IIE Simulation Competition Dalhousie University

Institute of Industrial Engineering Arena Arena Student 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 loading s+o(els and t+e (arious (arious material destinations 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 trucs -ill gro- -it+ eac+ p+ase. AMS must determine t+e optimal number of trucs re5uired for eac+ of t+e four stages in order to maximi6e profits b# b # exceeding production targets and maintaining a +ig+ le(el of truc utili6ation.















'+is report documents t+e problem sol(ing approac+ t+at -as used to arri(e at a set of recommendations for expanding trucing capacit# as time goes for-ard. '+e follo-ing steps -ere taen 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 trucs 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 trucs -as determined to be 3! trucs in %+ases 1 and , 31 trucs in %+ase 3, and 33 trucs in %+ase 7. It is recommended t+at AMS pro(ide t+is amount of trucs for p+ases of operation in order to ac+ie(e t+e +ig+est expected profit.















Table of Contents Executi(e Executi(e Summar#........ Summar#....................... ............................. ............................. .............................. ............................. ............................. .................................................... ..................................... i )ist of 'ables 'ables............. ............................ ............................. ............................. .............................. ............................. ............................. .............................. ............................. .......................... ............ iii )ist of &igures........ &igures....................... ............................. ............................. .............................. ............................. ............................. ............................. ............................................ .............................. iii 1.!2

%roblem %roblem Statement..... Statement................... ............................. .............................. ............................. ............................. .............................. ............................. ..............................1 ................1

1.12

8e# %erformance %erformance Indicators Indicators.............. ............................ ............................. ............................. ............................. ....................................... ........................ ........ ........ 

1.2

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

.!2

Met+odolo Met+odolog# g# and Ass Assumpti umptions..... ons................... ............................. .............................. ............................. ............................. .............................. ..........................3 ...........3

.12

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

.2

Model Specificat Specifications ions............. ........................... ............................. .............................. ............................. ............................. ............................................ ............................. 7

3.!2

Experimen Experimental tal Design............ Design.......................... ............................. .............................. ............................. ............................. ................................................ ................................. .9

7.!2

0esults....... 0esults..................... ............................. .............................. ............................. ............................. ............................. ............................. ............................................... ................................ :

7.12

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

7.2

%+ase ........................ ....................................... ............................. ............................. .............................. ............................. ............................. ............................. ......................... ...........< <

7.32

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

7.72

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

9.!2

Anal#sis...... Anal#sis..................... ............................. ............................. ............................. ............................. .............................. ............................. ........................................... ............................. 11

9.12

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

9.2

?umber ?umber of 0eplicatio 0eplications....... ns...................... .............................. ............................. ............................. ............................. ........................................... ............................. 11

:.!2

@erifica erification tion and @alidation. lidation................ ............................. ............................. .............................. ............................. .......................................... ............................ ......1 ...... 1

:.12

S+o(el S+o(el constraint constraint producti( producti(it# it# approxima approximation tion$............. $............................ .............................. .............................................. ............................... 13

:.2

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

:.32

?umerical ?umerical Calculatio Calculation.......... n......................... .............................. ............................. ............................. ............................. .......................................... ............................ 13

:.72

'ruc 'ruc constrain constraintt producti( producti(it# it# approximat approximation....... ion..................... ............................. .............................. .........................................13 ..........................13

:.92

ueuing ueuing t+eor# t+eor# (alidati (alidation........ on...................... ............................. .............................. ............................. ............................. .............................. .........................17 ..........17

;.!2

Implementat Implementation ion %lan................. %lan................................ ............................. ............................. ............................. ............................. .............................. ............................ ............. 19

<.!2

Conclusio Conclusions ns and 0ecommendat 0ecommendations ions............... .............................. ............................. ............................. ................................................ ................................. ..19

"ibliogra "ibliograp+#.. p+#................. .............................. ............................. ............................. ............................. ............................. .............................. ............................. .....................................1: .......................1: Appendix A > 0epresentati(e Data Distributions.......................................................................................1; Appendix " > Gradient Speed 0eduction Calculation................................................................................1< Appendix C > Mont+l# 'ruc Operating Cost Estimation..........................................................................1 Appendix D B Expected %rofit 'ables........................................................................................................















