Post on 14-Oct-2015
5/24/2018 Cap01 - Programaci n Din mica
1/70
P D
1
5/24/2018 Cap01 - Programaci n Din mica
2/70
P D (PD) T
B D 1957 S
:
.(R).
PD: T , .
2
5/24/2018 Cap01 - Programaci n Din mica
3/70
A P D
C P D
E B
P D D P D P
3
5/24/2018 Cap01 - Programaci n Din mica
4/70
P D U EE.UU.
, .
A ,
. E .
E
. L
.
4
5/24/2018 Cap01 - Programaci n Din mica
5/70
P D
E
C
C ( ) ?
1
2
2
3
3 3
3
3
3
4
4
4
4
4
4
1
6
7
6
5
610
9
8
3
2 5
4 7
1
5
5/24/2018 Cap01 - Programaci n Din mica
6/70
P D
1
2
2
3
3 3
3
3
3
4
4
4
4
4
4
1
6
7
6
5
6
10
9
8
3
2 5
4 7
1
S 1: 126910 > C 13
.146 126
S 2: ,
(13321=18)
6
5/24/2018 Cap01 - Programaci n Din mica
7/70
P D
S 3:PROGRAMACIN
DINMICA
P . E ,
, .
D A : E 4
7
5/24/2018 Cap01 - Programaci n Din mica
8/70
P DM S
V ,
E, (=1,2,3,4) .
E
),( nn xsf C , S (
) X .
10;1 44321 = xxxxx
( S ), ( S ), ( S ), ( S )1234
* * * *
*n
( S ) = MinXn
( S, Xn) =( S, Xn)n }{ n *
n
Xn
( S0 ,Xn )n
( S1 ,Xn )n
C S X
8
5/24/2018 Cap01 - Programaci n Din mica
9/70
P DM S
ETAPA 4 ; = 4
S X4
8 3 10 9 4 10
(S)4
**
ETAPA 3 ; = 3
S 8 9 X3
5 1 + 3 = 4 4 + 4 = 8 4 8
6 6 + 3 = 9 3 + 4 = 7 7 9
7 3 + 3 = 6 3 + 4 = 7 6 8
X3
(S,X3 )= CSX + (X3 )3*
*
3 4
(S)3*
9
5/24/2018 Cap01 - Programaci n Din mica
10/70
P DM S
ETAPA 2 ; = 2
S 5 6 7 X2
2 7 + 4 = 11 4 + 7 = 11 6 + 6 = 12 11 5 6
3 4 + 6 = 10
4
X2
(S,X2 )= CSX + (X3 )2*
2 3
*(S)2
*
ETAPA 1 ; = 1
S 2 3 4 X1
1 2 + 11 = 13 4 + 7 = 11 3 + 8 = 11 11 3 4
X1
(S,X1 )= C1X + (X1 )1*
1 2
*(S)1*
Identifiquemos
la solucinoptima.
}1 3 5 8 10
1 4 5 8 10
1 4 6 9 10
E , PD.
10
5/24/2018 Cap01 - Programaci n Din mica
11/70
C PD C : P
. P:
S .
E .
11
5/24/2018 Cap01 - Programaci n Din mica
12/70
E PD E ,
. C . E ,
. P . E
.
E . U .
12
5/24/2018 Cap01 - Programaci n Din mica
13/70
E PD L
. E :
D ,
(1, , +1). E
.
13
5/24/2018 Cap01 - Programaci n Din mica
14/70
E PD S
, (+1). U ,
, .
( S ) = Mx Min ( S, Xn)*
n n{ }Xn
( S ) = Min CSXn + ( Xn)* *
Xn{ }
n +1n
..
E A ()
R
(+1)
=),( nn xsf
)(* sfn
*
nx2x1x 3xs
14
5/24/2018 Cap01 - Programaci n Din mica
15/70
P D
DE 1:
U . L .
E .
