a constraint programming-based genetic algorithm for capacity output optimization

8/10/2019 A Constraint Programming-based Genetic Algorithm for Capacity Output Optimization

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Journal of Industrial Engineering and Management

JIEM, 2014 7(5): 1222-1249 Online ISSN: 2014-0953 Print ISSN: 2014-8423

htt:!!"#$"%i$%r&!10$392'!ie$1070

A Constraint Programming-based Genetic Algorithm (CPGA) for

Capacity utput ptimi!ation

Kate Ean Nee Goh1, Jeng Feng Chin1, Wei Ping Loh1, Melissa Chea-Ling Tan2

1School of Mechanical Engineering, Universiti Sains Malaysia (Malaysia)

2Ines-Nathan Creative Research Center (Malaysia)

goheannee@hotail!co, chin"engfeng@#s!y, eloh@#s!y,elissatcling@gail!co

Receive$% &an#ary2'1cce*te$% +ctoer2'1

Abstract"

Purpose" The manuscrit resents an in!estigation into a constraint rogramming-"ase#

genetic algorithm $or caacit% outut otimi&ation in a "ac'-en# semicon#uctor manu$acturing

coman%(

#esign$methodology$approach" )n the $irst stage, constraint rogramming #e$ining the

relationshis "et*een !aria"les *as $ormulate# into the o"+ecti!e $unction( genetic algorithm

mo#el *as create# in the secon# stage to otimi&e caacit% outut( Three #eman# scenarios

*ere alie# to test the ro"ustness o$ the roose# algorithm(

%indings" CPG imro!e# "oth the machine utili&ation an# caacit% outut once the

minimum reuirements o$ a #eman# scenario *ere $ul$ille#( Caacit% oututs o$ the three

scenarios *ere imro!e# "% 1./0, /0, an# 0, resecti!el%(

&esearch limitations$implications" The *or' relates to aggregate lanning o$ machine

caacit% in a single case stu#%( The constraints an# constructe# scenarios *ere there$ore

in#ustr%-seci$ic(

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J%*rn+l % In"*tri+l En&ineerin& +n" M+n+&eent htt:!!"#$"%i$%r&!10$392'!ie$1070

Practical implications"Caacit% lanning in a semicon#uctor manu$acturing $acilit% nee# to

consi#er multile mutuall% in$luence# constraints in resource a!aila"ilit%, rocess $lo* an#

ro#uct #eman#( The $in#ings ro!e that CPG is a ractical an# an e$$icient alternati!e to

otimi&e the caacit% outut an# to allo* the coman% to re!ie* its caacit% *ith uic'

$ee#"ac'(

riginality$'alue"The *or' integrates t*o contemorar% comutational metho#s $or a real

in#ustr% alication con!entionall% reliant on human +u#gement(

(ey)ords" constraint rogramming, genetic algorithm, semicon#uctor caacit% management,

ro#uction lanning

1. Introduction

.++/it l+nnin& +i t% iniie the "i/re+n/ eteen %r&+ni+ti%n /++/it +n" the

r%"*/t "e+n" t% %tiie reen*e$ .++/it l+nnin& in ei/%n"*/t%r in"*tr i

e#treel /h+llen&in& "*e t% it r%"*/t i#, liite" /++/it % re%*r/e +n" *neen

"e+n"$ .%ne*enti+ll, + ei/%n"*/t%r +n*+/t*rin& /%+n nee" t% +l+n/e

heter%&ene%* et % r%"*/t ith "ierent re*ire" tie %r re%*r/e in r%"*/ti%n

(N+*&ht%n, 2005)$

6e%*r/e ti/+ll in/l*"e +/hine, l+%r, %ne, tie, +n" r+ +teri+l$ he re%*r/e /%t

i /%%nl + /%ni"er+le r%"*/ti%n /%t in ei/%n"*/t%r in"*tr$ O thee re%*r/e,

+/hine +re the %t /riti/+l "*e t% their e#enie /%t +n" l%n& +/*iiti%n eri%"$ +

%r the /++/it % e#enie re%*r/e t% e hi&hl *tilie" i thr%*&h +/hine h+rin&$

M+/hine h+re their /++ilit t% /%e ith r%"*/t i#e, hi/h +ll% /h+n&e % %ne

r%"*/t t% +n%ther in the +e +/hine (i*, J%hi M/"%nell, 2004)$ ; ir%in& +/hine

*tili+ti%n, /++/it %*t*t i +#iie", hi/h in ret*rn re*lt in reen*e &+in t% the

/%+n$ One e#+le i ei/%n"*/t%r +el +n" tetin& (+/


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+e" t%/h+ti/ r%&r+in& %"el t% "e/rie the *n/ert+in /++/it +e" %n %er+ll

