Trabajo Análisis de Decisión Parte 1 (1)

APLICACIÓN DEL MÉTODO LP-GW-AHP Y DECISIÓN GRUPAL POR LÓGICA DIFUSA PARA EL ANÁLISIS DE CRITERIOS Y ALTERNATIVAS APLICADAS A

LA COMPRA DE UN TIQUETE AÉREO CON RUTA BOGOTÁ-MEDELLÍN

PRESENTADO POR:

GARCÍA BARRIOS DAVID ANDRÉS

GARCÍA LORA LILIBETH

HERRERA MURGAS ANDRES FELIPE

SAAVEDRA JIMÉNEZ PAUL ANDRÉS

ASIGNATURA:

INVESTIGACIÓN DE OPERACIONES 2

GRUPO 01

DOCENTE

ING. ADEL ALFONSO MENDOZA MENDOZA

MG

UNIVERSIDAD DEL ATLÁNTICO

FACULTAD DE INGENIERÍA

PROGRAMA DE INGENIERÍA INDUSTRIAL

BARRANQUILLA - 2015

PLANTEAMIENTO DEL PROBLEMA

Cuatro colegas universitarios que se encuentran actualmente en la ciudad de Bogotá (Colombia), deben realizar un viaje de ida a la ciudad de Medellín en el departamento de Antioquía, para ello se encuentran con que hay disponibles cinco compañías que ofrecen dentro de sus servicios dicho trayecto:

Alternativas Avianca Copa Airlines Viva Colombia LAN Satena

Para seleccionar la empresa donde comprarán los tiquetes aéreos, los cuatro universitarios, anuncian cuatro criterios principales:

Criterios Costo Servicio al cliente Prestigio Promociones

La estructura del problema de decisión se resume en el árbol del problema. Para realizar un análisis de decisión se aplica el método LP-GW-AHP, que consiste en un proceso de jerarquía analítica AHP para generar los pesos respectivos usando un modelo de programación lineal. Si las decisiones o preferencias de los cuatro expertos no coinciden, se llevará a cabo un desempate para tomar la decisión basándose en un método de decisión grupal por lógica difusa.

Árbol de decisión

EXPERTO 1

1. Criterios

Matriz de criterios

C SC P PRCosto ( C ) C 1 1/4 1/3 3Servicio al cliente (SC) SC 4 1 2 6Prestigio (P) P 3 1/2 1 4Promociones (PR) PR 1/3 1/6 1/4 1

Cálculo del parámetro β

Row ri∑j=1

R

aij r j1ri∑j=1

R

a ij r j Column c i∑j=1

n

aij c j1c i∑j=1

n

aij c j

1 4,5833 15,9167 3,4727 1 8,3333 31,4167 3,77002 13,000 58,8333 4,5256 2 1,9167 8,1250 4,23913 8,5000 35,7500 4,2059 3 3,5833 13,6944 3,82174 1,7500 7,5694 4,3254 4 14,0000 64,8333 4,6310

max i( 1r i∑j=1

R

aij r j)=4,5256 LINK Excel . Sheet .12 C:\\Users\\Lilly\\Desktop\\7mo semestre\\IO\\Trabajo-Solver-PL-AHP.xlsx Matriz1-Exp1!F20C16 ¿¿4 ¿¿MERGEFORMAT

max i( 1ci∑j=1

n

aij c j)=4,6310

β=min {maxi( 1ri∑j=1

R

aij r j),max i( 1ci∑j=1

n

aij c j)}β=4,5256

Modelo de programación lineal

Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

v1+1/ 4 v2+1/3v3+3 v4−w1=0

4 v1+v2+2 v3+6 v4−w2=0

3 v1+1/2 v2+v3+4 v4−w3=0

1/3v1+1/6 v2+1 /4 v3+v4−w4=0

w1+w2+w3+w4=1

v1−1/4,5256 w1≥ 0

v2−1/4,5256 w2≥ 0

v3−1/4,5256 w3≥ 0

v4−1/ 4,5256 w4≥ 0

v1−1/4 w1≤ 0

v2−1/4 w2 ≤0

v3−1/4 w3 ≤0

v4−1/ 4w4 ≤0

w1, w2 ,w3 ,w4 ≥ 0

v1 , v2 , v3 , v4 ≥ 0

2. Criterio: Costos

Matriz Costos

AV CA VC SA LAAV 1 3 1/3 2 1/2 AVIANCA (AV)CA 1/3 1 1/5 1/2 1/4 COPA AIRLINES (CA)VC 3 5 1 4 2 VIVA COLOMBIA (VC)SA 1/2 2 1/4 1 1/3 SATENA (SA)LA 2 4 1/2 3 1 LAN (LA)

Cálculo del parámetro β:

Row ri∑j=1

R

aij r j1ri∑j=1

R


n

aij c j1c i∑j=1

n

aij c j

1 6,8333 32,1000 4,6976 1 6,8333 32,1000 4,69762 2,2833 12,2278 5,3552 2 15,0000 84,2500 5,61673 15,000 84,2500 5,6167 3 2,2833 12,2278 5,35524 4,0833 19,3167 4,7306 4 10,5000 53,0500 5,05245 10,500 53,0500 5,0524 5 4,0833 19,3167 4,7306