P , . S , . L
:
N decargas
Tienda1 2 3
0 0 0 0
1 5 6 4
2 9 11 9
3 14 15 13
4 17 19 18
5 21 22 20
15
5/24/2018 Cap01 - Programaci n Din mica
16/70
E 1:
N decargas
Tienda1 2 3
0 0 0 0
1 5 6 4
2 9 11 9
3 14 15 13
4 17 19 18
5 21 22 20
16
P D
D
5/24/2018 Cap01 - Programaci n Din mica
17/70
E 1:
: (=1,2,3): , 0,1,2,3,4,5
: +1=
:
*
*
17
P D
D
5/24/2018 Cap01 - Programaci n Din mica
18/70
E 1:
E 3, =3, 4=0
3 3
0 0 0
1 4 1
2 9 2
3 13 3
4 18 4
5 20 5
*
18
P D
D
5/24/2018 Cap01 - Programaci n Din mica
19/70
E 1:E 2, =2
2/2 0 1 2 3 4 5 *
2() *2
0 0 0 0
1 0+4=4 6+0=6 6 1
2 0+9=9 6+4=10 11+0=11 11 2
3 0+13=13 6+9=15 11+4=15 15+0=15 15 123
4 0+18=18 6+13=19 11+9=20 15+4=19 19+0=19 20 25 0+20=20 6+18=24 11+13=24 15+9=24 19+4=23 22+0=22 24 123
19
P D
D
5/24/2018 Cap01 - Programaci n Din mica
20/70
E 1:E 1, =1
1/1 0 1 2 3 4 5 1*(1)
*1
5 0+24=24 5+20=25 9+15=24 14+11=25 17+6=23 21+0=21 25 13
1 2 2
3 2 0
S 1 S 2 S 3
2
20
P D
D
5/24/2018 Cap01 - Programaci n Din mica
21/70
E 2: I
U : 1, 1 ; 2, 3 ; 3, 2; 4, 4 .
D ,
3US$. A, 1 . A , 50 .
L 5 . L
4 , .S 0 .
L
. 21
P D
D
5/24/2018 Cap01 - Programaci n Din mica
22/70
E 2
: , =1,2,3,4,5: , 0,1,2,3,4,5
: : , 0,1,2,3,4
*
: , =1,2,3,41=05=0+1=+
22
P D
D
5/24/2018 Cap01 - Programaci n Din mica
23/70
E 2
E 4, =4, 4=4, 5=0
4\4 0 1 2 3 4 5
0 7
1 6
2 5
3 4
4 0
5=4+44
* *
4 4(4) 4
0 7 4
1 6 3
2 5 2
3 4 1
4 0 0
*
23
P D
D
5/24/2018 Cap01 - Programaci n Din mica
24/70
E 2
E 3, =3, 3=2
3*(3) *3
3\3 0 1 2 3 4 5
0 5+7 =12 6.5+6=12.5 8+5=13 9.5+4=13.5 12 2
1 4+7=11 5.5+6=11.5 7+5=12 8.5+4=12.5 10+0=10 10 5
2 0+7=7 4.5+6=10.5 6+5=11 7.5+4=11.5 9+0=9 7 0
3 0.5+6=6.5 5+5=10 6.5+4=10.5 8+0=8 6.5 0
4 1+5=6 5.5+4=9.5 7+0=7 6 0
4= 3+330
5/24/2018 Cap01 - Programaci n Din mica
25/70
E 2
E 2, =2, 2=3
*2(2) *2
2\2 0 1 2 3 4 5
0 6+12=18 7.5+10=17.5 9+7=16 16 5
1 5+12=17 6.5+10 =16.5 8+7=15 9.5+6.5=16 15 4
2 4+12=16 5.5+10=15.5 7+7 = 14 8.5+6.5=15 10+6=16 14 3
3 0+12=12 4.5+10=14.5 6+7=13 7.5+6.5=14 9+6=15 12 0
4 0.5+10=10.5 5+7=12 6.5+6.5=13 8+6=14 10.5 0
*
3=2+220
5/24/2018 Cap01 - Programaci n Din mica
26/70
E 2
E 1, =1, 1=1, 1=0
2=1+110
5/24/2018 Cap01 - Programaci n Din mica
27/70
E 2
1 5 0 4
1 3 2 4
0 2 0 0
M 1 M 2 M 3 M 4
27
P D
D
5/24/2018 Cap01 - Programaci n Din mica
28/70
E 3:
U .
N , , .
