Método de Dos Fases

Min: Z=30A + 20B s.a.

13A + 18B >= 200 28A + 23B >= 500 A,B>=0 Aplicar el método de las dos fases Organización

Min. Z =

t1 + t2

s.a. 131 + 18 182 ! "1 "1 281 + 23 232

+ tt1 1 ! "2

= 200 + tt2 2 = 500 1, 2 >=0

! t1 t 1 ! t2 t2 + Z = 131 + 18 182 ! "1 "1 281 + 23 232

+ tt1 1 ! "2

0

= 200 + tt2 2 = 500

Base

Z#!$#

X1

X2

S1

S2

t1

t2

Z

LD

13

18

!1

0

1

0

0

200

28

23

0

!1

0

1

0

500

0

0

0

0

1

1

1

0

FASE  Base

X1

X2

S1

S2

t1

t2

%la 1 &f1'

13

18

!1

0

1

0

%la 2 &f2'

28

23

0

!1

0

1

0

0

0

0

1

1

%la 3 &f3'

Z#!$#

(acer in)resar las ar*%ciales a la ase f3 ! f3 ! &f1 + f2'

"e -sca -e los indicadores o coe%cientes de las /a

&!1'f1

!13

!18

1

0

!1

0

&!1'f2

!28

!23

0

1

0

!1

0

0

0

0

1

1

!1

!1

1

1

0

0

f3 f3 ! f1 ! f2

Base

X1

X2

S1

S2

t1

t2

f1

t1

13

18

!1

0

1

0

f2

t2

28

23

0

!1

0

1

f3

Z#!$#

!1

!1

1

1

0

0

M!t"#" Si$%&e'

nicio 1era iteracin Base

X1

X2

S1

S2

t1

t2

f1

t1

13

18

!1

0

1

0

f2

t2

28

23

0

!1

0

1

f3

Z#!$#

!1

!1

1

1

0

0

col. 4i/ote f1 ! &113'f1 Base

X1

X2

S1

S2

1 1.3861538 !0.076231

t1

t2

f1

1

0 0.0762308

0

f2

t2

28

23

0

!1

0

1

f3

Z#!$#

!1

!1

1

1

0

0

f2! &!28'f1 + f2 Base

X1

X2

S1

S2

t1

t2

f1

1

1 1.3861538 !0.076231

0 0.0762308

0

f2

t2

0 !15.76231 2.1538615

!1 !2.153862

1

f3

Z#!$#

!1

!1

1

1

0

0

f3! &1'f1 + f3 Base

X1

X2

S1

S2

t1

t2

f1

1

1 1.3861538 !0.076231

0 0.0762308

0

f2

t2

0 !15.76231 2.1538615

!1 !2.153862

1

f3

Z#!$#

0 15.762308 !2.153862

1 3.1538615

0

col. 4i/ote 9in 1era iteracin nicio 2da iteracin f2 ! &1328'f2 Base

X1

X2

S1

S2

f1

1

1 1.3861538 !0.076231

f2

"1

0 !7.321286

f3

Z#!$#

t1

t2

0 0.0762308

1 !0.62857

0 15.762308 !2.153862

0

!1 0.628571

1 3.1538615

0

f1 ! &113'f2 + f1 Base

X1

X2

S1

S2

t1

t2

f1

1

1 0.8212857

0 !0.035713

0 0.035712

f2

"1

0 !7.321286

1 !0.62857

!1 0.628571

f3

Z#!$#

0 15.762308 !2.153862

1 3.1538615

0

f3 ! &2813'f2 + f3 Base

X1

X2

S1

S2

t1

t2

f1

1

1 0.8212857

0 !0.035713

0 0.035712

f2

"1

0 !7.321286

1 !0.62857

!1 0.628571

f3

Z#!$#

0

0

:odos los indicadores son posi*/os Z=0 la fase  ; se eliminan las col-mnas ar*%ciales

0

0

1

1

Z

LD

0

200

0

500

1

0

riales ar*%ciales sea 0 0

!200

0

!500

1

0

1

!700

Z

LD

0

200

0

500

1

!700

Z

LD

0

200 15.38615 %la pi/ote

0

500 17.85712

1

Z

!700

LD

0 15.38615 0

500

1

!700

Z

LD

0 15.38615 0 6.230762 1

Z

!700

LD

0 15.38615 0 6.230762 %la pi/ote

1 !6.23076

Z

LD

0 15.38615 0 32.128571 1 !6.23076

Z

LD

0 17.85712 0 32.128571 1 !6.23076

Z

LD

0 17.85712 0 32.128571 1

0

Fase 

4rimero se a)re)an los coe%cientes reales de las /ariales 1, 2

1

2

f3 ! &!30'f1

"1

"2

Z

?

1

1 0.8212857

0 !0.035713

0 17.85712

"1

0 !7.321286

1 !0.62857

0 32.128571

0

1

Z

30

20

0

0

"imple@ Base

1

2

"1

"2

Z

?

1

1 0.8212857

0 !0.035713

0 17.85712

"1

0 !7.321286

1 !0.62857

0 32.128571

Z

0 !.628571

0 1.0712857

1 !535.712

col. 4i/ote Base

1

2

"1

"2

Z

?

1

1 0.8212857

0 !0.035713

0 17.85712

"1

0 !7.321286

1 !0.62857

0 32.128571

Z

0 !.628571

0 1.0712857

1 !535.712

f1 ! &2328'f1 Base 1

1

2

0.8212857

"1

"2

Z

?

0.677

0 !0.023367

0 1.6683673

"1

0 !7.321286

1 !0.62857

0 32.128571

Z

0 !.628571

0 1.0712857

1 !535.712

+ f3

%la pi/ote