List of Tables Tables 'able 'able 1 > Experimen Experimentt Summar# Summar# 'able.... 'able................... ............................. ............................. .............................. ............................. ............................... ................. ........... : 'able  > Expected %rofit %+ase 12, Selection.............................................................................................; 'able 3 > Expected %rofit %+ase 2, Selection.............................................................................................< 'able 'able 7 > Expected Expected %rofit %rofit %+ase %+ase 32......................... 32........................................ ............................. ............................. .............................. ................................ ................. ........= ........ = 'able 'able 9 > Expected Expected %rofit %rofit %+ase %+ase 72......................... 72........................................ ............................. ............................. ..................................................... ...................................... 1! 'able 'able : > 'rial 'rial 0un 0esults...... 0esults.................... ............................. ............................. ............................. .............................. ............................. ........................................ .......................... .11 'able ; > Implementation %lan...................................................................................................................19 'able < > 0epresentati(e Data Distributions..............................................................................................1; 'able 'able = > p+ill p+ill Speed &actor............ &actor........................... ............................. ............................. .............................. ............................. ............................. ............................... ................ 1< 'able 1! > %it 0amp Do-n+ill Speed &actor..............................................................................................! 'able 11 > Dump 0amp Do-n+ill Speed &actor........................................................................................! 'able 'able 1 > Expected Expected %rofit %rofit %+ase %+ase 12........................ 12....................................... ............................. ............................. .................................................... .....................................  'able 'able 13 > Expected Expected %rofit %rofit %+ase %+ase 2........................ 2....................................... ............................. ............................. .................................................... .....................................  'able 'able 17 > Expected Expected %rofit %rofit %+ase %+ase 72........................ 72....................................... ............................. ............................. .................................................... ..................................... 3 'able 'able 19 > Expected Expected %rofit %rofit %+ase %+ase 32........................ 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















&igure 1 > Arena Animation of Spotted Dog Gold Mine %it.........................................................................1 &igure &igure  > Expected Expected Mont+l# %rofit %+ase %+ase 12.......................... 12......................................... ............................. ............................. .................................. ................... ....; &igure 3 > Asset tili6ation %+ase 12..........................................................................................................; &igure 7> Expected Mont+l# %rofit %+ase 2..............................................................................................< &igure 9 > Asset tili6ation %+ase 2..........................................................................................................< &igure &igure : > Expected Expected Mont+l# %rofit %+ase %+ase 32.......................... 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 &igure 11 > "irt+>Deat "irt+>Deat+ + %rocess.......... %rocess........................ ............................. .............................. ............................. ............................. ................................ ................. ............ 17 &igure 1 > Gradeabilit#/Speed/0impull....................................................................................................1< &igure 13 > Standard 0etarding, Continuous..............................................................................................1= &igure 17 > Standard 0etarding, 19!! m....................................................................................................!

















1.0) .0)

Problem blem Stat Statem emeent

'+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 '-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. 'rucs +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. 'rucs 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

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

is paid. If too man# man # trucs are onsite, lines -ill form at t+e (arious stations, resulting in a decrease of truc utili6ation. AMS must pro(ide a number of trucs t+at -ill balance balance bot+ t+ese considerations. In

















1.1) 1.1)

&ey &e y Per Perfo form rman ance ce 'n"i 'n"ica cato tors rs

*+en sol(ing an# problem, criteria are re5uired in order to e(aluate and compare solutions. '+ree e# performance indicators 8%I2 8%I2 -ere identified to anal#6e anal#6e results from t+e Spotted Spotted Dog Mine simulation. 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 !.

E [ R R ( n ) ] =226.8 ∙ 30 ∙ P F ∙ ( 0.9 P o ( n ) d o+ 0.65 P w ( n ) d w ) ^

^

^

where E [ R R ( n ) ] is the expecte expected d monthly monthly revenu revenuee ¿ a syst systemwit emwith h n truc trucks. ks.

where PF ( n )=( 0.8 p75 + p100+ 1.2 p130 ) where d o=2 ∙ ( 0.4 d crush + 0.6 d leach ) ^

where Po ( n )∧ Pw ( n ) are are the expect expected ed num number ber of loads loads of produ producti ction on per per day for n truck truck . ^

^

Expected profit per mont+ is t+e main indicator used to e(aluate t+e different experiments ran. '+is e(aluation is ultimatel# used to build t+e set of recommendations made.

















