Documents.tips Programacion Dinamica

8/19/2019 Documents.tips Programacion Dinamica

1/23

CONTENID

INTRODUCCIÓN..................................................................................................................3

OBJETIVOS...........................................................................................................................4

OBJETIVO GENERAL DEL TEMA:................................................................................4

OBJETIVOS ESPECÍFICOS DEL TEMA:........................................................................4

PROGRAMACIÓN DINÁMICA...........................................................................................5

MODELOS DE PROGRAMACIÓN DINÁMICA................................................................7


2/23

INTRODUCCIÓN

M"#$%& '(%)*+,-& + '(%/(-,-#02 ,-+,0#- ++(,02-2 &%*"#0%2+& "+ (+'+(#"+2 +2

*- 6%(,"*-#02 + *%& '(%)*+,-& - (+&%*+( +2 +* '(0,% '+(9%% % +-'-. U2- -*+(2-0-

+& #%2&("0( "2 20#% ,%+*% #%,'*+% "+ +2/- "2 /(-2 #%2;"2% + -(0-)*+& 02+--&

'%( +-'-& + 02+(2-*0


3/23

OBJETIVOS

OBJETIVO GENERAL DEL TEMA:

R+&%*+( '(%)*+,-& "&-2% +* ,%+*% + '(%/(-,-#02 D02,0#- +2 *- #"-* &+

)-&-( +2 *- )&"+- + "2- 6"2#02 /+2+(-* + %% +* &0&+,- *- #"-* #",'- #%2

*%& (+"0&0%& @ 2+#+&0-+& +2 *- +,'(+&-.

OBJETIVOS ESPECÍFICOS DEL TEMA:

• P(%)*+,-& +2 #"-*+& '%-,%& -'*0#-( '(%/(-,-#02 D02,0#-.• I+2060#-( *%& 06+(+2+& ,%+*%& + '(%/(-,-#02 02,0#-.

• E&-)*+#+( *%& (+"+(0,0+2%& '-(- -)-&+#+( *-& 2+#+&0-+& +2 *- +,'(+&-


4/23

+* ,%+*-% + '(%)*+,-& + '(%/(-,-#02 02,0#- 2% &0/"+ "2- 6%(,- +&2-(. A&9

'-(- #-- '(%)*+,- &+( 2+#+&-(0% +&'+#060#-( #-- "2% + *%& #%,'%2+2+& "+

#-(-#+(0


5/23

L%& 2%%& (+'(+&+2-2 L"/-(+& % #0"-+& +2 *- "+ &+ +2#"+2(- +* #"-* &+ %,+ *-

("- #%2+20+2+,+2+ >P(%)*+,- &%)(+ 0-;+(%? P-(,+(% +2 *- #"-* 020#- +* P+&% &%)(+ +* 0'% + -(9#"*% "+ &+ +2#"+2(- +2 *-

,%#$0*- >P(%)*+,- &%)(+ ,%#$0*-?

V"ri"(#e de deci%i* &d': +& +* -#% + *- %,- + "2- +#0&02 + #"-2% &+ - - '(%"#0(

% - (+-*0


6/23

MODELOS DE PROGRAMACIÓN DINÁMICA

• P(%)*+,- + *- 0*0/+2#0- % +* -/+2+ 0-;+(%• P(%)*+,- + *- ,%#$0*-• P(%)*+,- + '(%"##02 + 02+2-(0%&• E* ,%+*% + '(%/(-,-#02 02,0#- *02+-* +& +&0#% &+ "+*+ 02,0#% - (-&

+* 0+,'%.• U2 ,%+*% +& 02,0#% #"-2% '-&- - %(- +-'-.

E;+,'*%: '-(- +* #-&% + "2 +26+(,% *+ '"++ ,+0( *- T P '-(- &"& 7 +-'-& + *-

+26+(,+- @ *%& +&-%& &+(9-2 *%& 9-&

PROBLEMA SOBRE VIAJERO

U2 "(0&- &+ '(%'%2+ "2 0-;+ #%2 '%&0)*+& +-*-& +2 ! #0"-+& -2+& + **+/-( - &"

+&02% 602-*. C"* +& *- +#0&02 "+ %,-(9- &0 +& "+ "0+(+ **+/-( *% ,& ('0% '%&0)*+ -

&" +&02% '-&-2% '%( *-& +-*-& +&-)*+#0-& -2+& + **+/-( - &" +&02%

1 I+2060#-( *-& +-'-&: 3 +-'-& 7 +&-%&


7/23

Xn: ¿En qué lugar me encuentro?

Ejemplo: estado

3

L%& -(#%& '"++2 &+( (0+&/%& #%&%& @ #%,% #-,)0-2 + +-'- - +-'- +& 02,0#%

! E2 *-& +-'-& 0+2060#-(

Dn: porque ruta voy a ir

Xn-1: Variale de

estado de salida


8/23

2 H 7 H

3 8 7 8

E-'- !

d4 04 2 3 d4 F4.

4 !1 18 18

5 17 !! 5 17

6 1H 5 1H

E-'- 3

d5

054 5 6 d5 ,5.

/ !3 ! !3 3 !

En esta etapa (ay )rendimientos

*+,r+ *1.

*+, 1+ /,0+1

*+, 112,012

*+, 2/,01

63K(363

63K 513K!3

63K 317K!