e*ient ei/ien/$ .hen +n" D* (2012) "i/*e" h% the t%/h+ti/ i#e"-inte&er

r%&r+in& %"el /%*l" e *e" t% "eterine the r%*t /++/it +ll%/+ti%n +n" e#+ni%n

%li/$ S+in+th+n (2000) r%i"e" he*riti/ t% in" ei/ient t%%l r%/*reent l+n +n"

tet their *+lit *in& D+&r+n&i+n rel+#+ti%n$ Phr*


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+n" + /%ntr%ll+le r%/e % inn%+ti%n (;++i *+r, 2010)$ Sin/e the r%le i hi&hl

/%le#, + C i %*&ht t% %le the r%le ei/ientl$

Other n%t+le /%*ter %"el in/l*"e t+* e+r/h, i*l+te" +nne+lin&, +n" +nt /%l%n

%tii+ti%n$ ;il&in +n" i%l* (2009) *e" t+* e+r/h +l&%rith t% %tiie the /++/it

+ll%/+ti%n in the ei/%n"*/t%r in"*tr$ H* Di (2009) "eel%e" + he*riti/ %l*ti%n

+r%+/h +e" %n i*l+te" +nne+lin& t% "eterine the %ti+l +"*tin& "e/ii%n re&+r"in&

r%"*/ti%n re+ll%/+ti%n *n"er l*/t*+tin& "e+n"$ Other e%l*ti%n+r eth%" *e" the +nt

/%l%n %tii+ti%n +n" +rti/le +r %tii+ti%n$

.%*ter %"el, "eite rel+tie ili/it in r%&r+in&, "% n%t &*+r+ntee %ti+l

%l*ti%n$ he +re +r%#i+ti%n te/hni*e in hi/h %l*ti%n *+litie +re inl*en/e" the

rereent+ti%n, +r+eter, +n" r%le "%+in$ he "eel%ent % %e/tie *n/ti%n

nee" t% en/%+ +ll the +/t%r % interet, +rti/*l+rl the re+l-lie r%le$

.%ntr+int r%&r+in& (.P) i %ten inte&r+te" int% /%*ter %"el, */h + C, t% %le

the %re&%in& r%le$ C i + e+r/h eth%" t% i"enti the ne+r %ti+l %l*ti%n %r the

%e/tie *n/ti%n$ .P i + eth%"%l%& %r "e/l+r+tie "e/riti%n +n" %l*ti%n % "ii/*lt

/%in+t%ri+l r%le, +rti/*l+rl in the +re+ % l+nnin& +n" /he"*lin& (;+rt


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3. Case study

.%+n , + *ltin+ti%n+l ;E ei/%n"*/t%r +n*+/t*rin& /%+n l%/+te" in Pen+n&, ith

+r%#i+tel 4,'00 el%ee, + *e" + the /+e t*"$ .%+n *lie /*t%er

r% +r%#i+tel 150 /%*ntrie %rl"i"e$ In 2012, the /%+n +/hiee" + t*rn%er % 5

illi%n E*r%$ .%+n +n*+/t*re r%"*/t, */h + li&ht eittin& "i%"e %r +*t%%tie,

/%n*er, +n" in"*tri+l +li/+ti%n, inr+re" r%"*/t, l+er "i%"e, +n" %ti/+l en%r$

.%+n *e le+" r+e in +n*+/t*rin& /hi +/i&*re 1$ ;E r%/ein& te

Seer+l r%"*/t te ith iil+r r%/e te +re &r%*e" int% r%"*/t +ilie$ M+/hine

/++/itie +re re"%in+ntl h+re" +%n& the r%"*/t +il t% re"*/e the inetent /%t$

Set* tie %r the +/hine /%neri%n, +/hine /++ilit, +n" %ther *t*+ll inl*en/e"

