bu rosa tugas akhir.docx
TRANSCRIPT
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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