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Pemrograman Non

Linier(NLP)

Semester Ganjil 2013/2014

1/31/16 Dr. Rahma itriani! S.Si.! ".S# 1

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Konsep NLP

"en#ari nilai $ari s%at% &e%'ah e&%t%sanx1, ...!xn

$ari &ermasalahan

ma* (min)z +,(x1!...xn)

s.t. g1(x1!...*n) (-!+!)b1.

.

.

gm(x1!...xn) (-!+!)bm$i manaz $an gi! i + 1! ...! n s%at% ,%ngsi ang non

linier. Dim%nginan masimisasi/minimisasi tan&aen$ala

1/31/16 Dr. Rahma itriani! S.Si.! ".S# 2

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Perbedaan antara NLP danPemrograman Linier (LP)

Himpunan Konveks (Convex set):

him&%nan titititi S $i mana sem'arang&asangan titi $i $alam him&%nan S

$ih%'%ngan oleh garis ang sel%r%h titi&a$a garis terse'%t j%ga $i S

1/31/16 Dr. Rahma itriani! S.Si.! ".S# 3

(a) dan (b) himpunan

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Defnisi daerah easibe (feasible region):

im&%nan titi (x1!...xn) ang memen%hisel%r%h men$ala

1/31/16 Dr. Rahma itriani! S.Si.! ".S# 4

Defnisi sousi optima bagi NLP

as%s mas

as%s min

S%at% titi $i feasible region $imana

nt% sem%ax$i feasibleregion

S%at% titi $i feasible region $imana

nt% sem%ax$i feasibleregion

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Di $alam LP $engan $aerah ,easi'elang 'er%&a him&%nan ones!sol%si o&timal a$alah salah sat% $ari

titi estrim (titi &ojo)

Di $alam NLP! alal%&%n $aerah,easi'el 'er%&a him&%nan ones!

sol%si o&timal 'el%m tent% &a$a titiestrim (titi &ojo)

1/31/16 Dr. Rahma itriani! S.Si.! ".S# 5

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ontoh 1

7ia $ig%naan K%nit alat $an L orangtenaga erja! maa s%at% &er%sahaan$a&at mem&ro$%si KL%nit s%at% &ro$%.

7ia alat $a&at $i'eli 84 &er %nit! tenagaerja har%s $i'aar 81/orang! $an $imiliimo$al 89 %nt% mem'eli alat $an

mem'aar tenaga erja! 'agaimana&er%sahaan ta$i memasim%man j%mlah'arang ang aan $i&ro$%si:

1/31/16 Dr. Rahma itriani! S.Si.! ".S# 6

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1/31/16 Dr. Rahma itriani! S.Si.! ".S# ;

%ngsi o'eti, memasim%man j%mlah&ro$%si se'agai ,%ngsi $ari alat $an

tenaga erjaen$ala mo$al! $an non negati

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ontoh 2

as%s $i mana ,%ngsi o'eti, 'er%&a ,%ngsi%a$rati ang aan $imasim%man! $an$aerah ,easi'el a$alah selang tert%t%& $i

antara 0 sam&ai $engan 1.

1/31/16 Dr. Rahma itriani! S.Si.! ".S# 9

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Daerah ,easi'el 'er%&a selang

?iti estrim sehar%sna a$alahx=0 $anx=1

=an teta&i sol%sina a$alahx+ ang '%an titiestrim

1/31/16 Dr. Rahma itriani! S.Si.! ".S# @

Garis

iso&ro

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Astrem%m Loal(mas/min)

S%at% titi ,easi'el x+ (x1!... !xn)

a$alah titi masim%m loal jia

B nt% relati, e#il $an sem'arangtiti ,easi'el x!+ (x1!... !xn) $i mana

1/31/16 Dr. Rahma itriani! S.Si.! ".S# 10

>erla%

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Astrem%m Loal(mas/min)

S%at% titi ,easi'el x+ (x1!... !xn)

a$alah titi minim%m loal jia

B nt% relati, e#il $an sem'arangtiti ,easi'el x!+ (x1!... !xn) $i mana

1/31/16 Dr. Rahma itriani! S.Si.! ".S# 11

>erla%

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Astrem%m Loal(mas/min)

nt% s%at% LP masim%m/minim%mloal &asti sol%si o&timal! teta&i ti$a%nt% NLP

1/31/16 Dr. Rahma itriani! S.Si.! ".S# 12

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ontoh 3

%ngsi o'eti, non linier $engan $aerah,easi'el 'er%&a selang tert%t%& $i antara0 sam&ai $engan 10

1/31/16 Dr. Rahma itriani! S.Si.! ".S# 13

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?iti = $an > a$alah titi masim%m loal

=an teta&i hana ang mer%&aan sol%sio&timal arena 'ersi,at masim%m glo'al

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NLP ti$a mem&%nai as%msi a$iti,$an &ro&ortionalitas se&erti $i $alamLP

Pa$a LP jia nilai &e%'ah e&%t%sanx$inaian sat% %nit! maa ,%ngsio'eti, aan meningat/men%r%n

se#ara &ro&orsional ?i$a 'erla% 'agi NLP

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ontoh 4

Di'erian NLP 'eri%t ini

1/31/16 Dr. Rahma itriani! S.Si.! ".S# 16

7iax$i&er'esar 2 ali li&at! ontri'%si terha$a&

C ti$a aan 2 ali li&at ata%&%n eli&atanna.