/%ntr+int there%re +re ineit+le$ M+/hine /++ilit reer t% the te/hni/+l +n*+/t*rin&

+ilit % the +/hine t% eet /ert+in r%"*/t e/ii/+ti%n$ he r%"*/ti%n % + r%"*/t

&ener+ll in%le + erie % %er+ti%n %n "ierent +/hine +n" //le tie$ Bhile &ener+ll

the %ttlene/< %er+ti%n liit the %*t*t % the entire r%"*/t, + /h+n&e in the "e+n" %r +

e/ii/ r%"*/t hit the %ttlene/< %er+ti%n, hi/h +e/t the %*t*t % %ther r%"*/t$

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hi t*" ineti&+te +n +r%+/h th+t /+n +#iie %th the %*t*t +n" *tili+ti%n %

l+r&el h+re" +/hine$ he e/ii/ +n*+/t*rin& eri%" r+n&e r% %ne %nth t% i#

%nth$ Pre"i/ti%n % "e+n" %er + eri%" re*ire + h%rt-ter l+nnin& th+t relie %n

/*t%er %re/+t +n" /%itte" %r"er +n" %r< in r%&re (BIP) leel$ >re*ent reii%n

%n /*t%er %r"er i n%r+l e%re /%nir+ti%n$ he +n*+/t*rin& le+" tie +

+r%#i+tel t% eei&*re 2 "ei/t the ree+r/h r+e%r


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>i&*re 2$ 6ee+r/h r+e%ri&*re 3$ In h+e I, +ll the riitie

+ri+le th+t inl*en/e the %e/tie *n/ti%n ere i"entiie" +n" te+ti/+ll /+te&%rie"$

hee +ri+le in/l*"e +/hine ++il+ilit, r%"*/t r%/e "+t+, +n" r%"*/t "e+n"$ he

riitie +ri+le ere then %r*l+te" thr%*&h the "eri+ti%n % the e*+ti%n in h+e t%$

In the thir" h+e, "e/ii%n +ri+le ere "eel%e" +n" t+te"$ he "e/ii%n +ri+le ere

hel" + the "eine" /%ntr+int$ he %e/tie *n/ti%n + "eine" in h+e IG$ he %l*ti%n %

the r%le + e+*re" the %e/tie *n/ti%n hile +tiin& +ll the /%ntr+int$ In the

/++/it +ll%/+ti%n r%le, +/hine *tili+ti%n + %ne % the +in "e/ii%n +ri+le$ he

%r*l+ti%n % +/hine *tili+ti%n +re +l% "e/rie" in >i&*re 3$ he t+n"+r" %r*l+ %r

+/hine *tili+ti%n i e*+l t% +/t*+l h%*r r*n "ii"e" ++il+le %er+tin& h%*r (%%e,

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199')$ In thi t*", the %r*l+ti%n ere %"iie" + h%n in h+e "e%ntr+te" in

>i&*re 3$

he +*ti%n +lie" in %"elin& the .P +re + %ll%:

i$ .*rrent %r< in r%/e (BIP) i n%t /%ni"ere"$

ii$ *e*e tie +n" +teri+l h+n"lin& tie +re either +*e" t% e er% %r +re

in/%r%r+te" t% the r%/ein& tie % the re%*r/e$

iii$ ll /he"*le" "%ntie +re t+ti/ +n" n%t *e/te" t% t%/h+ti/ +ri+ti%n$

i$ he +/hine re+


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5.2. Stage II Constraint "rogramming%#ased genetic algorithm &C'()*

.PC + *e" t% %tiie the /++/it %*t*t$ .PC "e/rie" the inter+/ti%n eteen the

%e/tie *n/ti%n r% the .P +n" the &eneti/ %er+t%r, + h%n in >i&*re 4$

F(g)+n" S(g)rereent the +rent +n" %rin& % + &ener+ti%n (g), ree/tiel$ he in*t+r+eter +re /hr%%%e ie, /r%%er, +n" *t+ti%n r+te$ n initi+l %*l+ti%n %