max i( 1r i∑j=1

R

aij r j)=5,6167

max i( 1ci∑j=1

n

aij c j)=5,6167


R


n

aij c j)}β=5,6167


Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

w5≥ Z

v1+3 v2+1 /3 v3+2v4+1/2 v5−w1=0

1/3v1+v2+1 /5 v3+1 /2 v4+1/4 v5−w2=0

3 v1+5v2+v3+4 v4+2v5−w3=0

1/2v1+2 v2+1/4 v3+v 4+1/3 v5−w4=0

2 v1+4 v2+1/2v3+3 v4+v5−w5=0

w1+w2+w3+w4+w5=1

v1−1/5,6167 w1 ≥ 0

v2−1/5,6167 w2 ≥ 0

v3−1/5,6167 w3 ≥ 0

v4−1/5,6167 w4 ≥ 0

v4−1/5,6167 w4 ≥ 0

v5−1/5,6167 w5 ≥ 0

v1−1/5 w1 ≤0

v2−1/5 w2 ≤0

v3−1/5 w3 ≤ 0

v4−1/5 w4 ≤ 0

v5−1/5 w5 ≤ 0

w1, w2 ,w3 ,w4 ,w5≥ 0

v1 , v2 , v3 , v4 , v5 ≥ 0

3. Criterio: Servicio al cliente

Matriz servicio al cliente

AV CA VC SA LAAV 1 1/2 3 2 2 AVIANCA (AV)CA 2 1 5 2 4 COPA AIRLINERS (CA)VC 1/3 1/5 1 1/4 1/2 VIVA COLOMBIA (VC)SA 1/2 1/2 4 1 3 SATENA (SA)LA 1/2 1/4 2 1/3 1 LAN (LA)


Row ri∑j=1

R

aij r j1ri∑j=1

R


n

aij c j1c i∑j=1

n

aij c j

1 8,5000 48,5167 5,7078 1 4,3333 22,2750 5,14042 14,000

076,7500 5,4821 2 2,4500 13,0333 5,3197

3 2,283 12,2083 5,3467 3 15,0000 83,5833 5,57224 9,0000 41,6333 4,6259 4 5,5833 26,4000 4,72845 4,083 19,4000 4,7510 5 10,5000 53,2167 5,0683

max i( 1r i∑j=1

R

aij r j)=5,7078

max i( 1ci∑j=1

n

aij c j)=5,5722


R


n

aij c j)}β=5,5722


Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

w5≥ Z

v1+1/2v2+3 v3+2 v4+2 v5−w1=0

2 v1+v2+5 v3+2 v4+4 v5−w2=0

1/3v1+1/5 v2+v3+1 /4 v4+1/2 v5−w3=0

1/2v1+1/2 v2+4 v3+v 4+3 v5−w4=0

1/2v1+1/4 v2+2 v3+1/3v4+v5−w5=0

w1+w2+w3+w4+w5=1

v1−1/ 5,5722 w1≥ 0

v2−1/ 5,5722 w2≥ 0

v3−1/ 5,5722 w3≥ 0

v4−1/ 5,5722 w4 ≥ 0

v4−1/5,5722 w4 ≥0

v5−1/ 5,5722 w5≥ 0

v1−1/5 w1 ≤0

v2−1/5 w2 ≤0

v3−1/5 w3 ≤ 0

v4−1/5 w4 ≤ 0

v5−1/5 w5 ≤ 0

w1, w2 ,w3 ,w4 ,w5≥ 0

v1 , v2 , v3 , v4 , v5 ≥ 0

4. Criterio: Prestigio

Matriz prestigio

AV CA VC SA LAAV 1 3 5 5 2 AVIANCA (AV)CA 1/3 1 4 3 1/3 COPA AIRLINERS (CA)VC 1/5 1/4 1 1/2 1/5 VIVA COLOMBIA (VC)SA 1/5 1/3 2 1 1/5 SATENA (SA)LA 1/2 3 5 5 1 LAN (LA)


Row ri∑j=1

R

aij r j1ri∑j=1

R


n

aij c j1c i∑j=1

n

aij c j

1 16,0000 100,4167 6,2760 1 2,2333 12,9278 5,78862 8,6667 38,6333 4,4577 2 7,5833 34,5667 4,55823 2,150 12,2833 5,7132 3 17,0000 106,1667 6,24514 3,7333 17,0222 4,5595 4 14,5000 75,5833 5,21265 14,500 77,9167 5,3736 5 3,7333 17,0278 4,5610

max i( 1r i∑j=1

R

aij r j)=6,2760

max i( 1ci∑j=1

n

aij c j)=6,2451

β=min {m ax i( 1ri∑j=1

R

aij r j) ,max i( 1ci∑j=1

n

aij c j)}β=6,2451


Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

w5≥ Z

v1+3 v2+5 v3+5v4+2 v5−w1=0

1/3v1+v2+4 v3+3 v4+1/3 v5−w2=0

1/5v1+1/4 v2+v3+1/2 v 4+1/5 v5−w3=0

1/5v1+1/3 v2+2 v3+v4+1/5v5−w4=0

1/2v1+3 v2+5 v3+5 v4+v5−w5=0

w1+w2+w3+w4+w5=1

v1−1/ 6,2451 w1≥ 0

v2−1/ 6,2451 w2≥ 0

v3−1/ 6,2451 w3≥ 0

v4−1/ 6,2451 w4≥ 0

v4−1/6,2451 w4 ≥ 0

v5−1/ 6,2451 w5≥ 0

v1−1/5 w1 ≤0

v2−1/5 w2 ≤0

v3−1/5 w3 ≤ 0

v4−1/5 w4 ≤ 0

v5−1/5 w5 ≤ 0

w1, w2 ,w3 ,w4 ,w5≥ 0

v1 , v2 , v3 , v4 , v5 ≥ 0

5. Criterio: Promociones

Matriz promociones

AV CA VC SA LAAV 1 2 5 4 3 AVIANCA (AV)CA 1/2 1 4 4 2 COPA AIRLINERS (CA)VC 1/5 1/4 1 1/2 1/3 VIVA COLOMBIA (VC)SA 1/4 1/4 2 1 1/3 SATENA (SA)

LA 1/3 1/2 3 3 1 LAN (LA)