C
, . E :
Das
Puntos deCalificacinEstimados
Cursos
1 2 3 4
1 3 5 2 6
2 5 5 4 7
3 6 6 7 94 7 9 8 9
28
P D
D
5/24/2018 Cap01 - Programaci n Din mica
29/70
E 3:
: =(1,2,3,4): , (1,2,3,4)
: +1=
:
*
*
29
P D
D
5/24/2018 Cap01 - Programaci n Din mica
30/70
E 3:
E 4, =4, 5=0
4 4
1 6 1
2 7 2
3 9 3
4 9 4
*
30
P D
D
Das
Puntos deCalificacinEstimados
Cursos
1 2 3 41 3 5 2 6
2 5 5 4 7
3 6 6 7 9
4 7 9 8 9
5/24/2018 Cap01 - Programaci n Din mica
31/70
E 3:E 3, =3
3/3 1 2 3 4 3(3) 3
1
2 2+6=8 8 1
3 2+7=9 4+6=10 10 2
4 2+9=11 4+7=11 7+6=13 13 3
5 2+9=11 4+9=13 7+7=14 8+6=14 14 34
31
P D
D4 4
*(4) 4
1 6 1
2 7 2
3 9 3
4 9 4
5/24/2018 Cap01 - Programaci n Din mica
32/70
E 3:E 2, =2
2/2 1 2 3 4 2(2) 2
1
2
3 5+8=13 13 1
4 5+10=15 5+8=13 15 1
5 5+13=18 5+10=15 6+8=14 18 16 5+14=19 5+13=18 6+10=16 9+8=17 19 1
32
P D
D
5/24/2018 Cap01 - Programaci n Din mica
33/70
E 3:E 1, =1
1/1 1 2 3 4 1*() 1
7 3+19=22 5+18=23 6+15=21 7+13=20 23 2
2 1 3 1
C 1 C 2 C 3 C 4
33
P D
D
5/24/2018 Cap01 - Programaci n Din mica
34/70
E 4: E
. A , .
P ( )
. L : . (P , , , ).
N deEquiposMdicos
Miles de aos
de vidaadicional del
hombre
Pas
1 2 3
0 0 0 0
1 45 20 50
2 70 45 703 90 75 80
4 105 110 100
5 120 150 130
Q ,
? C
? Q
? 34
P D
D
5/24/2018 Cap01 - Programaci n Din mica
35/70
E 4:
E = P; = 1,2,3V: X = E
E: S = E
N deEquiposMdicos
Miles de aos
de vidaadicional delhombre
Pas
1 2 30 0 0 0
1 45 20 50
2 70 45 70
3 90 75 80
4 105 110 100
5 120 150 130
)( nn xP A () X .
=
=
=
=
=
ii
i
ni
i
ni
ii
xx
Sxas
xPZMax
;0
.
)(
3
3
N ;
35
P D
D
5/24/2018 Cap01 - Programaci n Din mica
36/70
E 4:
36
P D
D
5/24/2018 Cap01 - Programaci n Din mica
37/70
E 4:
E = P; = 1,2,3V: X = E
E: S = E
N deEquiposMdicos
Miles de aos
de vidaadicional delhombre
Pas
1 2 30 0 0 0
1 45 20 50
2 70 45 70
3 90 75 80
4 105 110 100
5 120 150 130
)( nn xP A
() X .
=
=
=
=
=
ii
i
ni
i
ni
ii
xx
Sxas
xPZMax
;0
.
)(
3
3
N ;
37
P D
D
5/24/2018 Cap01 - Programaci n Din mica
38/70
E 4:
=
=
+=
=
+=
+=
ii
nn
i
nii
ni
ii
nnnnn
xx
xSxas
xPZMax
xPxsf
;0
.
)(
)(),(
3
1
3
1
:),( nn xsfA , , S X.
