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TEMA: MODELO DE TRANSBORDO



UNIVERSIDAD NACIONAL JOSE FAUSTINO SANCHEZ CARRIONE.A.P INGENIERIA INDUSTRIAL

ESCULA PROFESIONAL DE INGENIERIA INDUSTRIAL

TEMA:

MODELO DE TRANSBORDO

DOCENTE:

Dr. ALCIBIADES SOSA PALOMINO

INTEGRANTES:

MEDINA CATIRI, ANDREA

MEJIA MORALES, WINSTON

ROJAS VELARDE, MAYUMI

VASQUEZ FERNANDEZ, FERNANDO

HUACHO – PERÚ

2015

INVESTIGACION DE OPERACIONESPágina 1




CONTENIDO

1. INTRTODUCCION:...................................................................................................... 4

2. OBJETIVO GENERAL:................................................................................................ 6

. MARCO TEORICO:......................................................................................................6

!. EL PROBLEMA DE TRANSBORDO:........................................................................7

!.1. SITUACIONES:..................................................................................................... 7

!.2. EL PROBLEMA:.................................................................................................... 8

". CONCLUSIONES Y RECOMENDACIONES.........................................................14

#. BIBLIOGRAFIA:.......................................................................................................... 15





DEDICATORIA:

E$%& %r'(')* +' $-* &'(*r'-* /*0 /+* &$3&r4*

5 '+60/*, 7*r &* &$ D&-/'-* 7'r' 0&$%r' /'$' -&

&$%-*$ 5 0&$%r' r&890 $&0-* & 30 7r0/7'

'7*r%'r 0&*$ /*0*/&0%*$ 5 %;/0/'$,

&)*r'0-* '$6 ' /'-'- -& 0&$%r*$ 7r*3&$*0'&$.





1. INTRTODUCCION:

E Pr*(&' -& Tr'0$(*r-*, I0%&r%r'0$7*r%& * R&&('r<& &$ 0' 'r'/90 -&

*-&* *r80' -& %r'0$7*r%& <& $& ')$%' ' ' 7*$(-'- /*=0 -& %r'0$7*r%'r

0-'-&$ &-'0%& 0*-*$ 3&0%&$, -&$%0*$ 5 %r'0$%*r*$, &0%r'$ & *-&*

%r'-/*0' $** 7&r%& &06*$ -r&/%*$ -&$-& 0*-*$ 3&0%&$ +'/' 0*-*$ -&$%0*$.

E>$%& ' 7*$(-'- -& r&$*&r 0 *-&* -& %r'0$(*r-* &-'0%& '$ %;/0/'$

%r'-/*0'&$ -& r&$*/90 -& *-&*$ -& %r'0$7*r%& 5 &$%& 7r*/&-&0%* $& ('$'

&0 ' 7r&7'r'/90 -& %'('-* 0/' +'/&0-* $* -& 'r%3/*$ /*0*/-*$ /*0 &

0*(r& -& '*r%8'-*r&$, *$ /'&$ -&(&0 $&r 8'&$ ' ' $'%*r' -& '$

*3&r%'$ -& *$ 0*-*$ -& *3&r%' 7r' 5 -& /*&3/&0%& /&r* ?@ &0 '%&r' -& /*$%*$.

S0 &('r8* ' r&$*/90 -& 0 7r*(&' -& %r'0$(*r-* +'/&0-* $* -& *$

'8*r%*$ -& r&$*/90 -& *-&*$ -& %r'0$7*r%& &$ 0' -&' '0'/r90/', %&0&0-*

&0 /&0%' ' 7*$(-'- -& '//&$* ' +&rr'&0%'$ -& /97%* /'7'/&$ -& r&$*&r

7r*(&'$ /*7&)*$ 0' &4 *-&'-*$ &-'0%& '$ %;/0/'$ -& programación

lineal. L' 7*r%'0/' -& *$ *-&*$ -& %r'0$(*r-* '&0%' /*0 '$ 0&'$

%&0-&0/'$ 8*('&$ -& 8&$%90 -& /'-&0'$ -& '('$%&/&0%*, &0 '$ /'&$ $&

-&(&0 -& *7%4'r *$ 3)*$ *86$%/*$ -& 7r*-/%*$ %&0&0-* &0 /&0%' '

7*r%'0/' -& 04'r *$ /*$%*$, '$&8r'r -$7*0(-'- -& 0-'-&$ 5

r&/*0*/&0-* ' 7*r%'0/' -& *$ /&0%r*$ -& -$%r(/90 &0 ' (=$<&-' -&

&<(r* &0%r& '$ 7r*5&//*0&$ 5 ' r&'-'- -& ' -&'0-'.