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, production, truc tra(el speeds and loading/unloading times. times. If (ariabilit# is not accounted for in a model, decision maers +a(e a limited abilit# to understand and account for t+e s#stems true be+a(iour. be+a(iour. '+is limits t+eir abilit# to mae 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 maret demand demand for gold is not included included in t+e model, nor is staffing re5uirements. 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) .0)

%et, %et,o" o"ol olog ogy y an" an" ss ssum um!t !tio ions ns

'+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 Arena in order to control (arious acti(ities, -+ile model specifications refer to assumptions t+at influenced t+e mae>up of t+e model.

.1)

'n!ut #a #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 distributions representing data sets is more representati(e t+an exact past data, t+e Arena Input

















'+e truc specifications also indicated t+at -+en loaded trucs 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 trucs tra(elling up+ill is +alf t+at of loaded trucs tra(elling on flat ground.

.) .)

%o"e %o"ell S!e S!eccifi ificat cations ions

A simulation 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 trucs, a @"A controller 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# sufficientl# +ig+ number of trucs, 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. destination. '+e s+o(el model maes 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 maes -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(els stop operations at = +ours -+ile t+e rest of t+e s#stem continues to -or until it is empt# 'rucs +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 'rucs 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$ • • • •

• •

.0) .0)

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# trucs 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 N9!,!!! see Appendix C

Ex!e Ex!eri rim men enta tall #esi #esign gn

'+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 lined 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 used to run t+e model under under a range of different truc 5uantities. '+e '+e experiments in 'able 'able 1 -ere run to produce results for anal#sis.



















Table 1 - Ex!eriment Summary Table

Experiment

0ange of 'rucs

Experiment

?umber of

parameters

replications da#s2/

&ilename

truc 5uantit#

%+ase 1 'ruc

1,9,1!,19,!,3,9,;,=,3!

%+ase 1 0oute

Optimi6ation %+ase  'ruc

31,3,33,37,39,3:,3;,3<,3=,7!P

'imes %+ase  0oute

Optimi6ation %+ase 3 'ruc

31,3,33,37,39,3:,3;,3<,3=,7!P

Optimi6ation %+ase 7 'ruc

31,3,33,37,39,3:,3;,3<,3=,7!P

Optimi6ation

31,3,33,37,39,3:,3;,3<,3=,7!P

.0)

1,9,1!,19,!,3,9,;,=,3!

1,9,1!,19,!,3,9,;,=,3!

1,9,1!,19,!,3,9,;,=,3!

'imes %+ase 3 0oute 'imes %+ase 3 0oute 'imes

1
ScenariosQScenarios%1> !!7.xlsx

1
ScenariosQScenarios%> !!7.xlsx

1
ScenariosQScenarios%3> !!7.xlsx

1
ScenariosQScenarios%7> !!<.xlsx

2esults

'+e Spotted Dog Mine simulation -as run using t+e current and future a(erage +aul profiles in order to determine t+e optimal number of trucs 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

















.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.

Ex!ec Ex!ecte" te" %ont,ly %ont,ly Profit Profit 3P 3 P ,ase 1) 1) N:!,!!!,!!! N7<,<7,7=;.=<

N9!,!!!,!!! N7!,!!!,!!! %ont,ly ont,l y 5alue 5aluess

%rofit 0e(enue

N3!,!!!,!!!

Costs

N!,!!!,!!! N1!,!!!,!!! N! !

9

1!

19

!

9

4umber 4umber of Trucs Truc s Figure  - Ex!ecte" %ont,ly Profit 3P,ase 1) Table  - Ex!ecte" Profit 3P,ase 1)6 Selection

3!

39

7!

79

















sset *tili+ *tili+ation ation 3P,ase 3P ,ase 1) 1) 1.! 1.!! !.
S+o(el tili6ation

!.:!

'ruc tili6ation tili6ation

!.7! !.! !.!! !

9

1!

19

!

9

3!

39

7!

79

4umb 4umber of Trucs Truc s

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

.)

P,ase 

Ex!ec Ex!ecte" te" %ont,ly %ont,ly Profit Profit 3P ,ase ) ) N;!,!!!,!!! N:!,!!!,!!!

