#stem structure, and (alidated to t+e output

c+aracteristics presented in Appendix A. '+e reasoning and calculations supporting t+e e#

approximations are described belo-.

Figure 10 - %o"el Com!arison


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;.1) S,ovel constraint !ro"uctivity a!!roximation(

*+en t+e number of trucs is increased be#ond t+e optimum le(el, t+e s+o(eling process becomes a

bottlenec in t+e material +andling process. In t+is situation, a large 5ueue of empt# trucs forms at t+e

s+o(el stations and t+e producti(it# of t+e mine as a function of number of trucs2 approac+es a constant(alue. '+is (alue can be gi(en b# t+e follo-ing e5uation$

Ps (n )≅1080∙3

t load

'+e loading times are represented b# a s+ifted lognormal distribution. '+e a(erage loading time is$

t load= E [2+ LOG (1.52,0 .716) ]=2+1.52=3.52

Sol(ing for t+e s+o(el producti(it# constraint gi(es$

Ps (n )≅920.45 ( loadsday )

;.) S,ovel constraint !ro"uctivity @it, s,ovel failures

*+en s+o(el failures are added to t+e model, t+e ne- stead# state producti(it# can be gi(en b#

multipl#ing t+e e5uation in Section 9.1 b# t+e stead# state a(ailabilit# of t+e s+o(el$

P!

s ( n )≅ "#$F

"#$F + "##R ∙1080∙3

t load

*+ere s+o(el failure times follo- t+e *eibull distribution, and repair times follo- a lognormal

distribution, t+is e5uation becomes$

P!

s ( n )≅ % & (1+ 1k )

% & (1+ 1k )+1.4∙1080 ∙3

t load P

!

s ( n )≅879.422( loadsday )

;.) 4umerical Calculation

sing a simple set of processes to model s+o(els in Arena, stead# state producti(it# -as estimated see

file S+o([email protected] for furt+er information2$

R2≅


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;.) Truc constraint !ro"uctivity a!!roximation

*+en t+e number of trucs is reduced belo- t+e optimum le(el, t+e trucing process becomes a

bottlenec in t+e material +andling process. In t+is situation, t+e s+o(els must -ait for trucs to arri(e,

and t+e a(erage loads/da# can be approximated b# t+e linear function$

Pt (n )i≅( 1080 ∙ v̂d̂ i+ v̂ (t load+t dump))ni

where Pt (n ) ismine productivity whentrucks are the constraint .( loadsday )

v̂ isthe avera'e tr uck velocity .( mmin )

d̂ i is the avera'e distance¿deliver a load∈ phasei . (m )

t load isthe avera'e loadin'time .(min)

t dump isthe avera≥dumpin' time .(min)

n isthe number of trucks∈the system.

'+e calculations for t+e producti(it# slope for eac+ p+ase can be found in Appendix &.

;.:) Aueuing t,eory vali"ation

Due to t+e capacit# constraints in t+e crus+ing or dumping processes, t+e s+o(els -ill ne(er +a(e to -ait

for trucs. As suc+, t+e utili6ation le(el of t+e s+o(els pro(ided b# t+e trucing s#stem can be estimated

anal#ticall# using a birt+>deat+ process to model t+e 5ueue of empt# trucs -aiting to be filled at t+e

s+o(els. An example is s+o-n in &igure 11 belo-.

Figure 11 - Birt,-#eat, Process


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In t+is model, t+e arri(al rate is defined as t+e rate t+at empt# trucs are added to t+e 5ueue. '+e ser(ice

rate is defined as t+e rate t+at t+e s+o(els can fill trucs and cause t+em to exit t+is simplified s#stem.

'+is model is analogous to an %%s 5ueuing s#stem -it+ finite calling !o!ulation.

'o appl# t+is model to t+e Spotted Dog gold mine, t+e arri(al and ser(ice rates -ere estimated from t+emodel parameters for %+ase 7 of operations. '+e arri(al rate -as found b# calculating t+e a(erage amount

of time a truc spends deli(ering a load. '+e total arri(al rate to t+e 5ueue is t+e number of trucs in t+e

s#stem t+at are currentl# deli(ering loads, di(ided b# t+e a(erage time to deli(er a load, as s+o-n in t+e

follo-ing e5uation$

% (( 1080 ∙ v̂d̂+ v̂ t dump )=( 1080 ∙472.82

13482.23+472.82 ∙0.90423 )=36.711

'+e ser(ice rate is e5ual to t+e production rate of a single s+o(el$

) (1080

t load=

1080

3.52=306.818


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reliabilit# of t+is result. '+ese results taen from t+e current perspecti(e -ill result in a plan to purc+ase

one truc for p+ase 3, and t+en t-o more additional trucs for t+e final p+ase of mine operations.