M&-'0%& &$%& /*0/&7%* $& 7'0%&'r' 0 7r*(&' '7/'-* ' 0 /'$* r&' /*0 *

/' $& -&*$%r'r' ' %-'- -& &$%-* -& &$%& %&', /'0-* 03&r& ' '$

&7r&$'$ 7'r' ' r&-//90 -& /*$%*$ 5 '>4'r*0 -& '$ %-'-&$.

I.


http://www.ingenieriaindustrialonline.com/herramientas-para-el-ingeniero-industrial/investigaci%C3%B3n-de-operaciones/programaci%C3%B3n-lineal/







2. OBJETIVO GENERAL:

E *()&%* &0 & 7r*(&' -& %r'0$(*r-* &$ -&%&r0'r /0%'$ 0-'-&$

-&(&r0 &('r/'r$& 7*r /'-' 0* -& *$ 'r/*$ -& ' r&-, -& '0&r' <& %*-'$ '$

-&'0-'$ -&$%0*$ $& $'%$3'8'0 ' /*$%* -& %r'0$7*r%& 60* 7*$(&.

3. MARCO TEORICO:

S*0 *-&*$ <& r&$%'0 -& 0' &>%&0$90 -& *-&* -& %r'0$7*r%&$ &0 -*0-& $&

& '8r&8' 0*-*$ 0%&r&-*$, -*0-& &$%*$ 0*-*$ '0 ' r&7r&$&0%'r *$ %r'0$(*r-*$.

SIENDO:





5. EL PROBLEMA DE TRANSBORDO:

U0 7r*(&' -& %r'0$7*r%& 7&r%& $9* &06*$ -r&/%'&0%& -&$-& *$ 70%*$

-& *r8&0 ' *$ 70%*$ -& -&'0-'. E0 /+'$ $%'/*0&$, $0 &('r8*, &>$%& '

7*$(-'- -& +'/&r &06*$ ' %r';$ -& 70%*$ 0%&r&-*$ ?70%*$ -& %r'0$(*r-*.

E0 &$%& /'$* $& +'(' -& 0 7r*(&' -& %r'0$(*r-*.

A /*0%0'/90 &r&*$ /** ' $*/90 -& 7r*(&' -& %r'0$(*r-* 7&-& $&r

&0/*0%r'-' ' %r';$ -& 0 7r*(&' -& %r'0$7*r%&.

D&30r&*$ *$ 70%*$ -& *3&r%' /** '<&*$ 70%*$ -&$-& -*0-& $9* $& 7&-&

-&$7'/+'r 0-'-&$. S'r&0%&, 0 70%* -& -&'0-' &$ 0 70%* -*0-& $9* $&

7&-&0 r&/(r 0-'-&$. U0 70%* -& %r'0$(*r-* &$ 70%* <& 7&-& r&/(r 5 &0'r

0-'-&$ ' *%r*$ 70%*$.

5.1. SITUACIONES:

E0'r 0 (&0 -&$-& 0*$ 70%*$ -& *r8&0 ' 0*$ 70%*$ -& -&$%0* 7&r* 7-&0-*

7'$'r 7*r 70%*$ 0%&r&-*$.





R&/*0*/& <& &0 ' -' r&' ' &/&$ r&$%' $ &/*09/* &0'r &r/'-&r6'$ '

%r';$ -& 70%*$ 0%&r&-*$ &0 8'r -& +'/&r*$ -r&/%'&0%& -&$-& & *r8&0 '

-&$%0*.

M*-&'r &-'0%& 7r*8r''/90 0&' & 7r*(&' -& %r'0$(*r-* &$(*4'-* &0 '

$8&0%& 38r'.