)(* 1 nnn xsf +
( S, Xn
) = Pn
( Xn
)+ ( S - Xn
)n+1n
*
L
38
P D
D
5/24/2018 Cap01 - Programaci n Din mica
39/70
E 4:
s *3x
0 0 0
1 1 50
2 2 70
3 3 80
4 4 100
5 5 130
)(*3 sf
( S, Xn) = Pn ( Xn)+ ( S - Xn)n+1n
* N deEquiposMdicos
Miles de aosde vida
adicional delhombre
Pas
1 2 30 0 0 0
1 45 20 50
2 70 45 70
3 90 75 80
4 105 110 100
5 120 150 130
39
P D
D
5/24/2018 Cap01 - Programaci n Din mica
40/70
E 4:
( S, Xn) = Pn ( Xn)+ ( S - Xn)n+1n
*
Miles de aos de vida adicionales
del hombre
N de Equipos Pas
Mdicos 1 2 3
0 0 0 0
1 45 20 50
2 70 45 70
3 90 75 80
4 105 110 100
5 120 150 130
0 1 2 3 4 5
0 0+0=0 0 0
1 0+50=50 20+0=20 50 0
2 0+70=70 20+50=70 45+0=45 70 01
3 0+80=80 20+70=90 45+50=95 75+0=75 95 2
4 0+100=100 20+80=100 45+70=115 75+50=125 110+0=110 125 3
5 0+130=130 20+100=120 45+80=125 75+70=145 110+50=160 150+0=150 160 4
)()(),( 2*
32222 xsfxPxsf += )(*2 sf*
2x
40
P D
D
P D
5/24/2018 Cap01 - Programaci n Din mica
41/70
E 4:
( S, Xn) = Pn ( Xn)+ ( S - Xn)n+1n
*
Miles de aos de vida adicionales
del hombre
N de Equipos Pas
Mdicos 1 2 3
0 0 0 0
1 45 20 50
2 70 45 70
3 90 75 80
4 105 110 100
5 120 150 130
s1x
0 1 2 3 4 5
5 0+160=160 45+125=170 70+95=165 90+70=160 105+50=155 120+0=120 170 1
)()(),( 1*
21111 xsfxPxsf +=)(*1 sf
*
1x
1 3 1
P 1 P 2 P 3
41
P D
D
P D
5/24/2018 Cap01 - Programaci n Din mica
42/70
E 5: V MU
M. T .
S ,
1, 2 3 0.40, 0.60 0.80. P , (0.40)(0.60)(0.80)=0.192 (19.2%).
D ,
.
N de
Cientficos
Nuevos
Probabilidad de Falla
Equipo de Investigacin
1 2 3
0 0,40 0,60 0,80
1 0,20 0,40 0,50
2 0,15 0,20 0,30
)( nn xP P X
=++
=
;0
2..
)(*)(*)(
321
332211
ix
xxxas
xPxPxPZMin
42
P D
D
P D
5/24/2018 Cap01 - Programaci n Din mica
43/70
E 5: V M
=
=
= +=
+=
;0
..
)(
*)(),(3
1
31
i
n
ni
i
iini
nnnn
x
xsxas
xPZMin
xPxsf
1)0(*4 =f
),( nn xsf P , +1,..3, S, X .
)(* 1 nn xsf +
)(*)(),( * 1 nnnnnn xsfxPxsf = +43
P D
D
P D
5/24/2018 Cap01 - Programaci n Din mica
44/70
E 5: V M N deCientficos
Nuevos
Probabilidad de Falla
Equipo de Investigacin
1 2 3
0 0,40 0,60 0,80
1 0,20 0,40 0,50
2 0,15 0,20 0,30
0 1 2
0 0.6*0.8=0.48 0.48 0
1 0.6*0.5=0.3 0.4*0.8=0.32 0.3 0
2 0.6*0.3=0.18 0.4*0.5=0.2 0.2*0.8=0.16 0.16 2
)(*)(),( 2*
32222 xsfxPxsf =
)(*
2 sf
*
2xs2x
0 0.8 0
1 0.5 1
2 0.3 2
)(*
3 sf*
3xs
44
P D
D
P D
5/24/2018 Cap01 - Programaci n Din mica
45/70
E 5: V MN de
Cientficos
Nuevos
Probabilidad de Falla
Equipo de Investigacin
1 2 3
0 0,40 0,60 0,80
1 0,20 0,40 0,50
2 0,15 0,20 0,30
0 1 2
2 0.4*0.16=0.064 0.2*0.3=0.06 0.15*0.48=0.072 0.06 1
)(*)(),( 2*
21111 xsfxPxsf =)(*1 sf
1xs
*
1x
1 0 1
E 1 E 2 E 3
45
P D
D
P D
5/24/2018 Cap01 - Programaci n Din mica
46/70
E 6: P V ( )L S O A. L
, .L .
