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  • 7/25/2019 BU ROSA TUGAS AKHIR.docx

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    TUGAS AKHIR

    OPERATION RESEARCH

    NAMA :

    Putri Citra Kusuma Dewi / 140!1"41

    U#i$ersitas Atma %a&a '()&a*arta

    !01"

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    SOAL 1

    +e ,(#$ert t-e .i#ear r()rammi#) r(.em i#t( t-e ,a#(#i,a. r(m2 T( a,,(m.is- t-is3

    we wi.. er(rm t-e (..(i#) stes:

    I#tr(u,e resiua. $aria.e S i 5 0 i#t( t-e ,(#strai#ts ( r(m 6

    I#tr(u,e reu#a#t $aria.eSi 5 0 i#t( t-e ,(#stra#ts ( r(m 5

    78 1 X

    1 9 ! X

    2 ma

    1X1 9 !

    X2 9 1

    S1 8 ;

    1 X

    1 9 1 X

    2 9 1 S

    2 8 4

    N(w we ,a# ,(#stru,t a# i#itia. sim.e ta.eau:

    1 x2 s1 s! ?ma@ 1 ! 0 0 0

    s1 1 ! 1 0 ;

    s! 1 1 0 1 4

    +e i#sert i#t( t-e asisX

    2 2 +e i# a .ea r(w:

    8 mi# {iip} 8 mi# {5

    2 34}85

    2

    iip B 0

    +e wit-raw r(m t-e asisS1 2 +e ,(#stru,t a sim.e ta.eau :

    1 x2 s1 s! ?ma@ 0 0 1 0 ;

    s1 1/! 1 1/! 0 ;/!

    s! 1/! 0 1/! 1 /!

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    Si#,e i# t-e (e,ti$e u#,ti(# r(w t-ere is #( #e)ati$e ,(ei,ie#t ?e,et R,(.um#s@3

    we -a$e (u# t-e (tima. (i#t2

    Si#,e t-e (..(wi#) ,(#iti(# is satisie:

    dN 5 0

    IN : ? d

    N @ 8 0

    T-e (tai#e (timum -as a# a.ter#ati$e2 a.ue ( t-e (e,ti$e u#,ti(# at t-e (tima.

    (i#t : ;

    SOAL 2

    +e ,(#$ert t-e .i#ear r()rammi#) r(.em i#t( t-e ,a#(#i,a. r(m2 T( a,,(m.is- t-is3

    we wi.. er(rm t-e (..(i#) stes:

    I#tr(u,e resiua. $aria.e

    S i5 0 i#t( t-e ,(#strai#ts ( r(m 6

    I#tr(u,e reu#a#t $aria.eSi 5 0 i#t( t-e ,(#stra#ts ( r(m 5

    78! X

    1 9 1 X

    2 ma

    X1 9 1

    X2 9 1

    S1 8 10

    ! X

    1 9 0 X

    2 9 1 S

    2 8 40

    N(w we ,a# ,(#stru,ts a# i#itia. sim.e ta.eau:

    x1 ! s1 s! ?ma@ ! 1 0 0 0

    s1 1 1 1 0 10

    s! ! 0 0 1 40

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    +e i#sert i#t( t-e asisX

    1 2 +e i# a .ea r(w:

    8 mi# {iip} 8 mi# {103!0}8 10

    iip B 0

    +e wit-raw r(m t-e asisS1

    2 +e ,(#stru,t a sim.e ta.eau :

    1 ! s1 s! ?ma@ 0 1 ! 0 !0

    s1 1 1 1 0 10

    s! 0 ! ! 1 !0

    Si#,e i# t-e (e,ti$e u#,ti(# r(w t-ere is #( #e)ati$e ,(ei,ie#ts ?e,et R,(.um#s@3

    we -a$e (u# t-e (tima. (i#tF

    Otima. P(i#t :X

    1 8 10 3X

    2 8 0 ?a.ue ( t-e (e,ti$e u#,ti(# at t-e (tima.

    (i#t : !0@

    SOAL 3

    +e ,(#$ert t-e .i#ear r()rammi#) r(.em i#t( t-e ,a#(#i,a. r(m2 T( a,,(m.is- t-is3

    we wi.. er(rm t-e (..(i#) stes:

    I#tr(u,e resiua. $aria.e S i 5 0 i#t( t-e ,(#strai#ts ( r(m 6

    I#tr(u,e reu#a#t $aria.eSi 5 0 i#t( t-e ,(#stra#ts ( r(m 5

    78 X

    1 9 ! X

    2 ma

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    2X1 9 1

    X2 9 1

    S1 8 !

    X

    1 9 4 X

    2 1 S

    2 8 1!

    Si#,e t-ere are ,(#strai#ts ( t-e (rm 5 a# ?(r@ 8 i# t-e (ri)i#a. s&stem (

    ,(#strai#ts3 t-e# we -a$e t( i#tr(u,eartificial $aria.esRi 5 0 i#t( su,-

    ,(#strai#ts2 T-e s(.uti(# met-( (r t-is *i# ( .i#ear r()rammi#) r(.em is ,a..e

    two-phase.

    78 X

    1 9 ! X

    2 ma

    2X1 9 1

    X2 9 1

    S1 8 !

    X

    1 9 4 X

    2 1 S

    2 8 1!

    Phase I

    N(w we ,a# ,(#stru,t a# i#itia. sim.e ta.eau:

    1 x2 s1 S! R1 ?ma@ ! 0 0 0 0

    s1 ! 1 1 0 0 !

    R1 4 0 1 1 1!

    +e -a$e t( wit-raw a.. t-e aui.iar& $aria.es r(m t-e asis a# )et ri ( (siti$e,(ei,ie#ts i# t-e aui..ar& (e,ti$e u#,ti(# ?O=@ ? as t-e tas* (r P-ase I is a

    mi#imum r(.em@2

    +e i#sert i#t( t-e asisX

    2 2 +e i# a .ea r(w:

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    8 mi# {iip} 8 mi# {!3}8 !

    i

    ipB 0

    +e wit-raw r(m t-e asisS1 2 +e ,(#stru,t a sim.e ta.eau :

    1 x2 s1 S! R1 ?ma@ 1 0 ! 0 0 4

    s1 ! 1 1 0 0 !

    R1 ; 0 4 1 1 4

    T-e (e,ti$e u#,ti(# ( t-e r(.em is u#(u#e2