5.2. EL PROBLEMA:

U0 0&r* +' <&-'-* '%r'7'-* &0 0' 0', ' &0%r'-' ' ' 0' $& &0/&0%r'

(/'-' &0 & 0*-* 1, $& /*0*/& -& '0%&'0* <& & 0&r* 7&r'0&/& '%r'7'-* &0

& 0*-* , 7'r' &8'r ' -/+* 0*-* +'5 <& '%r'&$'r 0' r&- -& %=0&&$ <& '0

/*0&/%'-*$ &0%r& $6. E %&7* -& -' <& & <&-' ' 0&r* $0 r&/(r '>* &$

/'-' &4 &0*r 5 $& +'/& 0-$7&0$'(& +''r ' r%' -& '//&$* ' 0*-* $/*r%'. L'$ -$%'0/'$ &0%r& 0*-*$ -& ' 0' $& &0/&0%r'0 &0 ' $8&0%& 8r3/'

-'-'$ &0 /&0%*$ -& &%r*$. F*r& 0 *-&* -& %r'0$(*r-* 5 r&$&' &-'0%&

/'<&r 7'<&%& -& +&rr'&0%'$ -& 0&$%8'/90 *7&r'%' <& 7&r%' &$%'(&/&r

' r%' $ /*r%' 7'r' 7*-&r '$6 '>'r ' 0&r*.





VARIABLES DE DECISIÓN

E 0*(r& -& '$ 'r'(&$ &0 &$%& /'$* 7*/* 7*r%', -'-* <& -& $&r &$/*8-'

7'r' ' $*/90 ($/' &$* $803/' $7&&0%& <& $&r &7&'-' /** r%' 7'r'

r ' r&$/'%'r ' 0&r*, $0 &('r8* 0'-' %&0& -& '* & <& $& & 7&-' '$*/'r

/*0 & &06* -& 0-'-&$ -&$-& ' &0%r'-' -& ' 0' +'/' & 0&r*, 7*r &0-&

7&-& $8&rr$& &$%& /** 0*(r& -& '$ 'r'(&$. Cantidad de unidades

enviadas desde el nodo i hacia el nodo j".

12 ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* 1, +'/' & 0*-* 2

13 ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* 1, +'/' & 0*-*

23 ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* 2, +'/' & 0*-*

2" ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* 2, +'/' & 0*-* 32 ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* , +'/' & 0*-* 2

3" ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* , +'/' & 0*-*

35 ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* , +'/' & 0*-* !

"# ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* , +'/' & 0*-* "

"$ ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* , +'/' & 0*-* #

5" ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* !, +'/' & 0*-*

5# ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* !, +'/' & 0*-* "

5$ ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* !, +'/' & 0*-* #

5% ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* !, +'/' & 0*-*

#$ ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* ", +'/' & 0*-* #

#& ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* ", +'/' & 0*-*

$# ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* #, +'/' & 0*-* "

$% ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* #, +'/' & 0*-*

$& ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* #, +'/' & 0*-*

%$ ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* , +'/' & 0*-* #

%& ! C'0%-'- -& 0-'-&$ &0'-'$ -&$-& & 0*-* , +'/' & 0*-*

RESTRICCIONES

R'()*+,,+-'( /' O'*) D'/





H'5 <& r&/*r-'r <& & *()&%* -& &$%& *-&* &$ ' /*0$&//90 -& 0 7'0 -&

r%' <& 0*$ 7&r%' &0/*0%r'r ' 0&r* * $ 7r*0%* 7*$(& ' r&/*rr&r '

-$%'0/' 60' 7*$(&, 7*r &0-& ' /'& 7'r' 7'0%&'r & *-&* /** $ 3&$& -&

%r'0$(*r-* &$ &$%'(&/&r 0' -&'0-' 5 *3&r%' 8' ' ' 0-'- ?1.