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Bibliogra!,y

Catepillar Inc. !1!2. ;=3& Mining 'ruc Operating Specifications. AEHQ6038-03 (03-2010).

4illier, &. S., )ieberman, G. . !1!2. Introduction to Operations Research, th Edition!

0ossetti, M. D. anuar# !!=2. "i#u$ation %ode$in& and Arena!

*alpole, 0. E., M#ers, 0. 4., M#ers, S. )., Te, 8. !!;2. 'roai$it * "tatistics +or En&ineers *

"cientists, 8th Edition!


26/37

!!en"ix - 2e!resentative #ata #istributions

Table = - 2e!resentative #ata #istributions

#ata Set #istribution rena Co"e %ean Comments

)oaded 'ruc

Speed

"eta 311 11U"E'A.==,3.=22¿311+211( * * +¿402.566

"est fit from t+e inputanal#6er

Empt# 'ruc

Speed

Erlang 3!< GAMM9;.=, 7.!:2

¿308+k,

¿543.074

0emo(ed truc speedst+at -ere o(er safedri(ing limit. "est fitfrom input anal#6ergamma fit +ad lo-er

urtosis2

S+o(el 'ime

"et-een

&ailure

*eibull *EI"3!.;,1.!:2

¿ % & (1+ 1k )

¿30.0054

Among t+e best fits frominput anal#6er. )inearl#increasing +a6ardfunction is a good modelfor failures.

S+o(el 'ime

to 0epair

)ognormal )OG?1.7,1.;=2 ¿1.4 Excluded 6eroes fromdata. "est fit from inputanal#6er .

S+o(el

)oading 'ime

)ognormal )OG?1.9, !.;1:2 ¿2+1.52

¿3.52


'ruc

Dumping

'ime

Gamma GAMM!.79=,1.=;2 ¿k,

¿0.904



27/37

!!en"ix B - $ra"ient S!ee" 2e"uction Calculation

Figure 1 - $ra"eabilityS!ee"2im!ull

&igure 1 -as used to calculate t+e proper gear and, subse5uentl#, t+e maximum speed2 of t+e ;=3&

Mining 'ruc -+ile tra(elling up+ill. 'able = displa#s t+e factor used to decrease t+e truc speed -+ile

tra(elling up+ill.

Table > - *!,ill S!ee" Factor

&ull p+ill %it 0amp$ea

r %ax S!ee" 3m,)

Truc %ax S!ee" 3m,)

Factor

%+ase 1 7t+ 3! :! 1/

%+ase 7t+ 3! :! 1/

%+ase 3 7t+ 3! :! 1/

%+ase 7 7t+ 3! :! 1/


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If t+e effecti(e grade is an#-+ere bet-een 1! and 19, t+e truc must be in 7 t+ gear.

Figure 1 - Stan"ar" 2etar"ing6 Continuous


Mining 'ruc -+ile tra(elling do-n+ill, for roads t+at are longer t+an 19!! metres.


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Figure 1 - Stan"ar" 2etar"ing6 1:00 m


truc -+ile tra(elling do-n+ill, for roads t+at are roug+l# 19!! metres. 'ables 1! and 11 s+o- t+e factor

used to decrease t+e truc speed -+ile tra(elling do-n+ill.

Table 10 - Pit 2am! #o@n,ill S!ee" Factor

Empt# Do-n+ill %it0amp

S!ee" 3m,) Factor

%+ase 1 19!! m2 3


30/37

!!en"ix C - %ont,ly Truc !erating Cost Estimation

Since t+e Spotted Dog Mine pa#s AMS on a mont+l# basis, it is useful to express all of t+e fixed and

operating costs of a single truc as a recurring mont+l# cost. A met+odolog# for calculating a mont+l#

truc cost is summari6ed belo-.