Row ri∑j=1

R

aij r j1ri∑j=1

R


n

aij c j1c i∑j=1

n

aij c j

1 15,0000

88,2500 5,8833 1 2,2833 12,6306 5,5316

2 11,5000

59,1333 5,1420 2 4,0000 18,7750 4,6938

3 2,283 12,6861 5,5560 3 15,0000 87,4167 5,82784 3,8333 17,6361 4,6007 4 12,5000 65,1333 5,21075 7,833 36,9333 4,7149 5 6,6667 30,6833 4,6025

max i( 1r i∑j=1

R

aij r j)=5,8833

max i( 1ci∑j=1

n

aij c j)=5,8278


R


n

aij c j)}β=5,8278


Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

w5≥ Z

v1+2 v2+5 v3+4 v4+3v5−w1=0

1/2v1+v2+4 v3+4 v 4+2 v5−w2=0

1/5v1+1/4 v2+v3+1/2 v 4+1/3 v5−w3=0

1/4 v1+1/4 v2+2v3+v 4+1/3v5−w4=0

1/3v1+1/2 v2+3 v3+3 v4+v5−w5=0

w1+w2+w3+w4+w5=1

v1−1/ 5,8278 w1≥ 0

v2−1/ 5,8278 w2≥ 0

v3−1/ 5,8278 w3≥ 0

v4−1/ 5,8278 w4≥ 0

v4−1/5,8278 w4 ≥ 0

v5−1/ 5,8278 w5≥ 0

v1−1/5 w1 ≤0

v2−1/5 w2 ≤0

v3−1/5 w3 ≤ 0

v4−1/5 w4 ≤ 0

v5−1/5 w5 ≤ 0

w1, w2 ,w3 ,w4 ,w5≥ 0

v1 , v2 , v3 , v4 , v5 ≥ 0

Árbol de decisión

RANKING

W PosiciónAVIANCA (AV) 0,287492 1º

COPA AIRLINERS (CA) 0,268022 2ºVIVA COLOMBIA (VC) 0,109757 5º

SATENA (SA) 0,146235 4ºLAN (LA) 0,188724 3º

EXPERTO 2

1. Criterios

Matriz criterios

C SC P PRCosto ( C) C 1 5 2 1/2Servicio al cliente (SC) SC 1/5 1 3 2Prestigio (P) P 1/2 1/3 1 1/3Promociones (PR) PR 2 1/2 3 1


Row ri∑j=1

R

aij r j1ri∑j=1

R


n

aij c j1c i∑j=1

n

aij c j

1 8,5000 47,0833 5,5392 1 3,7000 17,2333 4,65772 6,200 27,4000 4,4194 2 6,8333 30,2500 4,42683 2,1667 10,6500 4,9154 3 9,0000 48,4000 5,37784 6,5000 33,1000 5,0923 4 3,8333 22,3500 5,8304

max i( 1r i∑j=1

R

aij r j)=5,5392 LINK Excel . Sheet .12C:\\Users\\Lilly\\Desktop\\7mo semestre\\IO\\Trabajo-Solver-PL-AHP.xlsx Matriz1-Exp1!F20C16 ¿¿4 ¿¿MERGEFORMAT

max i( 1ci∑j=1

n

aij c j)=5,8304


R


n

aij c j)}

β=5,5392

Modelo de programación líneal

Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

v1+5 v2+2 v3+1 /2 v4−w1=0

1/5v1+v2+3 v3+2v4−w2=0

1/2v1+1/3 v2+v3+1 /3 v4−w3=0

2 v1+1/2 v2+3 v3+v4−w4=0

w1+w2+w3+w4=1

v1−1/5,5392 w1≥ 0

v2−1/5,5392 w2≥ 0

v3−1/5,5392 w3 ≥0

v4−1/5,5392 w4 ≥0

v1−1/4 w1≤ 0

v2−1/4 w2 ≤0

v3−1/4 w3 ≤0

v4−1/ 4w4 ≤0

w1, w2 ,w3 ,w4 ≥ 0

v1 , v2 , v3 , v4 ≥ 0

2. Criterio: Costos

Matriz Costos

AV CA VC SA LAAV 1 1/3 1/7 1/2 1/3 AVIANCA (AV)CA 3 1 1/6 1/2 1/2 COPA AIRLINERS (CA)

VC 7 6 1 4 5 VIVA COLOMBIA (VC)SA 2 2 1/4 1 2 SATENA (SA)LA 3 2 1/5 1/2 1 LAN (LA)


Row ri∑j=1

R

aij r j1ri∑j=1

R


n

aij c j1c i∑j=1

n

aij c j

1 2,3095 13,1758 5,7050 116,0000 101,8167 6,3635

2 5,1667 22,90364,4329

211,3333 57,8905 5,1080

3 23,000 132,66675,7681

31,7595 9,3258 5,3002

4 7,2500 41,35245,7038

46,5000 31,6214 4,8648

5 6,700 32,1869 4,8040 58,8333 41,6310 4,7129

max i( 1r i∑j=1

R

aij r j)=5,7681

ma xi( 1c i∑j=1

n

aij c j)=6,3635


R


n

aij c j)}β=5,7681


Max Z=Z

S.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

w5≥ Z

v1+1/3 v2+1 /7 v3+1/2 v4+1/3v5−w1=0

3 v1+v2+1 /6 v3+1/2 v4+1/2v5−w2=0

7 v1+6 v2+v3+4 v4+5 v5−w3=0

2 v1+2v2+1/4 v3+v 4+2v5−w4=0

3 v1+2v2+1/5 v3+1/2v 4+v5−w5=0

w1+w2+w3+w4+w5=1

v1−1/ 5,7681 w1≥ 0

v2−1/ 5,7681 w2≥ 0

v3−1/ 5,7681 w3≥ 0

v4−1/5,7681 w4 ≥0

v4−1/5,7681 w4 ≥0

v5−1/5,7681 w5 ≥0

v1−1/5 w1 ≤0

v2−1/5 w2 ≤0

v3−1/5 w3 ≤ 0

v4−1/5 w4 ≤ 0

v5−1/5 w5 ≤ 0

w1, w2 ,w3 ,w4 ,w5≥ 0

v1 , v2 , v3 , v4 , v5 ≥



AV CA VC SA LAAV 1 4 5 3 2 AVIANCA (AV)CA 1/4 1 3 4 1/3 COPA AIRLINERS (CA)VC 1/5 1/3 1 2 1/2 VIVA COLOMBIA (VC)SA 1/3 1/4 1/2 1 1/3 SATENA (SA)LA 1/2 3 2 3 1 LAN (LA)