/hr%%%e % ie N i &ener+te"$ he /hr%%%e i +"e * % + e*en/e % in+r

n*er rereente" Q0 %r Q1$ he len&th % /hr%%%e + +e" %n the n*er %

r%"*/t te *e/te" t% "e+n" /h+n&e, $ E+/h /hr%%%e /%nit the n*er %

&ene th+t rereent the *+ntit % + +rti/*l+r r%"*/t te$ he ie % the &ene %r the

n*er % it *e" t% rereent + +ri+le i i%rt+nt %r the +//*r+/ % the %l*ti%n +n"

the tie nee"e" %r the C t% /%ner&e (H+*t H+*t, 2004)$ lth%*&h 4-it trin&

/%ntri*te +ter /%ner&en/e % +l&%rith (@*% Aeri, 2010), the &ene in thi t*" irereente" 8-it trin&, + the in/re+e" n*er % it %*l" hel re"*/in& *+nti+ti%n

err%r (H+*t H+*t, 2004)$

>i&*re 4$ .%ntr+int r%&r+in&-+e" &eneti/ +l&%rith

/hr%%%e %r i# r%"*/t te i /%ntr*/te" in"i/+tin& 48-it trin&, + h%n in

>i&*re 5$ he %*l+ti%n ere +i&ne" + itne +l*e hi/h + e+l*+te" *in& the

e*+ti%n$ he itne *n/ti%n "e/i"e i the %ttlene/< +/hine h+e een *ll %//*ie" %r

the hi&het /++/it %*t*t % +ll r%"*/t te$

>i&*re 5$ /hr%%%e %r the /++/it %*t*t %tii+ti%n r%le

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he initi+l %*l+ti%n + %"iie" the &eneti/ %er+t%r, n+el, ele/ti%n, /r%%er, +n"

*t+ti%n, t% ir%e itne$ >%ll%in& H+*t +n" H+*t (2004), the t+n"+r" +r%+/h,

r%*lette heel ele/ti%n, + n%r+ll *e"$ E+/h /hr%%%e re/eie" + %rti%n % + r%*lette

heel +//%r"in& t% rel+tie itne$ D+r&er rele/te" %rti%n /%rre%n"e" t% + etter itne

+l*e +n" hi&her /h+n/e % ele/ti%n$ he r%*lette heel + *n +n" the /%rre%n"in&

/hr%%%e + ele/te" hen the +rr% rete" +t %ne % the %rti%n$ he ie %

/hr%%%e %*l+ti%n re+ine" *n/h+n&e" r% %ne &ener+ti%n t% the ne#t$ he r%*lette

heel + *n 10 tie t% et+lih the +e %*l+ti%n ie$ hi et* e+n 10

/hr%%%e ere +e" t% the ne#t &ener+ti%n$

.r%%er +n" *t+ti%n ere ree+te" *ntil +ti+/t%r re*lt + +/hiee"$ P+rti+ll +e"

+n" //le /r%%er ere +lie" (@*% Aeri, 2010)$ P+rti+ll +e" in&le %int

/r%%er + ele/te" + it /+n er%r etter th+n //le /r%%er (.hen Sith, 199')$ In

the +rti+ll +e" in&le %int /r%%er, + /r%%er %int, %r i&*re ')$ M*t+ti%n i e*i+lent t% r+n"% e+r/h it r%le i t% r%i"e + &*+r+ntee th+t the

e+r/h +l&%rith i n%t tr+e" %n + l%/+l %ti*$ >%r the in+r C, thi %er+ti%n

+%*nte" t% /h+n&in& + it r% + 0 t% + 1, +n" i/e er+ (H+*t H+*t, 2004)$ h*, it

trin& *t+ti%n i *e"$ he *t+ti%n % it trin& en*e thr%*&h it li +t r+n"%

%iti%n$ n 8-it &ene + r+n"%l ele/te" r% the /%rre%n"in& &ene %%l$ In the

e#+le h%n in >i&*re 7, the /hr%%%e i *t+te" in it 5th &ene, hi/h h% th+t01000101 i *t+te" t% 01001101 (r+n"%l li it r% 0 &%e t% 1 +n" 1 &%e t% 0)$ .PC