N9,;!!,:79.<7

















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

7 Tr Trucs

9 ; = 3! 31 3

E8Profit9

N79,9:3,<<3.7= N7;,<::,:3!.=7 N9,::7,3!9.= N9,;!!,:79.<7 N9,3:3,!<7.!< N9,31,<=.73

sset *tili+ *tili+ation ation 3P,ase 3P ,ase ) ) 1.! 1.!!

















Ex!ec Ex!ecte" te" %ont,ly %ont,ly Profit Profit 3P 3 P ,ase ) ) N;!,!!!,!!! N:!,!!!,!!! N9!,!!!,!!!

N9:,737,9!1.;9 %rofit

N7!,!!!,!!! %ont,ly ont,l y 5alue 5aluess

0e(enue

N3!,!!!,!!!

Costs

N!,!!!,!!! N1!,!!!,!!! N! !

9

1!

19

!

9

4umber 4umber of Trucs Truc s

Table  - Ex!ecte" Profit 3P,ase )

7 Tr Trucs

= 3! 31

E8Profit9

N9,; 9,;: :,3 ,3; ;3.<: .<: N99,9 99,9!: !:,: ,:9 99.<9 .<9 N9:,7 9:,737 37,9 ,9! !1.;9 .;9

3!

39

7!

79



















.)

P,ase 

'+e follo-ing grap+s and table s+o- t+e results of t+e simulation for %+ase 3 of t+e mine.

Ex!ecte" %ont,ly Profit 3P,ase ) N
















sset *tili+ *tili+ation ation 3P,ase 3P ,ase ) ) 1. 1. 1 !.< !.< *tili+ation

S+o(el tili6ation

!.: !.:

'ruc tili6ation tili6ation !.7 !.7 !. !. ! !

9

1!

19

!

9

3!

39

7!

79

















'o determine determine t+e appropriate number of replications, a trial run of 3! mont+s -as conducted for 3! trucs 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 c+osen because t+e optimal number number of trucs can be c+anged -it+ -it+ slig+t (ariations (ariations in t+e model. '+e results from t+is trial run are displa#ed in 'able 'able :. Table ; - Trial 2un 2esults

5ariable

5alue

Alp+a A(erage Standard De(iation =9 Confidence Inter(al

1.=: N 3,:99,!1:.; N <<,9=9.<= N 1!3,;.;1

















%o"el Com!arison( Ex!ecte" #aily Loa"s #elivere" 3P,ase ) 1!! Simulated A mount 1!!!

'ruc Cons traint Approximation

ueueing '+eor# Approximation

















;.1) ;.1)

S,ovel S,ovel constr constrain aintt !ro"uc !ro"uctiv tivity ity a!!ro a!!roxim ximati ation( on(

*+en t+e number of trucs is increased be#ond be #ond t+e optimum le(el, t+e s+o(eling process becomes a bottlenec in t+e material material +andling process. process. In t+is situation, situation, a large 5ueue of empt# trucs trucs forms at t+e s+o(el stations and t+e producti(it# of t+e mine as a function of number of trucs2 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. distribution. '+e a(erage loading time is$ 1.52,0 .716 ) ] =2 + 1.52=3.52 t load = E [ 2 + LOG ( ( 1.52,0



















;.) ;.)

Truc Tr uc constr constrain aintt !ro !ro"uc "uctiv tivity ity a!!ro a!!roxim ximati ation on

*+en t+e number of trucs is reduced belo- t+e optimum le(el, t+e trucing process becomes a bottlenec in t+e material material +andling process. process. In t+is situation, situation, t+e s+o(els must -ait -ait for trucs to arri(e,

















In t+is model, t+e arri(al rate is defined as t+e rate t+at empt# trucs 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 trucs 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.

















reliabilit# of t+is result. '+ese results taen 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 trucs for t+e final p+ase of mine operations.

















Bibliogra!,y Catepillar Inc. !1!2. ;=3& Mining 'ruc Operating Specifications. Specifications. AEHQ6038-03 (03-2010) (03-2010) . 4illier, &. &. S.,  )ieberman, G. . !1!2. Introduction Introduction to Operations Operations Research, Research, th Edition!

















!!en"ix  - 2e!resentative #ata #istributions Table = - 2e!resentative #ata #istributions











































































































































IIE Simulation Competition Dalhousie University

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