Row ri∑j=1

R

aij r j1ri∑j=1

R


n

aij c j1c i∑j=1

n

aij c j

1 15,0000

95,7500 6,3833 1 2,2833 13,1458 5,7573

2 8,5833 37,2667 4,3417 2 8,5833 37,3000 4,34563 4,033 19,4778 4,8292 3 11,5000 63,5000 5,52174 2,4167 14,7458 6,1017 4 13,0000 89,6833 6,89875 9,500 58,0667 6,1123 5 4,1667 21,6778 5,2027

max i( 1r i∑j=1

R

aij r j)=6,3833

max i( 1ci∑j=1

n

aij c j)=6,8987


R


n

aij c j)}β=6,3833


Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

w5≥ Z

v1+4 v2+5 v3+3 v4+2v5−w1=0

1/4 v1+v2+3 v3+4 v4+1/3v5−w2=0

1/5v1+1/3 v2+v3+2 v4+1/2v5−w3=0

1/3v1+1/4 v2+1/2 v3+v 4+1/3 v5−w4=0

1/2v1+3 v2+2 v3+3v 4+v5−w5=0

w1+w2+w3+w4+w5=1

v1−1/6,3833 w1 ≥ 0

v2−1/ 6,3833 w2≥ 0

v3−1/6,3833 w3 ≥ 0

v4−1/ 6,3833 w4 ≥0

v4−1/ 6,3833 w4 ≥0

v5−1/ 6,3833 w5 ≥0

v1−1/5 w1 ≤0

v2−1/5 w2 ≤0

v3−1/5 w3 ≤ 0

v4−1/5 w4 ≤ 0

v5−1/5 w5 ≤ 0

w1, w2 ,w3 ,w4 ,w5≥ 0

v1 , v2 , v3 , v4 , v5 ≥ 0


Matriz prestigio

AV CA VC SA LAAV 1 5 4 7 3 AVIANCA (AV)CA 1/5 1 3 4 1/2 COPA AIRLINERS (CA)VC 1/4 1/3 1 2 1/3 VIVA COLOMBIA (VC)SA 1/7 1/4 1/2 1 1/4 SATENA (SA)LA 1/3 2 3 4 1 LAN (LA)


Row ri∑j=1

R

aij r j1ri∑j=1

R


n

aij c j1c i∑j=1

n

aij c j

1 20,0000 125,1667 6,2583 1 1,9262 10,7837 5,59852 8,7000 38,1881 4,3894 2 8,5833 36,7143 4,27743 3,917 19,5468 4,9907 3 11,5000 69,2048 6,01784 2,1429 11,7167 5,4678 4 18,0000 109,1500 6,06395 10,333 54,7214 5,2956 5 5,0833 23,4869 4,6204

max i( 1r i∑j=1

R

aij r j)=6,2583

max i( 1ci∑j=1

n

aij c j)=6,0639


R


n

aij c j)}

β=6,0639


Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

w5≥ Z

v1+5 v2+4 v3+7 v4+3 v5−w1=0

1/5v1+v2+3 v3+4 v4+1/2 v5−w2=0

1/4 v1+1/3v2+v3+2 v4+1/3 v5−w3=0

1/7v1+1/ 4v2+1/2 v3+v4+1/4 v5−w4=0

1/3v1+2 v2+3 v3+4 v 4+v5−w5=0

w1+w2+w3+w4+w5=1

v1−6,0639 w1 ≥ 0

v2−6,0639 w2 ≥ 0

v3−1/ 6,0639 w3 ≥0

v4−1/ 6,0639 w4 ≥0

v4−1/ 6,0639 w4 ≥0

v5−1/ 6,0639 w5 ≥0

v1−1/5 w1 ≤0

v2−1/5 w2 ≤0

v3−1/5 w3 ≤ 0

v4−1/5 w4 ≤ 0

v5−1/5 w5 ≤ 0

w1, w2 ,w3 ,w4 ,w5≥ 0

v1 , v2 , v3 , v4 , v5 ≥ 0

5. Criterio: promociones

Matriz promociones

AV CA VC SA LAAV 1 4 1/2 2 1 AVIANCA (AV)CA 1/4 1 1/3 3 2 COPA AIRLINERS (CA)VC 2 3 1 5 3 VIVA COLOMBIA (VC)

SA 1/2 1/3 1/5 1 1/2 SATENA (SA)LA 1 1/2 1/3 2 1 LAN (LA)


