Trabalho de Pesquisa Operacional - Variáveis mistas
Por: 1LucasR • 28/11/2016 • Trabalho acadêmico • 4.620 Palavras (19 Páginas) • 438 Visualizações
UNIVERSIDADE DO VALE DO RIO DOS SINOS
Aluno: Lucas Rosa
Professor:Alexsander Longhi
Disciplina: Pesquisa Operacional
Data 21/11/2016
[pic 1]
- Definição das variáveis
! Y¡ : fabricar ou não os produtos Y, sendo Y = { zero ou 1} ;
!X¡ : quantidade máxima de produção do produto X,
sendo X = { 1,2,3,4,5,6};
- Função objetivo
MAX 85X1 + 78X2 + 69X3+ 69X4 + 58X5 + 99X6
- Restrições
Y1 + Y2 + Y3 + Y4 + Y5 + Y6 = 3
Os produtos 2 e 5 se forem produzidos devem ir juntos, então se Y2 receber 1 o Y5 deve receber também, se receber 0 de igual forma. Y2= Y5 ,
logo Y2- Y5=0.
P1 480/21= 22,86 = 23
P2 480/35 = 13,71 = 14
P3= 480/25= 19,20 = 19
P4 = 720/23 = 31,30 = 31
P5= 720/33 = 21,82 = 22
P6= 720/27 = 26,67= 27
200 y1 - x1 > 0
200 y2 - x2 > 0
200 y3 - x3 > 0
200 y4 - x4 > 0
200 y5 - x5 > 0
200 y6 – x6 > 0
ST
19x1 + 9x2 + 0x3 + 12x4 + 16x5 + 14x6 < 480
21x1 + 18x2 + 7x3+ 0x4 + 11x5 + 13x6< 480
13x1+ 35x2 + 25x3 + 19x4 + 0x5 + 24x6 < 480
0x1 + 14x2 + 17x3 + 23x4 + 33x5 + 27x6 < 720
- Solução no software
!y1:fabricar ou não os produtos Y, sendo Y = { zero ou 1};
!x1:quantidade máxima de produção do produto X, sendo X= {1,2,3,4,5,6};
MAX 85x1 + 78x2 + 69x3 + 69x4 + 58x5 + 99x6
ST
Etapa1)19x1+9x2+0x3+12x4+16x5+14x6<480
Etapa2)21x1+18x2+7x3+0x4+11x5+13x6<480
Etapa3)13x1+35x2+25x3+19x4+0x5+24x6<480
Etapa4)0x1+14x2+17x3+23x4+33x5+27x6<720
i)Y1+Y2+Y3+Y4+Y5+Y6=3
ii)Y2-Y5=0
200y1-x1>0
200y2-x2>0
200y3-x3>0
200y4-x4>0
200y5-x5>0
200y6-x6>0
END
INT Y1
INT Y2
INT Y3
INT Y4
INT Y5
INT Y6
GIN X1
GIN X2
GIN X3
GIN X4
GIN X5
GIN X6
- Resposta do Software
LP OPTIMUM FOUND AT STEP 10
OBJECTIVE VALUE = 2766.43457
SET Y1 TO <= 0 AT 1, BND= 2296. TWIN= 2766. 39
SET Y3 TO <= 0 AT 2, BND= 2296. TWIN= 2296. 44
SET Y4 TO <= 0 AT 3, BND= 2296. TWIN= 2296. 50
SET X5 TO <= 5 AT 4, BND= 2270. TWIN= 2281. 53
NEW INTEGER SOLUTION OF 2270.00000 AT BRANCH 4 PIVOT 53
BOUND ON OPTIMUM: 2766.435
FLIP X5 TO >= 6 AT 4 WITH BND= 2280.9163
SET X4 TO <= 0 AT 5, BND= 2281. TWIN=-0.1000E+31 53
SET X5 TO <= 6 AT 6, BND= 2281. TWIN=-0.1000E+31 53
SET X2 TO >= 1 AT 7, BND= 2262. TWIN= 2262. 57
DELETE X2 AT LEVEL 7
DELETE X5 AT LEVEL 6
DELETE X4 AT LEVEL 5
DELETE X5 AT LEVEL 4
FLIP Y4 TO >= 1 AT 3 WITH BND= 2296.3635
SET Y6 TO >= 1 AT 4, BND= 2296. TWIN= 1998. 61
DELETE Y2 AT LEVEL 5
DELETE Y6 AT LEVEL 4
DELETE Y4 AT LEVEL 3
FLIP Y3 TO >= 1 AT 2 WITH BND= 2296.3635
SET Y6 TO >= 1 AT 3, BND= 2296. TWIN= 2016. 67
SET Y2 TO <= 0 AT 4, BND= 1980. TWIN=-0.1000E+31 72
DELETE Y2 AT LEVEL 4
DELETE Y6 AT LEVEL 3
DELETE Y3 AT LEVEL 2
FLIP Y1 TO >= 1 AT 1 WITH BND= 2766.4346
SET Y3 TO >= 1 AT 2, BND= 2766. TWIN= 2644. 80
SET Y2 TO <= 0 AT 3, BND= 2504. TWIN=-0.1000E+31 89
SET Y4 TO >= 1 AT 4, BND= 2483. TWIN= 2475. 99
SET X3 TO >= 4 AT 5, BND= 2469. TWIN= 2463. 104
SET X1 TO <= 21 AT 6, BND= 2450. TWIN=-0.1000E+31 112
SET X4 TO <= 5 AT 7, BND= 2439. TWIN= 2429. 120
SET X3 TO <= 4 AT 8, BND= 2406. TWIN= 2428. 126
NEW INTEGER SOLUTION OF 2406.00000 AT BRANCH 16 PIVOT 126
BOUND ON OPTIMUM: 2644.028
FLIP X3 TO >= 5 AT 8 WITH BND= 2427.7896
SET X1 TO >= 21 AT 9, BND= 2428. TWIN=-0.1000E+31 126
SET X2 TO <= 0 AT 10, BND= 2428. TWIN=-0.1000E+31 126
SET X3 TO <= 5 AT 11, BND= 2428. TWIN=-0.1000E+31 126
SET X4 TO <= 4 AT 12, BND= 2406. TWIN=-0.1000E+31 129
DELETE X4 AT LEVEL 12
DELETE X3 AT LEVEL 11
DELETE X2 AT LEVEL 10
DELETE X1 AT LEVEL 9
DELETE X3 AT LEVEL 8
FLIP X4 TO >= 6 AT 7 WITH BND= 2429.2307
SET X2 TO <= 0 AT 8, BND= 2429. TWIN=-0.1000E+31 129
SET X3 TO <= 4 AT 9, BND= 2429. TWIN=-0.1000E+31 129
...