+ terin+te" +ter + e/iie" n*er % &ener+ti%n +n" the et /hr%%%e %*n" in the

%*l+ti%n + /h%en$

>i&*re '$ P+rti+ll +e" in&le %int /r%%er

>i&*re 7$ ;it trin& *t+ti%n

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he %l*ti%n i%l+tin& E*+ti%n 2, 3, +n" 5 + n%t e+ile +n" %*l" e ili/itl re%e"

thr%*&h +/%r e#+le, M+/hine 3 /+n e %er+te" in %th

Oer+ti%n 2 +n" ' /h+n&in& the +teri+l *e" in e+/h %er+ti%n$ h*, the *tilie" h%*r

% M+/hine 3 i the * % h%*r nee"e" r% %th %er+ti%n$ E+/h r%"*/t h+ in"ii"*+l

%er+ti%n l%$ >%r int+n/e the %er+ti%n l% %r Pr%"*/t 1 i 1 3 4 5 7, hile

Pr%"*/t 2 i 1 3 4 5 ' 7 8$ E+/h %er+ti%n i /+rrie" %*t %ne %r %re

+/hine te$ Oer+ti%n 1 in%le t% +/hine te, M+/hine 1 +n" 2, here+ Oer+ti%n

2 %nl in%le %ne +/hine te, M+/hine 3$ he three-%int rel+ti%nhi i i%rt+nt

e/+*e +n r%n& "e/l+r+ti%n %n the r%"*/ti%n +/hine e+iilit %*l" +e/t the re*lt %the +/hine *tili+ti%n "e/ii%n *n/ti%n +n" &ener+te in+li" /++/it %*t*t$

,"eration -achine y"e 'roduct 1 'roduct 2 'roduct 3 'roduct 4 'roduct 5 'roduct +

1M+/hine 1 1 0 1 1 0 0

M+/hine 2 0 1 0 0 1 1

2 M+/hine 3 0 1 0 1 0 1

3M+/hine 4 1 1 1 1 0 0

M+/hine 5 1 1 1 1 1 1

4 M+/hine ' 1 1 0 1 0 1

5 M+/hine 7 1 1 1 1 1 1

' M+/hine 3 0 1 1 1 0 1

7M+/hine 8 1 0 0 1 1 1

M+/hine 9 0 1 1 0 0 1

8 M+/hine ' 0 1 0 0 1 1

1: >e+ile rel+ti%nhi 0: Ine+ile rel+ti%nhi$

+le 1$ Pr%"*/ti%n +/hine e+iilit (Ai,r)

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he t%t+l n*er % h%*r *tilie" %r e+/h +/hine te i +e" %n the *nit er h%*r (=PH),

hi/h "eline+te the *+ntit % the r%"*/t r%"*/e" ithin +n h%*r$ +le 2 h% the &r%

=PH % r%"*/t te r in +/hine te i%r e+/h %er+ti%n$ =PH +rie %r "ierent r%"*/t

th+t r*n %n the +e +/hine te %r %r the +e r%"*/t th+t r*n %n "ierent +/hine

te$ >%ll%in& the /%+n r+/ti/e, the =PH + +"*te" t% +//%*nt %r ei/ien/ l%e

in/l*"in& the "ee/t, /r+ +/hine re+


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r%i"e re+%n+le %l*ti%n$ he ini* "e+n" t% /+l/*l+te +/hine *tili+ti%n i the

in*t +l*e t% .P$ It r%le i t% en*re th+t /*rrent ++il+le +/hine +re +le t% *%rt the

+i/ "e+n" re*ireent$ here+ter, .PC r%i"e the %l*ti%n ith the +#i* /++/it

%*t*t +e" %n "ierent "e+n" /en+ri% (ee +le 3)$ .PC *t +l% *lill the +i/

re*ire" "e+n"$

'roduct y"e-inimum demand &units/wee0* DLt,r -aimum demand &units/wee0* DMt,r

Scenario 1 Scenario 2 Scenario 3

Pr%"*/t 1 50,000 320,000 200,000 775,'5'