2elevant Cost %o"el(

A simple #et po-erful model for asset purc+ase costing breas t+e costs into t+ree classifications$ A fixed

unit purc+ase cost, a series of e5uall# spaced (ariable costs t+at are incurred t+roug+out t+e assets

operations, and finall# a sal(age (alue t+at is reco(ered at t+e end of its operational life. '+ese costs are

represented b# &igure 19.

Figure 1: - Cas, Flo@ #iagram

Conversion to mont,ly cost(

Due to t+e time (alue of mone#, t+ese costs cannot be compared unless t+e# are con(erted to a common

reference point. '+is can be accomplis+ed using t+e follo-ing e5uation$

- total=( P /"RR / ) ∙ - ¿+- var−( F / "RR / )∙ - salva'e

where - ¿ / - var / - salva'e are the relevantcosts .

where - total is expressed∈ 0ollars

"onth

where "RRis the companies ! "inimum cceptable Rate of Return


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where is the number of months a truck will operate for .

where

(

P / i / n

)= P

[

1−(1+i)−n

i

]

−1

ssum!tion of mont,ly cost(

sing t+is met+od -ould re5uire t+e estimation of se(eral unno-n parameters, so a total mont+l# cost of

N9!,!!! is assumed for t+e cost anal#sis. '+is (alue -as used to calculate expected mont+l# profits

based on t+e number of trucs used.

!!en"ix # D Ex!ecte" Profit Tables

Table 1 - Ex!ecte" Profit

3P,ase )

7 Trucs E8Profit9

1 N1,9;!,;!.9=

9 N;,


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33/37


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!!en"ix E D *tili+ation Tables

Table 1< - sset *tili+ation 3P,ase 1)

7 TrucsS,ovel*tili+ation

Truc

*tili+ation

1 !.!7 !.=<

9 !. !.=;

1! !.73 !.=:

19 !.:3 !.=9

! !.

3: 1.!! !.:;

3; 1.!! !.:9

3< 1.!! !.:3

3= 1.!! !.:1

7! 1.!! !.:!


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Table 1> - sset *tili+ation 3P,ase )

7 Trucs

S,ovel

*tili+atio

n

Truc

*tili+ation

1 !.!7 !.=<

9 !.1= !.=;

1! !.3< !.=;

19 !.9; !.=:

! !.;7 !.=7

3 !.

3! !.=; !.


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!!en"ix F D Pro"uctivity Slo!e Calculation

Eac+ truc t+at is filled b# a s+o(el must dri(e to its destination and return empt# to t+e s+o(el. As suc+

t+e a(erage speed is gi(en b#$

v̂=( 12 ) E [ vloaded ]+( 12 ) E [vempty ]

v loaded is gi(en b# a s+ifted beta distribution, andvempty is gi(en b# a s+ifted gamma distribution$

v̂=( 12 )( + * * + + )+(1

2 ) ($+k))

¿( 12 )(311+ 211∙2.992.99+3.9 )+( 12 ) (308+57.9∗4.06 )=472.82

d̂ i=(( 13 )(( 25 ) (dcrush+dcrush )+( 35 )( d leach+dcrush ))+( 23 ) (ddump+dcrush ))

d̂1=

((1

3

)((

2

5

)(4749+4553.38 )+

(

3

5

)(4483+4287.38 )

)+

(

2

3

)(6125+5828.63 )

)=10963.48

d̂2=(( 13 )(( 25 ) (5049+4834.625 )+(35 ) (4783+4568.625 ))+( 23 ) (6625+6297.375 ))=11803.058

d̂3=(( 13 )(( 25 ) (5349+5115.875)+( 35 ) (5083+4849.875 ))+( 23 ) (7125+6766.125 ))=12642.642

d̂4=(( 13 )((25 ) (5649+5397.13 )+( 35 ) (5383+5131.13 ))+( 23 ) (7625+7234.88 ))=13482.23 '+e

loading times are represented b# a s+ifted lognormal distribution. '+e a(erage loading time is$


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t load= E [2+ LOG (1.52,0 .716) ]=2+1.52=3.52 '+e dumping times at eac+ of t+e truc

destinations are represented b# a gamma distribution$

t dump= E [G"" (0.459,1 .97) ]=k,=0.90423

IIE Simulation Competition Dalhousie University

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