A, , .
1. P .2. R , =3,
=5, =US$ 1200, 1=$ 200, 2=$ 300, 3=$100 :
46
P D
D
5/24/2018 Cap01 - Programaci n Din mica
47/70
1. F: N (=1,2K).
: C .
: D .
: D .
: C .
: B .
n
nX
nS
nH
nC
( )n ng X
47
5/24/2018 Cap01 - Programaci n Din mica
48/70
F O:
1n n n nS S C X + = A :
C :
*
S1 = P
H1
= M
fn+1 = 0
Hn+1 > 0
Sn+1 > 0
48
5/24/2018 Cap01 - Programaci n Din mica
49/70
2.1 2 3
200, 300, 100, 3, 5
3
C US C US C US K M
n
= = = = =
=
0 1 2 3 4 5
(0-99; 0-5)
(100-1200; 0)0 - - - - - 0 0
(100-199; 1-5)
(200-1200; 1)0 1 - - - - 1 1
(200-299; 2-5)
(300-1200; 2)0 1 3 - - - 3 2
(300-399; 3-5)
(400-1200; 3)0 1 3 3 - - 3 23
(400-499; 4-5)
(500-1200; 4)0 1 3 3 2 - 3 23
(500-1200; 5) 0 1 3 3 2 1 3 23
*3f *3X(S3;H3)
*
49
5/24/2018 Cap01 - Programaci n Din mica
50/70
O
f3*(S3,H3) =
0
1
3
Si S3 < 100 o H3 = 0
Si (100 < S3 < 200 y H3 > 1)
o (S3 >100 y H3 = 1)
De otra manera
50
5/24/2018 Cap01 - Programaci n Din mica
51/70
2n =
0 1 2 3 4 5
200 0 0 - - - - - 0 0
400 1 0+1=1 1+0=1 - - - - 1 01
600 2 0+3=3 1+1=2 4+0=4 - - - 4 2
800 3 0+3=3 1+3=4 4+1=5 - - - 5 2
1000 4 0+3=3 1+3=4 4+3=7 6+1=7 - - 7 23
1200 5 0+3=3 1+3=4 4+3=7 6+3=9 8+0=8 - 9 3
2H2S *2f *2X*
51
5/24/2018 Cap01 - Programaci n Din mica
52/70
1n=
0 1 2 3 4 5
1200 5 0+9=9 1+7=8 2+5=7 3+4=7 4+1=5 5+0=5 9 0
1H1S *1f *1X
S ( )
L : 0*US 200 + 3*US 300 + 2*US 100 =
*
52
P D
5/24/2018 Cap01 - Programaci n Din mica
53/70
P D
PE R I
E . E
.
A , , .
53
P D
5/24/2018 Cap01 - Programaci n Din mica
54/70
P D
P E I
Sn XnDecisin
P1
P2
PN
1
C1
C2
CN
2
N
(1)*n+1
(1)*
n+1
(1)*
n+1
Etapa n ProbabilidadContribucin
de la etapa n Etapa n+1
Estado:
(Sn, Xn)
n
54
P D
5/24/2018 Cap01 - Programaci n Din mica
55/70
P D
P E I
E 1: P
L C. I H A M . S .
E ( ), .
A, L ; , ()L.
55
P D
5/24/2018 Cap01 - Programaci n Din mica
56/70
P D
P E I
E 1: P ()
S CM ( ) $ 100 ( ) .
A, $ 300, . E . S , $ 1600.
E , .
56
5/24/2018 Cap01 - Programaci n Din mica
57/70
O , K(xn) = 3*min(1,xn)
57
5/24/2018 Cap01 - Programaci n Din mica
58/70
* *
1 1
*
1
*
4
Por lo tanto para s 1,
1 1(1, ) ( ) (1) 1 (0)
2 2
1( ) (1)
2
Donde (1) es igual a 16, el costo terminal por no haber obtenido art culos ace
n n
n
n
x x
n n n n n n
x
n n n
f x K x x f f
K x x f
f
+ +
+
=
= + + +
= + +
* *
10,1,...
ptables
De esta manera, la relaci n recursiva para los clculos de programaci n din mica es
1(1) ( ) (1)
2
1,2,3.