Row ri∑j=1

R

aij r j1ri∑j=1

R


n

aij c j1c i∑j=1

n

aij c j

1 8,5000 51,7333 6,0863 1 4,7500 25,6917 5,40882 6,5833 30,6417 4,6544 2 8,8333 43,0167 4,86983 14,000 77,9167 5,565 3 2,3667 12,7861 5,40264 2,5333 14,1944 5,6031 4 13,0000 75,8333 5,83335 4,833 26,3583 5,4534 5 7,5000 43,5167 5,8022

max i( 1r i∑j=1

R

aij r j)=6,0863

max i( 1ci∑j=1

n

aij c j)=5,8333


R


n

aij c j)}β=5,8333


Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

w5≥ Z

v1+4 v2+1/2 v3+2v 4+v5−w1=0

1/4 v1+v2+1/3v3+3 v4+2 v5−w2=0

2 v1+3v2+v3+5 v4+3 v5−w3=0

1/2v1+1/3 v2+1/5v3+v4+1/2v5−w4=0

1 v1+1/2 v2+1/3 v3+2v4+v5−w5=0

w1+w2+w3+w4+w5=1

v1−1/ 5,8333 w1≥ 0

v2−1/ 5,8333 w2≥ 0

v3−1/ 5,8333 w3≥ 0

v4−1/ 5,8333 w4≥ 0

v4−1/5,8333 w4 ≥ 0

v5−1/ 5,8333 w5≥ 0

v1−1/5 w1 ≤0

v2−1/5 w2 ≤0

v3−1/5 w3 ≤ 0

v4−1/5 w4 ≤ 0

v5−1/5 w5 ≤ 0

w1, w2 ,w3 ,w4 ,w5≥ 0

v1 , v2 , v3 , v4 , v5 ≥ 0

Árbol de decisión:

RANKING




EXPERTO 3

1. Criterios

Matriz de criterios

C SC P PRCosto ( C) C 1 3 5 1Sev. al cliente (SC)

SC 1/3 1 3 1/5

Prestigio (P) P 1/5 1/3 1 1/3Promociones (PR) PR 1 5 3 1


Row ri∑j=1

R

aij r j1ri∑j=1

R


n

aij c j1c i∑j=1

n

aij c j

1 10,0000 42,9333 4,2933 1 2,5333 10,5778 4,17542 4,533 15,4667 3,4118 2 9,3333 33,6000 3,60003 1,8667 8,7111 4,6667 3 12,0000 60,2667 5,02224 10,0000 48,2667 4,8267 4 2,5333 10,9333 4,3158

max i( 1r i∑j=1

R

aij r j)=4,8267

LINK Excel . Sheet .12 C:\\Users\\Lilly\\Desktop\\7mo semestre\\IO\\Trabajo-Solver-PL-AHP.xlsx Matriz1-Exp1!F20C16¿¿ 4¿¿ MERGEFORMAT

max i( 1ci∑j=1

n

aij c j)=5,0222


R


n

aij c j)}β=4,8267


Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

v1+3 v2+5 v3+v4−w1=0

1/3v1+v2+1 /3 v3+1 /5 v4−w2=0

1/5v1+1/3 v2+v3+1 /3 v4−w3=0

v1+5 v2+3 v3+v4−w4=0

w1+w2+w3+w4=1

v1−1/4,8267 w1≥ 0

v2−1/4,8267 w2≥ 0

v3−1/4,8267 w3≥ 0

v4−1/ 4,8267 w4≥ 0

v1−1/4 w1≤ 0

v2−1/4 w2 ≤0

v3−1/4 w3 ≤0

v4−1/ 4w4 ≤0

w1, w2 ,w3 ,w4 ≥ 0

v1 , v2 , v3 , v4 ≥ 0

2. Criterio: Costos

Matriz Costos

AV CA VC SA LAAV 1 3 1/2 2 2 AVIANCA (AV)CA 1/3 1 1/3 1 1/3 COPA AIRLINERS (CA)VC 2 3 1 3 2 VIVA COLOMBIA (VC)SA 1/2 1 1/3 1 2 SATENA (SA)LA 1/2 3 1/2 1/2 1 LAN (LA)


Row ri∑j=1

R

aij r j1ri∑j=1

R


n

aij c j1c i∑j=1

n

aij c j

1 8,5000 43,6667 5,1373 1 4,3333 20,7500 4,78852 3,0000 16,1667 5,3889 2 11,0000 61,5000 5,59093 11,000 62,5000 5,6818 3 2,6667 14,6667 5,50004 4,8333 26,7500 5,5345 4 7,5000 38,8333 5,17785 5,500 26,6667 4,8485 5 7,3333 40,0000 5,4545

max i( 1r i∑j=1

R

aij r j)=5,6818

max i( 1ci∑j=1

n

aij c j)=5,5909


R


n

aij c j)}β=5,5909


Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

w5≥ Z

v1+3 v2+1 /2 v3+2 v4+2 v5−w1=0

1/3v1+1+1/3 v3+v4+1/3 v5−w2=0

2 v1+3v2+v3+3 v4+2 v5−w3=0

1/2v1+1 v2+1/3 v3+v 4+2 v5−w4=0

1/2v1+3 v2+1/2 v3+1/2 v4+1 v5−w5=0

w1+w2+w3+w4+w5=1

v1−1/5,5909 w1 ≥0

v2−1/5,5909 w2 ≥0

v3−1/5,5909 w3 ≥ 0

v4−1/5,5909 w4 ≥ 0

v4−1/5,5909 w4 ≥ 0

v5−1/5,5909 w5 ≥ 0

v1−1/5 w1 ≤0

v2−1/5 w2 ≤0

v3−1/5 w3 ≤ 0

v4−1/5 w4 ≤ 0

v5−1/5 w5 ≤ 0

w1, w2 ,w3 ,w4 ,w5≥ 0

v1 , v2 , v3 , v4 , v5 ≥ 0



AV CA VC SA LAAV 1 2 3 2 1 AVIANCA (AV)CA 1/2 1 3 2 1 COPA AIRLINERS (CA)VC 1/3 1/3 1 1/2 1/3 VIVA COLOMBIA (VC)SA 1/2 1/2 2 1 1/2 SATENA (SA)LA 1 1 3 2 1 LAN (LA)


