Simplex

MTODO SIMPLEX DE REDES

COSTOS

C12

3

C65

3

C13

5

C67

18

C14

4

C68

15

C15

4

C69

6

C16

3

C613

10

C21

3

C78

5

C23

6

C710

3

C24

3

C711

3

C25

5

C712

4

C26

3

C87

5

C34

4

C89

2

C37

14

C810

6

C38

9

C811

7

C39

16

C812

5

C310

12

C813

7

C43

4

C98

2

C45

2

C912

6

C47

13

C913

7

C48

14

C1011

9

C49

13

C1110

9

C54

2

C1112

8

C56

3

C1211

8

C57

15

C1213

7

C58

17

C1312

7

C59

16

C146

0

NODO

CAPACIDAD

NODO

CAPACIDAD

bl

2BO

bB

-7O

b2

32O

b9

-SO

b3

lOO

blO

-l6O

b4

O

bll

-lSO

bS

O

bl2

-l4O

b6

l2O

bl3

-l6O

b7

-BO

sl4

lO

MinF = 2(X26 + X45 + X54 + X S9 + X 9S) + 3(X12 + X21 + X16 + X61 + X24 + X42 + X56 + X65 + X71C + X711) + 4( X14 + X15 + X34 + X43 + X712) + 5( X13 + X25 + X7S + X S7 + X S12) + 6( X23 + X69 + X S1C + X 912) + 7( X S11 + X S13 + X 913 + X1213 + X1312) + S( X1112 + X1211) + 9( X 3S + X1C11 + X111C) + 1C X 613 +12 X 31C +13( X47 + X49) + 14(X 37 + X 4S) + 15(X 57 + X 6S) + 16(X39 + X59) +17X5S +1 SX 67

s. a

X12 + X13 + X14 + X15 + X16 - X21 = 2SC

-X12 + X21 + X23 + X24 + X25 + X26 = 32C

-X13 - X23 - X34 + X37 + X45 + X3S + X39 + X31C - X43 = 1CC

-X14 - X24 - X34 + X43 + X45 + X47 + X4S + X49 - X54 = C

-X15 - X25 - X45 + X54 + X56 + X57 + X5S + X59 - X65 = C

-X16 - X26 - X56 + X65 + X67 + X6S + X69 + X613 - X146 = 12C

-X37 - X47 - X57 - X67 + X7S + X71C + X711 + X712 - XS7 = -SC

-X3S - X4S - X5S - X6S - X7S + XS7 + XS9 + XS1C + XS11 + XS12 + XS13 - X9S = -7C

-X39 - X49 - X59 - X69 - XS9 + X9S + X912 + X913 = -5C

-X31C - X71C - XS1C + X1C11 - X111C = -16C

-X711 - XS11 - X1C11 + X11C + X1112 - X1211 = -15C

-X712 - XS12 - X912 - X1112 + X1211 + X1213 - X1312 =-14C

-X613 - XS13 - X913 - X1213 + X1312 = -16C X146 = 1C

Xij > C

DUAL

MaxF = 280W1 + 320W2 +100W3 +120W6 + 10W14 - 80W7 - 70W8 - 50W9 -160W10 - 150W11 -140W12 -160W13

s. a

W1 - W 2 3

W4-W52

W 2 - W1 3

W 4 - W 7 13

W1 - W 3 5

W 4 - W 8 14

W1 - W 4 4

W 4 - W 9 13

W1 - W 5 4

W 5 - W 4 2

W1 - W 6 3

W 5 - W 6 3

W2-W36

W 5 - W 7 15

W2-W43

W5 -W8 17

W2-W55

W 5 - W 9 16

W2-W62

W6-W53

W 3 - W 4 4

W14-W6 0

W 3 - W 9 16

W 6 - W 7 18

W 3 - W 8 9

W 6 - W 8 15

W 3 - W 7 14

W6-W96

W 3 - W10 12

W 6 - W13 10

W4-W34

W 7 - W 8 5

W 7 - W10 3 W 7 - W11 3 W 7 - W12 4 W 8 - W 7 5

W8 -W10 6

W 8 - W11 7

W8 -W12 5 W8 -W13 7 W9-W82

W 9 - W12 6 W 9 - W13 7 W10 - W11 9 W11 - W10 9 W11 - W12 8 W12 - W11 8

W12 -W13 7

W13 - W12 7

> 0 Q

13

^10^^11^ ^12"^

xl-2 = 280

x9-13 = 80

x2-5 = 600

x8-7 = 630

x5-4 = 600

x 7 = 550

x4-3 = 600

x10 -ii = 390

x3-8 = 700

x11-12 = 240

x14 - 6 = 10

x12 -13 = 100

x6-9 = 130

x13 = 20

f =26010

Matriz de Incidencia

(1-2)