n
n
x
n n n nx
f mn K x x f
para n
+=
= + +
=
58
5/24/2018 Cap01 - Programaci n Din mica
59/70
3
3
x
s
3
3 3 3 3
1(1, ) ( ) 16
2
x
f x K x x
= + +
*
3 3( )f s *
3x 0 1 2 3 4 5
0 0 0 0
1 16 12 9 8 8 8,5 8 3 4
P =3
2
2
x
s
2
*
2 2 2 2 3
1(1, ) ( ) (1)
2
x
f x K x x f
= + +
*
2 2( )f s *
2x 0 1 2 3 4
0 0 0 0
1 8 8 7 7 7,5 7 2 3
P =2
59
5/24/2018 Cap01 - Programaci n Din mica
60/70
P =1
1
1
x
s
1
*
1 1 1 1 2
1(1, ) ( ) (1)
2
x
f x K x x f
= + +
*
1 1( )f s *1x 0 1 2 3 4
1 7 7,5 6,75 6,875 7,4375 6,75 2
E, ; , ; , . E
$675.
60
P D
5/24/2018 Cap01 - Programaci n Din mica
61/70
P E I
E 2: J V
U . S , , , . C .
E 2/3 .
S , ( ) . L .
E .
61
5/24/2018 Cap01 - Programaci n Din mica
62/70
F:E: (=1,2,3)
V.E : F .
V.D : C .
P
.
nS
nX
( , )n n n
f X S =
* *
1 1
1 2( , ) ( ) ( )
3 3n n n n n n n n nf X S f S X f S X+ += + +
62
5/24/2018 Cap01 - Programaci n Din mica
63/70
P :=3
P .
0 01 0
2 0
3 2
4 1
>=5 1 0
2 / 3
*
3X*
3f
2 / 3
3S
63
5/24/2018 Cap01 - Programaci n Din mica
64/70
=2
0 1 2 3 4
0 0 0
1 0 0 0
2 0 1 23 0, 2 3
4 1
>=5 1 1 0
2S
2X 2f *
2
f*
2
X
4 / 9 4 / 94 / 92 / 3 2 / 3 2 / 3
2 / 3 2 / 3 2 / 3 2 / 38 / 9
4 / 92 / 3
8 / 9
64
5/24/2018 Cap01 - Programaci n Din mica
65/70
=1
R :
E 20/27
.
0 1 2 33 1
1S1X 1f *
1f*
1X
2 / 3 2 0 / 2 7 2 / 3 2 / 3 2 0 / 2 7
*3*
2 *
3
* *1 2*
3* *
2 2
, 0, 1
, 2 3
1 2 3 ( 1),
, 1 2 1,2,3 4 ( 2),
si gana X si gana X
si pierde X o
X o para X si gana X
si pierde X o o para X si pierde la apuesta esta perdida
== =
= =
=
= =
65
P D
5/24/2018 Cap01 - Programaci n Din mica
66/70
P C ,
E 3: S
L S , 1/, 6 .
C 2 /. L
50 / .
D S, . L
1.S 6 ( ) . M S 6 .
Demanda diaria
Tiendas Galones Probabilidad
Tienda
1
1 0,60
2 0
3 0,40
Tienda2
1 0,50
2 0,10
3 0,40
Tienda3
1 0,40
2 0,30
3 0,30
66
F
5/24/2018 Cap01 - Programaci n Din mica
67/70
F
67
F
5/24/2018 Cap01 - Programaci n Din mica
68/70
F
$4.2
68
5/24/2018 Cap01 - Programaci n Din mica
69/70
P E 3:
*
*
0 0 0
1 1 2
2 2 3.4
>=3 3 4.35
*
*
0 0 0 0
1 2 2 01 2
2 3.4 4 3.25 1 4
3 4.35 5.4 5.25 4.35 1 5.4
4 4.35 6.35 6.65 6.35 2 6.65
5 4.35 6.35 7.6 7.75 3 7.75
6 4.35 6.35 7.6 8.7 3 8.7
E 2:
69
5/24/2018 Cap01 - Programaci n Din mica
70/70
P E 1:
*
*
6 8.7 9.75 9.75 9.45 1 2 9.75
P , 2 , ,
T 1 T 3T 2
1 3 2C 1
C 2 2 2 2
70