Row ri∑j=1

R

aij r j1ri∑j=1

R


n

aij c j1c i∑j=1

n

aij c j

1 9,0000 48,5000 5,3889 1 3,3333 17,3333 5,20002 7,5000 36,5000 4,8667 2 4,8333 23,0833 4,77593 2,500 12,9167 5,1667 3 12,0000 63,0000 5,25004 4,5000 21,7500 4,8333 4 7,5000 37,5000 5,00005 8,000 41,0000 5,1250 5 3,8333 19,7500 5,1522

max i( 1r i∑j=1

R

aij r j)=5,3889

max i( 1ci∑j=1

n

aij c j)=5,2500


R


n

aij c j)}β=5,2500


Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

w5≥ Z

v1+2 v2+3 v3+2v4+1 v5−w1=0

1/2v1+v2+3 v3+2 v4+v5−w2=0

1/3v1+1/3 v2+v3+1 /2 v4+1/3v5−w3=0

1/2v1+1/2 v2+2 v3+v 4+1/2v5−w4=0

v1+v2+3 v3+2 v4+v5−w5=0

w1+w2+w3+w4+w5=1

v1−1/ 5,2500 w1≥ 0

v2−1/ 5,2500 w2≥ 0

v3−1/ 5,2500 w3≥ 0

v4−1/ 5,2500 w4≥ 0

v4−1/5,2500 w4 ≥ 0

v5−1/ 5,2500 w5≥ 0

v1−1/5 w1 ≤0

v2−1/5 w2 ≤0

v3−1/5 w3 ≤ 0

v4−1/5 w4 ≤ 0

v5−1/5 w5 ≤ 0

w1, w2 ,w3 ,w4 ,w5≥ 0

v1 , v2 , v3 , v4 , v5 ≥ 0


Matriz prestigio

AV CA VC SA LAAV 1 2 4 3 2 AVIANCA (AV)CA 1/2 1 3 3 2 COPA AIRLINERS (CA)VC 1/4 1/3 1 1 1/3 VIVA COLOMBIA (VC)SA 1/3 1/3 1 1 1/2 SATENA (SA)LA 1/2 1/2 3 2 1 LAN (LA)


Row ri∑j=1

R

aij r j1ri∑j=1

R

a i j r j Column c i∑j=1

n

aij c j1c i∑j=1

n

aij c j

1 12,0000 66,1667 5,5139 1 2,5833 13,9167 5,38712 9,5000 47,7500 5,0263 2 4,1667 19,5833 4,70003 2,917 14,5833 5,0000 3 12,0000 62,3333 5,19444 3,1667 16,7500 5,2895 4 10,0000 53,9167 5,39175 7,000 32,8333 4,6905 5 5,8333 28,3333 4,8571

max i( 1r i∑j=1

R

aij r j)=5,5139

max i( 1ci∑j=1

n

aij c j)=5,3917


R


n

aij c j)}β=5,3917


Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

w5≥ Z

v1+2+4 v3+3 v4+2v5−w1=0

1/2v1+v2+3 v3+3 v4+2 v5−w2=0

1/4 v1+1/3v2+v3+v4+1/3v5−w3=0

1/3v1+1/3 v2+v3+v4+1 /2 v5−w4=0

1/2v1+1/2 v2+3 v3+2v4+v5−w5=0

w1+w2+w3+w4+w5=1

v1−1/ 5,3917 w1≥ 0

v2−1/ 5,3917 w2≥ 0

v3−1/ 5,3917 w3 ≥0

v4−1/ 5,3917 w4 ≥0

v4−1/5,3917 w4 ≥ 0

v5−1/ 5,3917 w5 ≥0

v1−1/5 w1 ≤0

v2−1/5 w2 ≤0

v3−1/5 w3 ≤ 0

v4−1/5 w4 ≤ 0

v5−1/5 w5 ≤ 0

w1, w2 ,w3 ,w4 ,w5≥ 0

v1 , v2 , v3 , v4 , v5 ≥ 0


Matriz promociones

AV CA VC SA LAAV 1 2 1/3 2 2 AVIANCA (AV)CA 1/2 1 1/3 2 2 COPA AIRLINERS (CA)VC 3 3 1 2 3 VIVA COLOMBIA (VC)SA 1/2 1/2 1/2 1 4 SATENA (SA)LA 1/2 1/2 1/3 1/4 1 LAN (LA)


Row ri∑j=1

R

aij r j1ri∑j=1

R


n

aij c j1c i∑j=1

n

aij c j

1 7,3333 41,1667 5,6136 1 5,5000 26,1250 4,75002 5,8333 31,6667 5,4286 2 7,0000 35,1250 5,01793 12,000 72,2500 6,0208 3 2,5000 14,2917 5,71674 6,5000 29,4167 4,5256 4 7,2500 40,2500 5,55175 2,583 14,7917 5,7258 5 12,0000 73,5000 6,1250

max i( 1r i∑j=1

R

aij r j)=6,0208

max i( 1ci∑j=1

n

aij c j)=6,1250


R


n

aij c j)}β=6,0208


Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

w5≥ Z

v1+2 v2+1/3 v3+2 v4+2 v5−w1=0

1/2v1+v2+1/3 v3+2 v4+2 v5−w2=0

3 v1+3v2+v3+2v4+3 v5−w3=0

1/2v1+1/2 v2+1/2v3+v 4+4 v5−w4=0

1/2v1+1/2 v2+1/3v3+1/4 v4+v5−w5=0

w1+w2+w3+w4+w5=1

v1−1/ 5,8278 w1≥ 0

v2−1/ 5,8278 w2≥ 0

v3−1/ 5,8278 w3≥ 0

v4−1/ 5,8278 w4≥ 0

v4−1/5,8278 w4 ≥ 0

v5−1/ 5,8278 w5≥ 0

v1−1/5 w1 ≤0

v2−1/5 w2 ≤0

v3−1/5 w3 ≤ 0

v4−1/5 w4 ≤ 0

v5−1/5 w5 ≤ 0

w1, w2 ,w3 ,w4 ,w5≥ 0

v1 , v2 , v3 , v4 , v5 ≥ 0

Árbol de decisión

RANKING

W PosiciónAVIANCA (AV) 0,25005614 2°

COPA AIRLINERS (CA) 0,15233042 3°VIVA COLOMBIA (VC) 0,30973399 1°

SATENA (SA) 0,14564085 4°LAN (LA) 0,1422386 5°

EXPERTO 4

1. Criterios

Matriz de criterios

C SC P PRCosto ( C) C 1 5 6 1/2Sev. al cliente (SC) SC 1/5 1 3 1/6Prestigio (P) P 1/6 1/3 1 1/6Promociones (PR) PR 2 6 6 1