12 4 13 ! 1

#& 4 $& 4 %& ! 1

R'()*+,,+-'( /' B,'

12 4 32 6 23 6 2" ! 0

13 4 23 6 32 6 3" 6 35 ! @

2" 4 3" 4 5" 6 "# 6 "$ ! @

35 6 5" 6 5# – 5$ – 5% ! @

"# 4 5# 4 5$ 6 #$ – #& ! @

#$ 4 "$ 4 5$ 4 %$ – $# – $% – $& ! @

$% 4 5% – %& ! @

E0 7''(r'$ $&0/'$: T*-* * <& &0%r' ' /'-' 0*-* &$ 8' ' * <& $'& -& ;FUNCIÓN OBJETIVO

7MIN ! "12 4 213 4 223 4 $2" 4 "32 4 &3" 4 #35 4 1"# 4 5"$ 4 25" 4 "5# 435$ 4 25% 4 1#$ 4 5#& 4 "$# 4 3$% 4 5$& 4 2%$ 4 $%&

INGRESANDO LOS DATOS A 8IN9SB

INVESTIGACION DE OPERACIONESPágina




SOLUCIÓN OBTENIDA MEDIANTE 8IN9SB

INVESTIGACION DE OPERACIONESPágina 1!




L' r%' $ /*r%' 7'r' r&$/'%'r ' 0&r* %&0& /** -$%'0/' %*%' 1"@@ &%r*$

?-'-* <& '$ -$%'0/'$ &$%'('0 -'-'$ &0 /&0%*$ -& &%r*$ 5 &$ %' /** $&

&$%r' &0 ' $8&0%& 8r3/'.





#. CONCLUSIONES RECOMENDACIONES

CONCLUSIONES:

S& r&'4'r* & 7r*(&' %4'0-* & $*3%'r& WINQSB

E ;%*-* %4'-* &$ & -90&*.

L' r%' $ /*r%' 7'r' r&$/'%'r ' 0&r* %&0& /** -$%'0/' %*%' 1"@@

&%r*$

RECOMENDACIONES:

H'/&r &$%-*$ '-/*0'&$ 7'r' &r 7*$(&$ r%'$ &)*r&$ 7'r' 7r&&0r 3%r*$ '//-&0%&$.





$. BIBLIOGRAFIA:

• Cr5, T*05 ?2@11. !@ /*$'$ <& +'5 <& $'(&r $*(r& '%&%/'$. E-. Ar&.

• +'/+5'0, L. ?1#. A 7*50*' '8*r%+ 0 0&'r 7r*8r'08 2@. S*&%

M'%+. D*'-5.

• L**(', N.P. L0&'r Pr*8r'08: A0 0%r*-/%*r5 '0'5$$. M/Gr'H,

N& Y*r, 1"

• U0&r$-'- P&r'0' U090 B(*%&/' C&0%r' (r* 0=&r* @.@@12!K312

Pr*8r''/90 0&'.

• T&$$ D&%&r0'/90 -& /*$%* &0 '6/*'$ ' 0& 0'/*0' U0&r$-'- J*$;

F'$%0* S0/+&4 C'rr90 E$/&' -& I08&0&r',2@1

8EB:

;))<(:=='(.>+?+<'/+.-*@=>+?+=P*-@*,+C3B3+'

;))<:==>>>.+@'+'*++/()*+-+'.,-=;'**+')(6<*6'6+@'+'*-6+/()*+=+'()+@,+C3B36/'6-<'*,+-'(=

C3A&)-/-6(+<'=

;))<:==>>>.--@*+(.,-=)*-($5=')-/-6(+<'6++,+-=')-/-6(+<'6++,+-2.(;)

;))<:==>>>.+'()+@,+-/'-<'*,+-'(.')=')-/-(+<'.;)

;))<:==>>>.+.)(.,=,*+=IOUAI=(+<'200362.</


https://es.wikipedia.org/wiki/Programaci%C3%B3n_lineal

http://www.ingenieriaindustrialonline.com/herramientas-para-el-ingeniero-industrial/investigaci%C3%B3n-de-operaciones/m%C3%A9todo-simplex/



http://www.monografias.com/trabajos75/metodo-simplex-maximizacion/metodo-simplex-maximizacion2.shtml


http://www.investigaciondeoperaciones.net/metodo_simplex.html

http://www.inf.utfsm.cl/~mcriff/IOUAI/simplex2003-2.pdf

https://es.wikipedia.org/wiki/Programaci%C3%B3n_lineal






http://www.investigaciondeoperaciones.net/metodo_simplex.html

http://www.inf.utfsm.cl/~mcriff/IOUAI/simplex2003-2.pdf

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