Modelo de programación lineal

INVESTIGACION DE OPERACIONES

[pic 1]

        SOLUCION

Representación de Red

[pic 2]

Restricciones de Oferta

Modelo de programación lineal

[pic 3]

Restricciones de Oferta:

X14+X15 <  450

X24+ X25    <  600

X34+X35  <  380

Restricciones de Demanda:

X46+X56=300

X47+X57=300

X48+X58=300

X49+X59=400

F.O.= 4X1,4 + 7X1,5 + 8X2,4 + 5X2,5 + 5X3,4 + 6X3,5+6X4,6 + 4X4,7 + 8X4,8 + 4X4,9+ 3X5,6 + 6X5,7 + 7X5,8 + 7X5,9

7 restricciones

14 decisiones

[pic 4]

X13+X14 =100

X23+X24=200

X13+X14=100

X43+X45+X46-X14-X24-X34=0

X56-X35-X4<150

-X56-X46<150

La solución optima es:

Camino 1-3-5 = 100 unidades

2-4-5 = 50 unidades

2-4-5-6 = 150  unidades

[pic 5]

[pic 6]

[pic 7]

[pic 8]

F.O.= 10X1,1 + 4X1,2 + 10X1,3 + 7X1,4 + 8X1,5 + 9X1,6 + 9X1,7+9X2,1 + 10X2,2 + 9X2,3 + 9X2,4 + 5X2,5 + 7X2,6 + 9X2,7+6X3,1 + 5X3,2 + 10X3,3 + 8X3,4 + 6X3,5 + 5X3,6 + 9X3,7+5X4,1 + 7X4,2 + 8X4,3 + 10X4,4 + 5X4,5 + 6X4,6 + 5X4,7+8X5,1 + 6X5,2 + 9X5,3 + 10X5,4 + 6X5,5 + 4X5,6 + 6X5,7+7X6,1 + 6X6,2 + 8X6,3 + 8X6,4 + 7X6,5 + 8X6,6 + 7X6,7+6X7,1 + 4X7,2 + 7X7,3 + 9X7,4 + 8X7,5 + 9X7,6 + 8X7,7

Restricciones:

X1,1 + X1,2 + X1,3 + X1,4 +X1,5+X1,6+X1,7 = 1

X2,1 + X2,2 + X2,3 + X2,4 +X2,5+X2,6+X2,7= 1

X3,1 + X3,2 + X3,3 + X3,4 +X3,5+X3,6+X3,7= 1

X4,1 + X4,2 + X4,3 + X4,4 +X4,5+X4,6+X4,7= 1

X5,1 + X5,2 + X5,3 + X5,4 +X5,5+X5,6+X5,7= 1

X6,1 + X6,2 + X6,3 + X6,4 +X6,5+X6,6+X6,7= 1

X7,1 + X7,2 + X7,3 + X7,4 +X7,5+X7,6+X7,7= 1

Restricción de cada maquina

X1,1 + X2,1 + X3,1+ X4,1+ X5,1+ X6,1+ X7,1 = 1

X1,2 + X2,2 + X3,2 +X4,2+ X5,2+ X6,2+ X7,2= 1

X1,3 + X2,3 + X3,3 +X4,3+ X5,3+ X6,3+ X7,3= 1

X1,4 + X2,4 + X3,4 +X4,4+ X5,4+ X6,4+ X7,4= 1

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