Row ri∑j=1

R

aij r j1ri∑j=1

R


n

aij c j1c i∑j=1

n

aij c j

1 12,5000 51,8333 4,1467 1 3,3667 12,1667 3,61392 4,367 14,3667 3,2901 2 12,3333 45,5000 3,68923 1,6667 7,7056 4,6233 3 16,0000 84,2000 5,26254 15,0000 76,2000 5,0800 4 1,8333 8,2389 4,4939

max i( 1r i∑j=1

R

aij r j)=5,0800

LINK Excel . Sheet .12 C:\\Users\\Lilly\\Desktop\\7mo semestre\\IO\\Trabajo-Solver-PL-AHP.xlsx Matriz1-Exp1!F20C16¿¿ 4¿¿ MERGEFORMAT

max i( 1ci∑j=1

n

aij c j)=5,2625


R


n

aij c j)}β=5,0800


Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

v1+5 v2+6 v3+1/2v4−w1=0

1/5v1+v2+3 v3+1 /6 v4−w2=0

1/6 v1+1/3 v2+v3+1/6 v4−w3=0

2 v1+6 v2+6 v3+v4−w4=0

w1+w2+w3+w4=1

v1−1/5,0800 w1 ≥0

v2−1/5,0800 w2 ≥ 0

v3−1/5,0800 w3 ≥ 0

v4−1/5,0800 w4 ≥ 0

v1−1/4 w1≤ 0

v2−1/4 w2 ≤0

v3−1/4 w3 ≤0

v4−1/ 4w4 ≤0

w1, w2 ,w3 ,w4 ≥ 0

v1 , v2 , v3 , v4 ≥ 0

2. Criterio: Costos

Matriz Costos

AV CA VC SA LAAV 1 4 1/5 6 1/3 AVIANCA (AV)CA 1/4 1 1/6 4 1/4 COPA AIRLINERS (CA)VC 5 6 1 8 4 VIVA COLOMBIA (VC)SA 1/6 1/4 1/8 1 1/5 SATENA (SA)LA 3 4 1/4 5 1 LAN (LA)


Row ri∑j=1

R

aij r j1ri∑j=1

R


n

aij c j1c i∑j=1

n

aij c j

1 11,5333 53,8667 4,6705 1 9,4167 43,2875 4,59692 5,6667 22,8292 4,0287 2 15,2500 92,5000 6,06563 24,000 182,6000 7,6083 3 1,7417 10,6125 6,0933

4 1,7417 10,7306 6,1611 4 24,0000184,350

07,6813

5 13,250 85,2250 6,4321 5 5,7833 24,5014 4,2366

max i( 1r i∑j=1

R

aij r j)=7,6083

max i( 1ci∑j=1

n

aij c j)=7,6813


R


n

aij c j)}β=7,6083


Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

w5≥ Z

v1+4 v2+1/5 v3+6 v4+1/3 v5−w1=0

1/4 v1+v2+1/6+4 v4+1/4 v5−w2=0

5 v1+6 v2+v3+8v 4+4 v5−w3=0

1/6 v1+1/ 4v2+1/8 v3+v4+1 /5 v5−w4=0

3 v1+4 v2+1/4 v3+5v 4+v5−w5=0

w1+w2+w3+w4+w5=1

v1−1/7,6083 w1 ≥0

v2−1/7,6083 w2 ≥ 0

v3−1/7,6083 w3 ≥ 0

v4−1/7,6083 w4 ≥ 0

v4−1/7,6083 w4 ≥ 0

v5−1/7,6083 w5 ≥ 0

v1−1/5 w1 ≤0

v2−1/5 w2 ≤0

v3−1/5 w3 ≤ 0

v4−1/5 w4 ≤ 0

v5−1/5 w5 ≤ 0

w1, w2 ,w3 ,w4 ,w5≥ 0

v1 , v2 , v3 , v4 , v5 ≥ 0


AV CA VC SA LA

AV 1 1/4 4 3 1/4 AVIANCA (AV)CA 4 1 7 5 2 COPA AIRLINERS (CA)VC 1/4 1/7 1 1/3 1/5 VIVA COLOMBIA (VC)SA 1/3 1/5 3 1 1/4 SATENA (SA)LA 4 1/2 5 4 1 LAN (LA)