63K 41HK!3


9/23

PROBLEMA SOBRE PRODUCCIÓN

L-& +-'-& '"++2 &+( &+,-2-*,+2+ ,+2&"-*,+2+ 0-(0-,+2+. S+ 0+2+2 #%,% -%

'-(,+(%&. P-(,+(%&: -2 #-,)0-2% +-'- '%( +-'- (0KL%& (+20,0+2%& 0+2+2 "+ +(

#%2 #%&%& + '(%"##02 @ #%&% + -*,-#+2-,0+2%

E;+,'*%: U2- +,'(+&- "+ &+ +0#- - *- 6-)(0#-#02 + -"%,0*+& +2 *- #0"- +


10/23

Me%e% Di Pi 7i CP8+ C9

A(ri# / 3 ! 3 5 1

M"o 4 1 3 ! ! !J+io 5 ! ! ! 4 1

I-e!"rio iici"#; 5

D1 +


11/23

X3,+

5nventario inicial,3

X+,X3 d3-3

5nv6!inal3,5nv6 5nicial +

7ril3

'3,+83,3

d3,?

D3,3

X1,X+ d+-1

5nv6!inal+,5nv6 5nicial 1

9ayo+

'3,3

8+,+

d+,?

D+,1

X,X1 d1-+ unio1

'3,+81,+

d1,?

D1,+

( 3K53 1>333? ( !K!! !>!!1? ( 1K41 1>11!?

M02 ( 3K333 M02 ( !K4!!!! M02 ( 1K511!

A#m"c


12/23

A#m"c?: -(0-)*+ + +&-%

21 K 2 2 D2

-@ "+ (+&%*+( +* ,%+*% PL +2 #-- +-'- M%% '(-#0#%

M%% G(-60#%

M%% A*/%(0,% S0,'*+

E I 0 * 0 0

2 K I2+2-(0% I20#0-*

2 K C-20- "+ %@ - '(%"#0( +2 +&+ ,+&

D2 K D+,-2-

2 K C-'-#0- + -*,-#+2-,0+2%

P2 K C-'-#0- + '(%"##02

21 K 02. F02-* +-'- 2K02. I20#0-* +-'- 21


13/23

61K( 1 6 6 K (

M02 (1K51 1 !

d4

04= / 4 5 d4 ,4. )/; )4>d4?/

= 1 1 1 1!3 1 1!

/ 8 8 8 1! 8 1!

4 1 1!

5 4 4 !

ETAPA !

6!K( ! 61

M02 ( !K41 !! !

S0 !K ( ! K ! 1K 61 K 8 ! 8 K1

!K 1

S0 !K ( ! K 1K1 61 K 4 4 K1


14/23

ETAPA 3

d5 05 = / 4 d5 ,5. )4; )5>d5?5

4 15 1H 1 15 1

63K( 3 6!

M02 (3K3 3 3

S0 3K! ( 3 K 5 !K 6! K 1 5 1 K15

3K 1

S0 3K! ( 3 K 11 !K1 6! K 8 11 8 K1H

3K !

C%&% %-* + A*,-#+2-,0+2%C%&% + '(%"##02 %-*C-20- "+ %@ - '(%"#0(

>CP CQ?


15/23

E2 A)(0* %@ - '(%"#0( 1 ,0 +,-2- +& #")0+(- #%2 ,0 I2+2-(0% I20#0-* + ! E2 M-@% '(%"


16/23

PROBLEMA DE LA MOCILA

E-'-: U2 +&"0-2+ +&+- &-)+( #"* +& *- #%,)02-#02 + '(%/(-,-& % +* '(%/(-,- "+

+)+ 02&-*-( +2 &" LAPTOP '-(- "2 #%2#"(&% &0 +* 0&'%2+ + 1GB + ,+,%(0- @ *%&

%(/-20


17/23

X3,1

d3= ¿?

X2,X3 ;+d3 X1,X+ ; 1d+

d1= ¿?

Xo,X1 ;1d1

d2= ¿?

17

r4K3! r/K4r K!


18/23


19/23

ETAPA 5:

1H

f3 =r3 + f2* r5K!3


20/23

RESUMEN:

!


21/23

CONCLUSIONES

• L- #20#- + '(%/(-,-#02 02,0#- +0- +'*%(-( %-& *-& &+#"+2#0-& '%&0)*+& '%( ,+0% + *- (+&%*"#02 + &")'(%)*+,-&

+ -,-=% #(+#0+2+ @ -*,-#+2-,0+2% +2 "2- -)*- + *-& &%*"#0%2+& '0,-& + +&%& &")'(%)*+,-& '-(- 6-#0*0-( *- &%*"#02

+ *%& '(%)*+,-& ,& /(-2+&.

•

E2 +&- %#-&02 (+-*0


22/23

BIBLIOGRAFÍA

EPPEN, GOULD Y SCHMIDT. Investigación de Operacines en !a ciencia ad"inistrativa. #$inta Edición.

%re$nd, &'n E., Mdern Estad(stica E!e"enta!, N$eva De!'i) Prentice*Ha!! de !a India Private Li"ited, +-

HMDY . TH. Investigación de Operacines. S/pti"a Edición

Editria! Prentice 'a!!.

!!


23/23