Pr%"*/t 2 50,000 93,000 200,000 3'0,000

Pr%"*/t 3 50,000 '2,000 10,000 4'1,700

Pr%"*/t 4 50,000 100,000 10,000 340,000

Pr%"*/t 5 50,000 85,000 10,000 415,530

Pr%"*/t ' 50,000 35,000 10,000 24',240

+le 3$ 6+n&e % "e+n"

hree "e+n" /en+ri% ( 1,1,3)ere t*"ie"$ hee three /en+ri% ere t*"ie" "*e t%

the *n/ert+in +r


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'roduct y"e Scenario 1 Scenario 2 Scenario 3

Pr%"*/t 1 1 1 0

Pr%"*/t 2 1 1 0

Pr%"*/t 3 1 1 1

Pr%"*/t 4 1 1 1

Pr%"*/t 5 1 1 1Pr%"*/t ' 1 1 1

1: "e+n" /+n e *e/te" t% /h+n&e 0: "e+n" i i#$

+le 4$ .h+n&e+ilit % "e+n" ( )

. Results and discussion

+le 5 h% the +/hine *tili+ti%n e%re +n" +ter the ileent+ti%n % .PC, +e" %n

the ineti&+te" "e+n" /en+ri%$ In the in"*tr, the +i/ "e+n" *+ntit i re/%r"e" inthe /++/it l+nnin& re+"heet %r +/hine *tili+ti%n e+l*+ti%n e%re /++/it l+nnin&

*in& the .PC +r%+/h$ he re*ire" *+ntit % +/hine +n" +/hine *tili+ti%n /%*l" e

/+l/*l+te" +e" %n the +the+ti/+l %r*l+ti%n ill*tr+te" in >i&*re 3$ he /%ntr+int %r

e#/e % /++/it /%*l" e i"entiie" %rtin& the er/ent+&e % +/hine *tili+ti%n$

;e%re .PC ileent+ti%n, the +/hine ere n%t *ll *tilie"$ hi %er+ti%n in"i/+te

th+t ith the re*ire" +i/ "e+n", e#/e /++/itie ere till reent in the r%"*/ti%n line$

+il+le +/hine h%*l" e *ll *tilie" t% in/re+e the /++/it %*t*t$ Ileent+ti%n %

.PC in/re+e" the %er+ll +/hine *tili+ti%n %r +ll +/hine +n" %ttlene/< +/hine th+t

h% 100? %//*ie" er%r+n/e$

Aierent "e+n" /en+ri% /le+rl h+e "ierent +/hine te, hi/h +""e" /%ntr+int t%

the /++/it %*t*t$ S/en+ri% 1 h% th+t M+/hine 5, ', +n" 7 +""e" /%ntr+int t% the

/++/it %*t*t, hile M+/hine ' +n" 7 liite" the /++/it %*t*t in /en+ri% 2$ M+/hine 3,

', +n" 7 +""e" /%ntr+int t% the /++/it %*t*t in "e+n" /en+ri% 3$

=%n tetin& %n three "e+n" /en+ri%, re*lt r%e th+t .PC r%i"e" the +r%#i+te

%ti* /++/it %*t*t + ++il+le +/hine ere *ll *tilie"$ +le ' lit the re*lt %

the +r%#i+te %ti+l /++/it %*t*t$

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-achine y"e )vaila#le machine

uantityMoi,t

Scenario1 Scenario 2 Scenario 3

efore )fter efore )fter efore )fter

M+/hine 1 1 17? 44? 59? '1? 28? 51?

M+/hine 2 1 24? 51? 32? 34? 34? 45?

M+/hine 3 1 45? 9'? 72? 74? '1? 100?

M+/hine 4 1 42? 7'? 89? 92? 71? 99?

M+/hine 5 1 44? 100? 4'? 52? 18? 42?

M+/hine ' 1 47? 100? 9'? 100? 81? 100?

M+/hine 7 2 53? 100? 93? 100? 72? 100?

M+/hine 8 1 27? 73? '8? 72? 28? 42?

M+/hine 9 1 22? 49? 33? 3'? 45? 90?