Ro w ri∑j=1

R

aij r j1ri∑j=1

R


n

aij c j1c i∑j=1

n

aij c j

1 8,5000 38,9298 4,5800 1 9,5833 42,1992 4,4034

219,000

0 119,4000 6,2842 2 2,0929 11,8625 5,66813 1,926 11,2599 5,8457 3 20,0000 131,4833 6,57424 4,7833 20,8202 4,3527 4 13,3333 74,0143 5,55115 14,500 86,7643 5,9837 5 3,7000 17,6149 4,7608

max i( 1r i∑j=1

R

aij r j)=6,2842

max i( 1ci∑j=1

n

aij c j)=6,5742


R


n

aij c j)}β=6,2842


Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

w5≥ Z

v1+1/ 4 v2+4 v3+3 v4+1/4 v5−w1=0

4 v1+v2+7 v3+5 v4+2v5−w2=0

1/4 v1+1/7v2+v3+1 /3 v4+1/5 v5−w3=0

1/3v1+1/5 v2+3 v3+v4+1/ 4 v5−w4=0

4 v1+1/2 v2+5v3+4 v4+v5−w5=0

w1+w2+w3+w4+w5=1

v1−1/ 6,2842 w1≥ 0

v2−1/ 6,2842 w2≥ 0

v3−1/ 6,2842 w3≥ 0

v4−1/ 6,2842 w4≥ 0

v4−1/6,2842 w4 ≥ 0

v5−1/ 6,2842 w5≥ 0

v1−1/5 w1 ≤0

v2−1/5 w2 ≤0

v3−1/5 w3 ≤ 0

v4−1/5 w4 ≤ 0

v5−1/5 w5 ≤ 0

w1, w2 ,w3 ,w4 ,w5≥ 0

v1 , v2 , v3 , v4 , v5 ≥ 0


Matriz prestigio

AV CA VC SA LAAV 1 1/4 4 3 1/3 AVIANCA (AV)CA 4 1 7 5 2 COPA AIRLINERS (CA)VC 1/4 1/7 1 1/3 1/5 VIVA COLOMBIA (VC)SA 1/3 1/5 3 1 1/4 SATENA (SA)LA 3 1/2 5 4 1 LAN (LA)


Row ri∑j=1

R

aij r j1ri∑j=1

R


n

aij c j1c i∑j=1

n

aij c j

1 8,5833 39,8881 4,6472 1 8,5833 37,7492 4,3980

219,000

0 117,7333 6,1965 2 2,0929 11,6542 5,56853 1,926 11,0808 5,7527 3 20,0000 127,9000 6,39504 4,7833 20,5980 4,3062 4 13,3333 71,3476 5,35115 13,500 77,5143 5,7418 5 3,7833 18,1635 4,8009

max i( 1r i∑j=1

R

aij r j)=6,1965

max i( 1ci∑j=1

n

aij c j)=6,3950


R


n

aij c j)}β=6,1965


Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

w5≥ Z

v1+1/ 4 v2+4 v3+3 v4+1/3v5−w1=0

4 v1+v2+7 v3+5 v4+2v5−w2=0

1/4 v1+1/7v2+v3+1 /3 v4+1/5 v5−w3=0

1/3v1+1/5 v2+3 v3+v4+1/ 4 v5−w4=0

3 v1+1/2 v2+5 v3+4 v 4+v5−w5=0

w1+w2+w3+w4+w5=1

v1−1/ 6,1965 w1≥ 0

v2−1/ 6,1965 w2≥ 0

v3−1/ 6,1965 w3 ≥0

v4−1/ 6,1965 w4 ≥0

v4−1/6,1965 w4 ≥ 0

v5−1/ 6,1965 w5 ≥0

v1−1/5 w1 ≤0

v2−1/5 w2 ≤0

v3−1/5 w3 ≤ 0

v4−1/5 w4 ≤ 0

v5−1/5 w5 ≤ 0

w1, w2 ,w3 ,w4 ,w5≥ 0

v1 , v2 , v3 , v4 , v5 ≥ 0


Matriz promociones

AV CA VC SA LAAV 1 3 4 6 2 AVIANCA (AV)CA 1/3 1 4 5 1/3 COPA AIRLINERS (CA)VC 1/4 1/4 1 1/2 1/5 VIVA COLOMBIA (VC)SA 1/6 1/5 2 1 1/6 SATENA (SA)LA 1/2 3 4 6 1 LAN (LA)


Row ri∑j=1

R

aij r j1ri∑j=1

R


n

aij c j1c i∑j=1

n

aij c j

116,000

0 107,0000 6,6875 1 2,2500 13,4167 5,9630

210,666

7 47,3000 4,4344 2 7,4500 32,7500 4,39603 2,200 13,5333 6,1515 3 15,0000 105,6000 7,04004 3,5333 15,1500 4,2877 4 18,5000 98,9500 5,34865 14,500 84,5000 5,8276 5 3,7000 16,7667 4,5315

max i( 1r i∑j=1

R

aij r j)=6,6875

max i( 1ci∑j=1

n

aij c j)=7,0400


R


n

aij c j)}β=6,6875


Max Z=ZS.A:

w1≥ Z

w2≥ Z

w3≥ Z

w4 ≥ Z

w5≥ Z

v1+3 v2+4 v3+6 v4+2 v5−w1=0

1/3v1+v2+4 v3+5 v4+1/3 v5−w2=0

1/4 v1+1/4 v2+v3+1/2v4+1/5v5−w3=0

1/6 v1+1/5 v2+2 v3+v4+1/6 v5−w4=0

1/2v1+3 v2+4 v3+6 v4+v5−w5=0

w1+w2+w3+w4+w5=1

v1−1/ 6,6875 w1≥ 0

v2−1/ 6,6875 w2≥ 0

v3−1/ 6,6875 w3 ≥0

v4−1/ 6,6875 w4 ≥0

v4−1/6,6875 w4 ≥ 0

v5−1/ 6,6875 w5 ≥0

v1−1/5 w1 ≤0

v2−1/5 w2 ≤0

v3−1/5 w3 ≤ 0

v4−1/5 w4 ≤ 0

v5−1/5 w5 ≤ 0

w1, w2 ,w3 ,w4 ,w5≥ 0

v1 , v2 , v3 , v4 , v5 ≥ 0

Árbol de decisión

RANKING




Trabajo Análisis de Decisión Parte 1 (1)

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Transcript of Trabajo Análisis de Decisión Parte 1 (1)