(2-5)

(5-4)

(4-3)

(14-6)

(6-9)

(9-13)

(3-8)

(8-7)

(7-10)

(10-11)

(11-12)

(12-13)

13

1

1

2

-1

1

3

-1

1

4

-1

1

5

-1

1

6

-1

1

7

-1

1

8

-1

1

9

-1

1

10

-1

1

11

-1

1

12

-1

1

13

-1

-1

1

14

1

Iteracin 1

[e 10 W = c

w1 - w 2 = 3 w 2 - w 5 = 5 w 5 - w 4 = 2 w 4 - w 3 = 4 w 3 - w 8 = 9 w 8 - w 7 = 5 w 7 - w10 = 3

Complementarios:

w10 - w11 = 9 w11 - w12 = 8 w12 - w13 = 7 w14 - w 6 = 0 w 6 - w 9 = 6 w 9 - w13 = 7

w13=0

=>

w13=0 w 9 = 7 w 6 = 13

w14 = 13

w12=7

w11 = 15 w10 = 24

w 7 = 27

w 8 = 32

w 3 = 41 w 4 = 45 w 5 = 47 w 2 = 52

w1 = 55

w1 - w2 - c12 = 55 - 41 - 5 = 9

45 - 4 = 6

47-4=4

w1 - w 4 - c14 = 55-w1 - w 5 - c15 = 55-

w1 - w6 - c16 = 55 -13 - 3 = 39

290- 140

180

0

i

ti

D = min{280,600,700,630,550,390,240,100}

F = 26010 - 3(500) = 24510

Iteracin 2

W13 = 0 W 9 = 7 W 6 = 13 W14 = 13

W1 = 16 W 2 = 13 W 5 = 8

W4=6

W 3 = 2

W 8 = -7 W 7 = -12 W10 = -15

W11=-24

W12 = -32

Complementarios:

W 8 - W12 - C 812 = -7 + 32 - 5 = 20 W 8 - W13 - C 813 = -7 - 0 - 7 = -14 W 9 - W 8 - C 98 = 7 + 7 - 2 = 12 W 9 - W12 - C 912 = 7 + 32 - 6 = 33

Iteracin 3

W13 = CW14 = 13W 4 = 6

W 9 = 7W1 = 16W 3 = 2

W12 = 1W 2 = 13W S = -7

W 6 = 13W 5 = SW 7 = -12

Complementarios:

W6 - W7 - C67 = 13 +12 - 1S = 7 W 6 - W S - C 6S = 13 + 7 -15 = 5 W 6 - W13 - C 613 = 13 +15 - 1C = 1S W 7 - W11 - C 711 = -12 + 24 - 3 = 9

W1C = -15 W11 = -24

3 4>.

co

D = min{37C,1SC}

F = 23670 -10(180) = 21870

Iteracin 4

W13 = 0 W 6 = 10 W 9 = 4 W12 = -2

W1 = 13

W2=10 W 5 = 5 W4=3

W 3 = -1 W 8 = -10 W 7 = -15 W10 = -18

W11 = -27 W14 = 10

Complementarios:

W11 - W10 - C1110 = -27 +18 - 9 = -18 W11 - W12 - C1112 = -27 + 2 - 8 = -33 W12 - W11 - C1211 = -2 + 27 - 8 = 17 W12 - W13 - C1213 = -2 - 0 - 7 = -9

0)

( 34 )

(O

0

270

180

0- 0 0

D = mm{4C,36C,46C,39C,31C,15C}

A = 40

F = 21S7C - S(4C) = 2155C