+le 5$ M+/hine *tili+ti%n e%re +n" +ter the .PC ileent+ti%n

'roduct y"e Ca"acity out"ut &units/wee0*

Scenario 1 Scenario 2 Scenario 3

Pr%"*/t 1 95,177 321,773 (200,000)

Pr%"*/t 2 '5,'81 94,039 (200,000)

Pr%"*/t 3 1'2,13' 75,997 219,153

Pr%"*/t 4 138,01' 101,8'8 27,977

Pr%"*/t 5 227,787 110,722 54,182

Pr%"*/t ' 81,307 35,822 42,173

%t+l 770,104 740,221 743,485

(In r+/


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.1. Sensitivity analysis

he re*lt ere e#+ine" ine-t*nin& the ie % /hr%%%e %*l+ti%n N, r%+ilit %

/r%%er (Pc), r%+ilit % *t+ti%n (Pm)+n" n*er % &ener+ti%n It% en*re th+t the ne+r

%ti+l %l*ti%n i re+/he"$ Per%r+n/e + +ee" ith ree/t t% the enitiit tet %

the .PC, +t hi/h ne+r %ti+l %l*ti%n i +/hiee"$

he &ener+ti%n n*er + i#e" +t 100 %r +ll i*l+ti%n$ +le 7 in"i/+te the ee/t %

"ierent .PC +r+eter %n itne +l*e$ E+/h "e+n" /en+ri% h+ ei&ht i*l+ti%n ith

"ierent +r+eter ettin&$ hi&h %*l+ti%n ie ith Pc 0$85 +n"Pm 0$02 r%"*/e" the

hi&het itne +l*e in /en+ri% 1 +n" 3$ S/en+ri% 2 h+ the hi&het itne +l*e +t l%er

*t+ti%n r+te$ >r% thee i*l+ti%n, the l%er %*l+ti%n ie % Pc 0$85 +n" Pm 0$01

+n" re*lte" in %re itne +l*e$ +le 7 h% the et %l*ti%n %r e+/h /en+ri%$

C'() "arameters Pc6 7.85 Pc6 7.

Pm6 7.71 Pm6 7.72 Pm6 7.71 Pm6 7.72

N 10

S/en+ri% 1 725,141 742,203 747,544 742,203

S/en+ri% 2 -789,908 734,4'9 724,'03 728,113

S/en+ri% 3 '39,597 '75,1'5 '45,710 741,034

N 20

S/en+ri% 1 704,550 +9813 '7',100 7'0,'50

S/en+ri% 2 39127 735,79' 731,02' 735,310

S/en+ri% 3 701,979 42127 70',502 737,410

+le 7$ .PC i*l+ti%n re*lt

he er%r+n/e % the et %l*ti%n %r e+/h /en+ri% +re "ei/te" in >i&*re 9(+), () +n" (/)

he /*re &r+h % /en+ri% 1 +n" 2 h% in/re+e +t e+rlier &ener+ti%n (e&innin& t+&e %

n*er % &ener+ti%n), /%+re" ith the /*re in the &r+h % /en+ri% 3$ "r+ti/ rie +

%ere" +r%*n" the 10th &ener+ti%n in >i&*re 9(+) +n" () +n" +t the '1t &ener+ti%n in

>i&*re 9(/)$ he &r+h in"i/+te th+t the et %l*ti%n %r /en+ri% 1, 2 +n" 3 ere %t+ine"

+t the e&innin& % the 23r", 78th, +n" 71t &ener+ti%n, ree/tiel$

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(+) S/en+ri% 1

() S/en+ri% 2

(/) S/en+ri% 3

>i&*re 9$ Per%r+n/e &r+h % %ti+l %l*ti%n +e" %n three "e+n" /en+ri%

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he /%+ri%n +n+li h% th+t the r*n tie + h%rter +n" the re*lt ere etter ith

hi&her *t+ti%n r+te$ >%r int+n/e, >i&*re 10(+) +n" () in /en+ri% 2 h% er%r+n/e

&r+h ith "ierent *t+ti%n r+te *t e*i+lent /r%%er r+te +n" %*l+ti%n ie$ Cr+h

in >i&*re 10(), hi/h h+ + hi&her *t+ti%n r+te, h% th+t the /*re t+rte" t% in/re+e +t

the e+rlier 35th &ener+ti%n /%+re" ith >i&*re 10(+), here &r+h in/re+e" +t the ''th

&ener+ti%n$

(+)

()

>i&*re 10$ he ee/t % *t+ti%n r+te %r (+) Pm 0$01, () Pm 0$02

>i&*re 11(+) +n" () /%+re the er%r+n/e &r+h *n"er "ierent %*l+ti%n ie, ith

e*i+lent /r%%er r+te$ he i&*re rele/t th+t the /*re %r %th er%r+n/e &r+h

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in/re+e" +t +l%t the +e &ener+ti%n eri%", +r%#i+tel +t the 50th$ H%eer, the

itne +l*e %t+ine" + */h hi&her hen the %*l+ti%n ie + l+r&er, hi/h *&&et

th+t l+r&er %*l+ti%n ie r%"*/e etter %l*ti%n /%+re" t% %ne ith + +ller ie$ =n"er

"ierent /r%%er r+te +n" iil+r *t+ti%n r+te +n" %*l+ti%n ie, the er%r+n/e &r+h

+ttern ere +l%t iil+r (>i&*re 12(+) +n" ()), hi/h rele/t th+t /h+n&e in /r%%er

r+te h+ n% ee/t %n the *+lit % %l*ti%n$

(+)

()

>i&*re 11$ he ee/t % %*l+ti%n ie %r (+) N 10, () N 20

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(+)

()

>i&*re 12$ he ee/t % /r%%er r+te %r (+) Pc 0$7, () Pc 0$85

8. Conclusion

Pr%"*/t i#e +n" *n/ert+in "e+n", hi/h +re /+*e" "r+ti/ /h+n&e in r%"*/t

inn%+ti%n, h+e +"e ei/ient +/hine /++/it +ll%/+ti%n e#treel "ii/*lt$ M%ti+te"

the r%le +/e" ei/%n"*/t%r +n*+/t*rer, + .PC +r%+/h + "eel%e" t%

+r%#i+te +n %ti+l %l*ti%n %r /++/it %*t*t$ In /%ntr+t ith the /%nenti%n+l t*"ie,

the r%%e" +r%+/h e#li/itl /+t*re + three-%int (r%"*/tre%*r/e%er+ti%n)

rel+ti%nhi +n" l+ter +ll% the +ll%/+ti%n % ri&ht i# % r%"*/t t% +#iie the /++/it

%*t*t$ O*r /+e t*" "e%ntr+te th+t the .PC ei/ientl %le" the r%le$ heer%r+n/e +n" enitiit +n+li % .PC h% th+t the r%%e" +l&%rith + +le t%

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"eterine the hi&het /++/it %*t*t in +ll three /en+ri%$ Si&nii/+ntl ir%e" +/hine

*tili+ti%n + +l% +/hiee"$ he r%%e" +r%+/h /+n e e+il e#ten"e" t% %ther %re

/%le# /+e /en+ri%, */h + ith l%n&er r%*tin& %er+ti%n % l+r&er n*er % +/hine

te$

he *t*re %rirt, ne r+/ti/+l eleent +re t% e

/%ni"ere" in the te in/l*"in& e#itin& r%"*/t inent%r, "ierent l+nnin& eri%", r%it

+r&in +n" r%"*/t ri%riti+ti%n$ Se/%n" i t% e#ten" .PC int% +/t*+l +li/+ti%n hi/h

re*ire %t+re inte&r+ti%n, h*+n-+/hine inter+/e "ei&n +n" +n+&eent te$

>in+ll, %re ei/ient &eneti/ +l&%rith, */h "ierenti+l e%l*ti%n %r %ther e+r/h +l&%rith

/+n e e#l%re", ith the in/re+e in r%le /%le#it$

)c0nowledgments

hi ree+r/h i %n%re" *ll =SM PER &r+nt (n%: 910345) +n" >6CS (n%: '07127')$

References

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@%*, >$, B+i/

a constraint programming-based genetic algorithm for capacity output optimization

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